## David Bell's engineless caterpillar idea revisited

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### Re: David Bell's engineless caterpillar idea revisited

dvgrn wrote: There's an interesting Doppler effect between the positive and negative helices, that I hadn't really thought about -- upship streams are closer together by 2*(step size) than downship streams. (Right?)

Yes the Doppler effect is very vivid here (and yes I think 2 * step is correct). You can see the difference in length in the forward and backward readers.

dvgrn wrote:As far I can see, the other way to adjust the relative MWSS placement location is by adding empty cycles to the helix.

There is another pretty trivial way to adjust - use block moving slow salvo recipe. To clarify this, lets assume we have 15 gliders movement recipe from any point to any point. Now we always apply this recipe, and it takes exactly the same gliders which are always placed in (0, step size) range (as we don't use the +59 trick because we 0 mod 8 ). Now lets say we move the block not to (X, Y) but to (X, Y + 1). Because everything else remained constant, the *WSS recipe applied to (X, Y+1) will have latency of 8 ticks relative to (X, Y), 4 ticks because the SL moved 2 cells and the gliders fire with latency of 4, and another 4 ticks as the *WSS will be created 4 ticks bellow.

Now if we agree with the above logic, I claim we can remove the 15 gliders constrain. The only thing that was really matter is that the last emitted glider from (X, Y) and (X, Y + 1) were 4 ticks apart (activated by the same reading head). Now if we have two block movements, one takes 10 and other 15, we just don't do anything for 5 glider emission timing. Doing nothing will equalize the timing as if we did something for 15 ticks instead of 10.

I can say that my small tests with 59 step did show this is also working in practice, but yet again D59 is a bit different.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

Fully adjustable front with self destruct completed (17 *WSS):

`x = 179, y = 558, rule = LifeHistory6.C\$5.C.C\$5.C.C\$6.C2\$.2C7.2C\$C2.C5.C2.C\$.2C7.2C2\$6.C\$5.C.C\$5.C.C\$6.C3\$9.3C\$9.C2.C\$9.C\$9.C3.C\$9.C\$10.C.C40\$63.3C\$62.C2.C\$65.C\$61.C3.C\$65.C\$62.C.C8\$70.3C\$69.C2.C\$72.C\$68.C3.C\$68.C3.C\$72.C\$69.C.C14\$93.C\$92.3C\$91.2C.C\$91.3C\$91.3C\$91.3C\$92.2C27\$6.C\$5.3C\$4.2C.C\$4.3C\$4.3C\$5.2C27\$105.C\$104.3C\$103.2C.C\$103.3C\$103.3C\$103.3C\$104.2C30\$146.C\$145.C.C\$145.C2.C\$146.2C67\$164.C\$163.3C\$162.2C.C\$162.3C\$162.3C\$163.2C68\$176.C\$175.3C\$175.C.2C\$176.3C\$176.3C\$176.3C\$176.2C8\$139.3C\$139.C2.C\$139.C\$139.C3.C\$139.C\$140.C.C39\$163.C\$162.3C\$162.C.2C\$163.3C\$143.3C17.3C\$142.C2.C17.3C\$145.C17.2C\$141.C3.C\$141.C3.C\$145.C\$142.C.C55\$89.C\$88.3C\$87.2C.C\$87.3C\$87.3C\$87.3C12.C\$88.2C11.3C\$100.2C.C\$100.3C\$101.2C14\$84.C\$83.3C\$82.2C.C\$82.3C\$82.3C\$83.2C38.C\$122.3C\$122.C.2C\$123.3C\$123.2C50\$156.3C\$156.C2.C\$156.C\$156.C3.C\$156.C\$157.C.C4\$145.3C\$145.C2.C\$145.C\$145.C3.C\$145.C3.C\$145.C\$146.C.C!`

----

I was thinking, if we limit ourselves to p8N we can use monochromatic p2. We can assume all the gliders are all of the same parity, and this assumption will not force us to exclude any speeds (as mentioned few messages above).
Last edited by simsim314 on June 27th, 2015, 4:28 pm, edited 1 time in total.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

simsim314 wrote:There is another pretty trivial way to adjust - use block moving slow salvo recipe... Because everything else remained constant, the *WSS recipe applied to (X, Y+1) will have latency of 8 ticks relative to (X, Y), 4 ticks because the SL moved 2 cells and the gliders fire with latency of 4, and another 4 ticks as the *WSS will be created 4 ticks bellow.

Ah, of course. That makes it easy. Also it takes up a lot less space than adjustments by adding empty helix cycles! Here's my trial pattern showing the 4-cell difference between two adjacent block positions, for an even-step system:

`x = 416, y = 3219, rule = LifeHistory108.C.C227.C.C\$111.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$111.C229.C\$108.C2.C226.C2.C\$109.3C227.3C212\$182.C.C227.C.C\$181.C229.C\$181.C3.C225.C3.C\$181.C3.C225.C3.C\$181.C229.C\$181.C2.C226.C2.C\$181.3C227.3C23\$180.C.C227.C.C\$183.C229.C\$179.C3.C225.C3.C\$179.C3.C225.C3.C\$183.C229.C\$180.C2.C226.C2.C\$181.3C227.3C5\$166.2C228.2C\$165.3C227.3C\$165.3C227.3C\$165.3C227.3C\$165.2C.C226.2C.C\$166.3C227.3C\$167.C229.C76\$151.2C228.2C\$150.3C227.3C\$150.2C.C226.2C.C\$151.3C227.3C\$152.C229.C76\$108.C.C227.C.C\$107.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$107.C229.C\$107.C2.C226.C2.C\$107.3C227.3C55\$118.2C228.2C\$118.3C227.3C\$118.3C227.3C\$117.C.2C226.C.2C\$117.3C227.3C\$118.C229.C7\$97.C.C227.C.C\$96.C229.C\$96.C3.C225.C3.C\$96.C229.C\$96.C2.C226.C2.C\$96.3C227.3C14\$108.C.C227.C.C\$111.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$111.C229.C\$108.C2.C226.C2.C\$109.3C227.3C212\$182.C.C227.C.C\$181.C229.C\$181.C3.C225.C3.C\$181.C3.C225.C3.C\$181.C229.C\$181.C2.C226.C2.C\$181.3C227.3C23\$180.C.C227.C.C\$183.C229.C\$179.C3.C225.C3.C\$179.C3.C225.C3.C\$183.C229.C\$180.C2.C226.C2.C\$181.3C227.3C5\$166.2C228.2C\$165.3C227.3C\$165.3C227.3C\$165.3C227.3C\$165.2C.C226.2C.C\$166.3C227.3C\$167.C229.C76\$151.2C228.2C\$150.3C227.3C\$150.2C.C226.2C.C\$151.3C227.3C\$152.C229.C76\$108.C.C227.C.C\$107.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$107.C229.C\$107.C2.C226.C2.C\$107.3C227.3C55\$118.2C228.2C\$118.3C227.3C\$118.3C227.3C\$117.C.2C226.C.2C\$117.3C227.3C\$118.C229.C7\$97.C.C227.C.C\$96.C229.C\$96.C3.C225.C3.C\$96.C229.C\$96.C2.C226.C2.C\$96.3C227.3C14\$108.C.C227.C.C\$111.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$111.C229.C\$108.C2.C226.C2.C\$109.3C227.3C212\$182.C.C227.C.C\$181.C229.C\$181.C3.C225.C3.C\$181.C3.C225.C3.C\$181.C229.C\$181.C2.C226.C2.C\$181.3C227.3C23\$180.C.C227.C.C\$183.C229.C\$179.C3.C225.C3.C\$179.C3.C225.C3.C\$183.C229.C\$180.C2.C226.C2.C\$181.3C227.3C5\$166.2C228.2C\$165.3C227.3C\$165.3C227.3C\$165.3C227.3C\$165.2C.C226.2C.C\$166.3C227.3C\$167.C229.C76\$151.2C228.2C\$150.3C227.3C\$150.2C.C226.2C.C\$151.3C227.3C\$152.C229.C76\$108.C.C227.C.C\$107.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$107.C229.C\$107.C2.C226.C2.C\$107.3C227.3C55\$118.2C228.2C\$118.3C227.3C\$118.3C227.3C\$117.C.2C226.C.2C\$117.3C227.3C\$118.C229.C7\$97.C.C227.C.C\$96.C229.C\$96.C3.C225.C3.C\$96.C229.C\$96.C2.C226.C2.C\$96.3C227.3C14\$108.C.C227.C.C\$111.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$111.C229.C\$108.C2.C226.C2.C\$109.3C227.3C212\$182.C.C227.C.C\$181.C229.C\$181.C3.C225.C3.C\$181.C3.C225.C3.C\$181.C229.C\$181.C2.C226.C2.C\$181.3C227.3C23\$180.C.C227.C.C\$183.C229.C\$179.C3.C225.C3.C\$179.C3.C225.C3.C\$183.C229.C\$180.C2.C226.C2.C\$181.3C227.3C5\$166.2C228.2C\$165.3C227.3C\$165.3C227.3C\$165.3C227.3C\$165.2C.C226.2C.C\$166.3C227.3C\$167.C229.C76\$151.2C228.2C\$150.3C227.3C\$150.2C.C226.2C.C\$151.3C227.3C\$152.C229.C76\$108.C.C227.C.C\$107.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$107.C229.C\$107.C2.C226.C2.C\$107.3C227.3C55\$118.2C228.2C\$118.3C227.3C\$118.3C227.3C\$117.C.2C226.C.2C\$117.3C227.3C\$118.C229.C7\$97.C.C227.C.C\$96.C229.C\$96.C3.C225.C3.C\$96.C229.C\$96.C2.C226.C2.C\$96.3C227.3C14\$108.C.C227.C.C\$111.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$111.C229.C\$108.C2.C226.C2.C\$109.3C227.3C212\$182.C.C227.C.C\$181.C229.C\$181.C3.C225.C3.C\$181.C3.C225.C3.C\$181.C229.C\$181.C2.C226.C2.C\$181.3C227.3C23\$180.C.C227.C.C\$183.C229.C\$179.C3.C225.C3.C\$179.C3.C225.C3.C\$183.C229.C\$180.C2.C226.C2.C\$181.3C227.3C5\$166.2C228.2C\$165.3C227.3C\$165.3C227.3C\$165.3C227.3C\$165.2C.C226.2C.C\$166.3C227.3C\$167.C229.C76\$151.2C228.2C\$150.3C227.3C\$150.2C.C226.2C.C\$151.3C227.3C\$152.C229.C76\$108.C.C227.C.C\$107.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$107.C229.C\$107.C2.C226.C2.C\$107.3C227.3C55\$118.2C228.2C\$118.3C227.3C\$118.3C227.3C\$117.C.2C226.C.2C\$117.3C227.3C\$118.C229.C7\$28.2A67.C.C158.2A67.C.C\$28.2A66.C161.2A66.C\$96.C3.C225.C3.C\$19.2A75.C152.2A75.C\$18.A2.A74.C2.C148.A2.A74.C2.C\$19.2A75.3C150.2A75.3C3\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A8\$108.C.C227.C.C\$111.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$111.C229.C\$108.C2.C226.C2.C\$109.3C227.3C49\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A223.2A2.A2.A\$251.A2.A\$252.2A31\$28.2A228.2A\$28.2A228.2A2\$19.2A228.2A\$18.A2.A226.A2.A\$19.2A228.2A3\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A63\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A223.2A2.A2.A\$251.A2.A\$252.2A31\$28.2A228.2A\$28.2A152.C.C73.2A152.C.C\$181.C229.C\$19.2A160.C3.C63.2A160.C3.C\$18.A2.A159.C3.C62.A2.A159.C3.C\$19.2A160.C67.2A160.C\$181.C2.C226.C2.C\$181.3C227.3C\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A19\$180.C.C227.C.C\$183.C229.C\$179.C3.C225.C3.C\$179.C3.C225.C3.C\$183.C229.C\$180.C2.C226.C2.C\$181.3C227.3C5\$166.2C228.2C\$165.3C227.3C\$165.3C227.3C\$165.3C227.3C\$165.2C.C226.2C.C\$166.3C227.3C\$167.C229.C27\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A223.2A2.A2.A\$251.A2.A\$252.2A25\$27.2A\$26.A2.A\$26.A2.A\$27.2A3\$6.3D19.2A206.3D19.2A\$6.D2.D18.2A206.D2.D18.2A\$6.D229.D\$6.D3.D8.2A215.D3.D8.2A\$6.D11.A2.A214.D11.A2.A\$7.D.D9.2A130.2C84.D.D9.2A130.2C\$150.3C227.3C\$150.2C.C226.2C.C\$23.2A3.2A121.3C99.2A3.2A121.3C\$23.2A2.A2.A121.C100.2A2.A2.A121.C\$27.A2.A226.A2.A\$28.2A228.2A63\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A84.C.C136.2A2.A2.A83.C.C\$107.C143.A2.A82.C\$107.C3.C140.2A83.C3.C\$107.C3.C225.C3.C\$107.C229.C\$107.C2.C226.C2.C\$107.3C227.3C21\$257.2A\$256.A2.A\$256.A2.A\$257.2A3\$28.2A228.2A\$28.2A228.2A2\$19.2A228.2A\$18.A2.A226.A2.A\$19.2A228.2A3\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A17\$118.2C228.2C\$118.3C227.3C\$118.3C227.3C\$117.C.2C226.C.2C\$117.3C227.3C\$118.C229.C3\$3D\$D2.D\$D\$D3.D\$D96.C.C130.3D94.C.C\$.D.D92.C6.2C125.D2.D92.C6.2C\$96.C3.C.C2.C124.D95.C3.C.C2.C\$96.C5.C.C125.D3.D91.C5.C.C\$96.C2.C3.C126.D95.C2.C3.C\$96.3C132.D.D92.3C29\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A223.2A2.A2.A\$251.A2.A\$252.2A22\$103.2C\$102.C2.C\$102.C.C228.2C\$103.C228.C2.C\$332.C.C\$333.C4\$28.2A228.2A\$28.2A228.2A2\$19.2A228.2A\$18.A2.A226.A2.A\$19.2A228.2A3\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A63\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A223.2A2.A2.A\$251.A2.A\$252.2A!`

simsim314 wrote:Now if we agree with the above logic, I claim we can remove the 15 gliders constrain.

Yes, it isn't really a N-glider constraint, it's an "N-helix-cycle" constraint. Generally speaking, adding a helix cycle will change the timing (by 40 or whatever, as shown in my last post) but it's easy to make adjustments on top of that.

Re: the "40" constant for 512-spaced recipes -- not surprisingly, moving the read-head spacing up to 514 also changes the timing differential for helix cycles from 40 to 42:

`x = 416, y = 3344, rule = LifeHistory338.C.C\$341.C\$337.C3.C\$337.C3.C\$341.C\$338.C2.C\$339.3C3\$108.C.C\$111.C\$107.C3.C\$107.C3.C\$111.C\$108.C2.C\$109.3C203\$412.C.C\$411.C\$411.C3.C\$411.C3.C\$411.C\$411.C2.C\$411.3C3\$182.C.C\$181.C\$181.C3.C\$181.C3.C\$181.C\$181.C2.C\$181.3C14\$410.C.C\$413.C\$409.C3.C\$409.C3.C\$413.C\$410.C2.C\$411.3C3\$180.C.C\$183.C\$179.C3.C212.2C\$179.C3.C211.3C\$183.C211.3C\$180.C2.C211.3C\$181.3C211.2C.C\$396.3C\$397.C3\$166.2C\$165.3C\$165.3C\$165.3C\$165.2C.C\$166.3C\$167.C67\$381.2C\$380.3C\$380.2C.C\$381.3C\$382.C5\$151.2C\$150.3C\$150.2C.C\$151.3C\$152.C67\$338.C.C\$337.C\$337.C3.C\$337.C3.C\$337.C\$337.C2.C\$337.3C3\$108.C.C\$107.C\$107.C3.C\$107.C3.C\$107.C\$107.C2.C\$107.3C46\$348.2C\$348.3C\$348.3C\$347.C.2C\$347.3C\$348.C4\$118.2C\$118.3C\$118.3C\$117.C.2C206.C.C\$117.3C206.C\$118.C207.C3.C\$326.C\$326.C2.C\$326.3C4\$97.C.C\$96.C\$96.C3.C\$96.C\$96.C2.C\$96.3C7\$338.C.C\$341.C\$337.C3.C\$337.C3.C\$341.C\$338.C2.C\$339.3C\$108.C.C\$111.C\$107.C3.C\$107.C3.C\$111.C\$108.C2.C\$109.3C205\$412.C.C\$411.C\$411.C3.C\$411.C3.C\$411.C\$411.C2.C\$411.3C\$182.C.C\$181.C\$181.C3.C\$181.C3.C\$181.C\$181.C2.C\$181.3C16\$410.C.C\$413.C\$409.C3.C\$409.C3.C\$413.C\$410.C2.C\$411.3C\$180.C.C\$183.C\$179.C3.C\$179.C3.C\$183.C212.2C\$180.C2.C211.3C\$181.3C211.3C\$395.3C\$395.2C.C\$396.3C\$397.C\$166.2C\$165.3C\$165.3C\$165.3C\$165.2C.C\$166.3C\$167.C69\$381.2C\$380.3C\$380.2C.C\$381.3C\$382.C3\$151.2C\$150.3C\$150.2C.C\$151.3C\$152.C69\$338.C.C\$337.C\$337.C3.C\$337.C3.C\$337.C\$337.C2.C\$337.3C\$108.C.C\$107.C\$107.C3.C\$107.C3.C\$107.C\$107.C2.C\$107.3C48\$348.2C\$348.3C\$348.3C\$347.C.2C\$347.3C\$348.C2\$118.2C\$118.3C\$118.3C\$117.C.2C\$117.3C\$118.C208.C.C\$326.C\$326.C3.C\$326.C\$326.C2.C\$326.3C2\$97.C.C\$96.C\$96.C3.C\$96.C\$96.C2.C\$96.3C9\$338.C.C\$341.C\$337.C3.C\$337.C3.C\$341.C\$108.C.C227.C2.C\$111.C227.3C\$107.C3.C\$107.C3.C\$111.C\$108.C2.C\$109.3C207\$412.C.C\$411.C\$411.C3.C\$411.C3.C\$411.C\$182.C.C226.C2.C\$181.C229.3C\$181.C3.C\$181.C3.C\$181.C\$181.C2.C\$181.3C18\$410.C.C\$413.C\$409.C3.C\$409.C3.C\$413.C\$180.C.C227.C2.C\$183.C227.3C\$179.C3.C\$179.C3.C\$183.C\$180.C2.C\$181.3C212.2C\$395.3C\$395.3C\$395.3C\$395.2C.C\$166.2C228.3C\$165.3C229.C\$165.3C\$165.3C\$165.2C.C\$166.3C\$167.C71\$381.2C\$380.3C\$380.2C.C\$381.3C\$382.C\$151.2C\$150.3C\$150.2C.C\$151.3C\$152.C71\$338.C.C\$337.C\$337.C3.C\$337.C3.C\$337.C\$108.C.C226.C2.C\$107.C229.3C\$107.C3.C\$107.C3.C\$107.C\$107.C2.C\$107.3C50\$348.2C\$348.3C\$348.3C\$347.C.2C\$347.3C\$118.2C228.C\$118.3C\$118.3C\$117.C.2C\$117.3C\$118.C2\$327.C.C\$326.C\$326.C3.C\$326.C\$326.C2.C\$97.C.C226.3C\$96.C\$96.C3.C\$96.C\$96.C2.C\$96.3C11\$338.C.C\$341.C\$337.C3.C\$108.C.C226.C3.C\$111.C229.C\$107.C3.C226.C2.C\$107.C3.C227.3C\$111.C\$108.C2.C\$109.3C209\$412.C.C\$411.C\$411.C3.C\$182.C.C226.C3.C\$181.C229.C\$181.C3.C225.C2.C\$181.C3.C225.3C\$181.C\$181.C2.C\$181.3C20\$410.C.C\$413.C\$409.C3.C\$180.C.C226.C3.C\$183.C229.C\$179.C3.C226.C2.C\$179.C3.C227.3C\$183.C\$180.C2.C\$181.3C2\$396.2C\$395.3C\$395.3C\$166.2C227.3C\$165.3C227.2C.C\$165.3C228.3C\$165.3C229.C\$165.2C.C\$166.3C\$167.C73\$381.2C\$380.3C\$380.2C.C\$151.2C228.3C\$150.3C229.C\$150.2C.C\$151.3C\$152.C73\$338.C.C\$337.C\$337.C3.C\$108.C.C226.C3.C\$107.C229.C\$107.C3.C225.C2.C\$107.C3.C225.3C\$107.C\$107.C2.C\$107.3C52\$348.2C\$348.3C\$348.3C\$118.2C227.C.2C\$118.3C226.3C\$118.3C227.C\$117.C.2C\$117.3C\$118.C4\$327.C.C\$326.C\$326.C3.C\$97.C.C226.C\$96.C229.C2.C\$96.C3.C225.3C\$96.C\$96.C2.C\$96.3C12\$338.C.C\$341.C\$108.C.C226.C3.C\$111.C225.C3.C\$107.C3.C229.C\$107.C3.C226.C2.C\$111.C227.3C\$108.C2.C\$109.3C210\$412.C.C\$411.C\$182.C.C226.C3.C\$181.C229.C3.C\$181.C3.C225.C\$181.C3.C225.C2.C\$181.C229.3C\$181.C2.C\$181.3C21\$410.C.C\$413.C\$180.C.C226.C3.C\$183.C225.C3.C\$179.C3.C229.C\$179.C3.C226.C2.C\$183.C227.3C\$180.C2.C\$181.3C3\$396.2C\$395.3C\$166.2C227.3C\$165.3C227.3C\$165.3C227.2C.C\$165.3C228.3C\$165.2C.C228.C\$166.3C\$167.C74\$381.2C\$380.3C\$151.2C227.2C.C\$150.3C228.3C\$150.2C.C228.C\$151.3C\$152.C74\$338.C.C\$337.C\$108.C.C226.C3.C\$107.C229.C3.C\$107.C3.C225.C\$107.C3.C225.C2.C\$107.C229.3C\$107.C2.C\$107.3C53\$348.2C\$348.3C\$118.2C228.3C\$118.3C226.C.2C\$118.3C226.3C\$117.C.2C227.C\$117.3C\$118.C5\$327.C.C\$326.C\$28.2A67.C.C158.2A66.C3.C\$28.2A66.C161.2A66.C\$96.C3.C225.C2.C\$19.2A75.C152.2A75.3C\$18.A2.A74.C2.C148.A2.A\$19.2A75.3C150.2A3\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A8\$108.C.C227.C.C\$111.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$111.C229.C\$108.C2.C226.C2.C\$109.3C227.3C49\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A223.2A2.A2.A\$251.A2.A\$252.2A31\$28.2A228.2A\$28.2A228.2A2\$19.2A228.2A\$18.A2.A226.A2.A\$19.2A228.2A3\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A63\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A223.2A2.A2.A\$251.A2.A\$252.2A31\$28.2A228.2A\$28.2A152.C.C73.2A152.C.C\$181.C229.C\$19.2A160.C3.C63.2A160.C3.C\$18.A2.A159.C3.C62.A2.A159.C3.C\$19.2A160.C67.2A160.C\$181.C2.C226.C2.C\$181.3C227.3C\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A19\$180.C.C227.C.C\$183.C229.C\$179.C3.C225.C3.C\$179.C3.C225.C3.C\$183.C229.C\$180.C2.C226.C2.C\$181.3C227.3C5\$166.2C228.2C\$165.3C227.3C\$165.3C227.3C\$165.3C227.3C\$165.2C.C226.2C.C\$166.3C227.3C\$167.C229.C27\$22.2A\$22.2A\$252.2A\$13.2A237.2A\$12.A2.A\$13.2A228.2A\$242.A2.A\$243.2A\$17.2A3.2A\$17.2A2.A2.A\$21.A2.A222.2A3.2A\$22.2A223.2A2.A2.A\$251.A2.A\$252.2A25\$27.2A228.2A\$26.A2.A226.A2.A\$26.A2.A226.A2.A\$27.2A228.2A3\$6.3D19.2A206.3D19.2A\$6.D2.D18.2A206.D2.D18.2A\$6.D229.D\$6.D3.D8.2A215.D3.D8.2A\$6.D11.A2.A214.D11.A2.A\$7.D.D9.2A130.2C84.D.D9.2A130.2C\$150.3C227.3C\$150.2C.C226.2C.C\$23.2A3.2A121.3C99.2A3.2A121.3C\$23.2A2.A2.A121.C100.2A2.A2.A121.C\$27.A2.A226.A2.A\$28.2A228.2A63\$22.2A228.2A\$22.2A228.2A2\$13.2A228.2A\$12.A2.A226.A2.A\$13.2A228.2A3\$17.2A3.2A223.2A3.2A\$17.2A2.A2.A222.2A2.A2.A\$21.A2.A226.A2.A\$22.2A84.C.C141.2A84.C.C\$107.C229.C\$107.C3.C225.C3.C\$107.C3.C225.C3.C\$107.C229.C\$107.C2.C226.C2.C\$107.3C227.3C21\$230.3D24.2A\$230.D2.D22.A2.A\$230.D25.A2.A\$230.D3.D22.2A\$230.D\$231.D.D\$28.2A228.2A\$28.2A228.2A2\$19.2A228.2A\$18.A2.A226.A2.A\$19.2A228.2A3\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A17\$118.2C228.2C\$118.3C227.3C\$118.3C227.3C\$117.C.2C226.C.2C\$117.3C227.3C\$118.C229.C3\$3D\$D2.D\$D\$D3.D\$D96.C.C227.C.C\$.D.D92.C6.2C221.C6.2C\$96.C3.C.C2.C220.C3.C.C2.C\$96.C5.C.C221.C5.C.C\$96.C2.C3.C222.C2.C3.C\$96.3C227.3C29\$22.2A228.2A\$22.2A228.2A2\$13.2A228.2A\$12.A2.A226.A2.A\$13.2A228.2A3\$17.2A3.2A223.2A3.2A\$17.2A2.A2.A222.2A2.A2.A\$21.A2.A226.A2.A\$22.2A228.2A24\$103.2C\$102.C2.C\$102.C.C\$103.C6\$28.2A228.2A\$28.2A228.2A2\$19.2A228.2A\$18.A2.A226.A2.A\$19.2A228.2A3\$23.2A3.2A223.2A3.2A\$23.2A2.A2.A222.2A2.A2.A\$27.A2.A226.A2.A\$28.2A228.2A63\$22.2A228.2A\$22.2A228.2A2\$13.2A228.2A\$12.A2.A226.A2.A\$13.2A228.2A3\$17.2A3.2A223.2A3.2A\$17.2A2.A2.A222.2A2.A2.A\$21.A2.A226.A2.A\$22.2A228.2A24\$333.2C\$332.C2.C\$332.C.C\$333.C6\$258.2A\$258.2A2\$249.2A\$248.A2.A\$249.2A3\$253.2A3.2A\$253.2A2.A2.A\$257.A2.A\$258.2A63\$252.2A\$252.2A2\$243.2A\$242.A2.A\$243.2A3\$247.2A3.2A\$247.2A2.A2.A\$251.A2.A\$252.2A!`

I think this means that for 118-step systems, the zero point I was worried about will never occur -- because the read heads can't be moved 40 steps closer together without colliding, and if they're moved farther apart, the distance between the upships increases in lockstep. (And again, I agree that there was no reason to worry about the zero point anyway.)

Maybe there's some N-step system where the read heads can be moved close enough together to allow a zero point. If so, it would be somewhat easier to work with, since recipes would all work the same no matter how many cycles they took. But it would be a very special case, and it looks as if it won't be particularly difficult to factor in a per-cycle offset.

dvgrn
Moderator

Posts: 5620
Joined: May 17th, 2009, 11:00 pm

### Re: David Bell's engineless caterpillar idea revisited

simsim314 wrote:I was thinking, if we limit ourselves to p8N we can use monochromatic p2. We can assume all the gliders are all of the same parity, and this assumption will not force us to exclude any speeds (as mentioned few messages above).

Hmm, I hadn't followed that line of thought far enough. I suppose the range of caterloopillar periods is relatively limited anyway -- can't get below the base period defined by the repeat time and distance of the reading heads. So every rational speed lower than c/4 is about as universal as it's possible to get, anyway.

In that case, an idea I had yesterday might be vaguely useful after all, at least as a sanity check. Of the 8,313 monochromatic block-move recipes I posted way back when on the Serizawa thread, 820 of them are P2-even:

`1m2  ,1  :E113m5  ,12 :E-9 E-29 E313m5  ,12 :E-9 E-29 E353m5  ,12 :E-9 E-29 E273m7  ,-8 :E-9 E-29 E-93m7  ,-8 :E-9 E-29 E-173m7  ,-8 :E-9 E-29 E-134m-3 ,1  :E-9 E-13 E-9 E-134m1  ,-2 :E-9 E-13 E-29 E-54m5  ,12 :E-9 E-29 E19 E234m5  ,12 :E-9 E-29 E19 E274m5  ,12 :E-9 E-29 E19 E314m6  ,14 :E-9 E-29 E-25 E274m6  ,14 :E-9 E-29 E-25 E314m6  ,14 :E-9 E-29 E-25 E354m7  ,-8 :E-9 E-29 E-25 E-214m7  ,-8 :E-9 E-29 E-25 E-174m7  ,-8 :E-9 E-29 E-25 E-134m8  ,-6 :E-9 E-29 E19 E-134m8  ,-6 :E-9 E-29 E19 E-174m8  ,-6 :E-9 E-29 E19 E-95m-8 ,7  :E-9 E7 E-21 E-5 E-295m-5 ,3  :E-9 E-13 E-9 E-21 E-215m-5 ,4  :E-9 E-13 E-13 E-29 E75m-2 ,10 :E-9 E7 E-21 E3 E-95m-1 ,4  :E-9 E-13 E-9 E-1 E-15m-1 ,9  :E-9 E7 E-17 E-25 E35m1  ,12 :E-9 E-1 E-1 E19 E235m4  ,0  :E-9 E7 E11 E-29 E75m5  ,12 :E-9 E-29 E19 E39 E315m5  ,12 :E-9 E-29 E39 E43 E275m5  ,12 :E-9 E-29 E19 E39 E355m5  ,12 :E-9 E-29 E19 E39 E275m7  ,-8 :E-9 E-29 E-5 E-1 E-175m7  ,-8 :E-9 E-29 E-25 E-5 E-135m7  ,-8 :E-9 E-29 E-25 E-5 E-95m7  ,-8 :E-9 E-29 E-25 E-5 E-175m8  ,15 :E-9 E-29 E-25 E-5 E275m8  ,15 :E-9 E-29 E-25 E-5 E355m8  ,15 :E-9 E-29 E-25 E-5 E315m10 ,-5 :E-9 E-29 E19 E39 E-135m10 ,-5 :E-9 E-29 E19 E39 E-95m10 ,-5 :E-9 E-29 E19 E39 E-176m-16,11 :E-9 E7 E-9 E-25 E-21 E-776m-16,11 :E-9 E7 E-9 E-25 E-21 E-816m-8 ,7  :E-9 E7 E-21 E-5 E-37 E-256m-6 ,7  :E-9 E7 E-17 E11 E-1 E196m-5 ,4  :E-9 E7 E7 E11 E-29 E196m-5 ,4  :E-9 E7 E7 E11 E-29 E156m-4 ,-10:E-9 E11 E11 E19 E7 E276m-4 ,-10:E-9 E11 E11 E19 E7 E356m-4 ,6  :E-9 E-13 E-13 E-29 E-29 E76m-3 ,11 :E-9 E7 E-17 E-33 E-33 E36m-2 ,-5 :E-9 E-13 E-13 E-1 E-13 E116m-2 ,0  :E-9 E-1 E-5 E7 E3 E-216m-2 ,0  :E-9 E-1 E-5 E7 E3 E-136m-1 ,-1 :E-9 E-29 E39 E59 E39 E-136m-1 ,-1 :E-9 E-29 E39 E59 E39 E-176m-1 ,-1 :E-9 E-29 E39 E59 E39 E-96m-1 ,8  :E-9 E7 E7 E-17 E3 E-576m-1 ,8  :E-9 E7 E7 E-17 E3 E-536m-1 ,8  :E-9 E7 E7 E-17 E3 E-496m-1 ,8  :E-9 E7 E7 E-17 E-49 E36m0  ,8  :E-9 E-13 E-17 E-5 E-37 E-416m0  ,8  :E-9 E7 E-5 E11 E7 E-336m0  ,11 :E-9 E7 E-21 E3 E-13 E-96m1  ,6  :E-9 E-13 E-17 E-21 E-41 E-96m1  ,6  :E-9 E-13 E-17 E-21 E-41 E-296m1  ,7  :E-9 E-13 E-13 E-9 E3 E116m1  ,7  :E-9 E-13 E-13 E-9 E3 E156m1  ,28 :E-9 E7 E7 E-17 E-5 E156m1  ,28 :E-9 E7 E7 E-17 E3 E-176m1  ,28 :E-9 E7 E7 E-17 E-13 E36m1  ,28 :E-9 E7 E7 E-17 E3 E-136m1  ,28 :E-9 E7 E7 E-17 E-5 E-56m1  ,28 :E-9 E7 E7 E-17 E3 E-216m4  ,9  :E-9 E7 E-5 E-17 E-1 E-256m4  ,9  :E-9 E7 E-5 E-17 E-1 E-336m4  ,9  :E-9 E7 E-17 E-29 E-25 E36m5  ,12 :E-9 E-29 E39 E27 E27 E356m5  ,12 :E-9 E-29 E39 E43 E39 E396m5  ,12 :E-9 E-29 E39 E43 E39 E356m5  ,12 :E-9 E-29 E39 E43 E31 E396m5  ,12 :E-9 E-29 E39 E27 E27 E556m5  ,12 :E-9 E-29 E39 E59 E39 E36m5  ,12 :E-9 E-29 E39 E59 E39 E-16m5  ,12 :E-9 E-29 E39 E59 E-1 E476m5  ,12 :E-9 E-29 E39 E59 E-1 E436m5  ,12 :E-9 E-29 E39 E23 E59 E316m5  ,12 :E-9 E-29 E39 E23 E59 E396m5  ,12 :E-9 E-29 E39 E59 E-1 E396m5  ,12 :E-9 E-29 E39 E43 E31 E596m6  ,14 :E-9 E-29 E39 E43 E-25 E276m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-56m7  ,-8 :E-9 E-29 E-5 E-1 E-13 E-56m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E-96m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E-56m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E116m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-136m7  ,-8 :E-9 E-29 E-5 E-1 E-13 E156m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E-96m8  ,-6 :E-9 E-29 E-5 E-1 E19 E-176m8  ,4  :E-9 E-1 E-17 E3 E-9 E-216m8  ,4  :E-9 E-1 E-17 E3 E-9 E-136m11 ,3  :E-9 E7 E-17 E11 E-9 E36m14 ,-16:E-9 E7 E-5 E-9 E-9 E596m19 ,-3 :E-9 E-29 E39 E59 E-1 E-96m19 ,-3 :E-9 E-29 E39 E59 E-1 E-176m19 ,-3 :E-9 E-29 E39 E59 E-1 E-136m24 ,2  :E-9 E11 E11 E23 E-21 E-17m-25,13 :E-9 E-13 E-17 E-33 E-17 E-37 E77m-25,13 :E-9 E-13 E-17 E-33 E-17 E-21 E117m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E157m-25,13 :E-9 E-13 E-17 E-33 E-17 E-37 E-137m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E-17m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-257m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-297m-18,6  :E-9 E7 E-9 E-57 E-53 E-25 E-497m-18,6  :E-9 E7 E-9 E-57 E-53 E-25 E-577m-16,11 :E-9 E7 E-9 E-25 E-21 E-89 E-937m-12,9  :E-9 E7 E-5 E11 E3 E-53 E117m-12,16 :E-9 E-1 E-17 E-9 E19 E7 E-297m-11,4  :E-9 E7 E-9 E-37 E-41 E-53 E-337m-11,4  :E-9 E7 E-9 E-57 E-53 E-45 E-577m-11,4  :E-9 E7 E-9 E-57 E-53 E-45 E-497m-10,16 :E-9 E7 E-17 E-29 E-41 E-45 E37m-9 ,9  :E-9 E7 E-17 E-29 E-41 E-45 E-217m-8 ,0  :E-9 E-13 E-13 E-29 E-29 E-9 E-177m-8 ,0  :E-9 E-13 E-13 E-29 E-29 E-9 E-217m-8 ,0  :E-9 E-13 E-13 E-29 E-29 E-9 E-257m-8 ,3  :E-9 E11 E11 E23 E39 E11 E397m-8 ,3  :E-9 E11 E11 E23 E39 E11 E477m-8 ,3  :E-9 E11 E11 E23 E39 E11 E357m-8 ,4  :E-9 E-1 E-17 E11 E-25 E-37 E277m-8 ,4  :E-9 E-1 E-17 E11 E-25 E-37 E237m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E117m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E157m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E197m-8 ,17 :E-9 E-1 E-1 E19 E19 E-17 E-257m-8 ,17 :E-9 E-1 E-1 E19 E19 E-17 E-297m-6 ,-8 :E-9 E11 E11 E19 E-1 E-1 E357m-6 ,-8 :E-9 E11 E11 E19 E-1 E-1 E277m-6 ,-5 :E-9 E7 E-5 E-29 E-9 E-1 E-177m-6 ,-5 :E-9 E7 E-5 E-29 E-9 E-29 E-137m-6 ,9  :E-9 E11 E11 E-29 E-29 E-17 E37m-6 ,11 :E-9 E11 E11 E-29 E-29 E3 E77m-5 ,4  :E-9 E-13 E-13 E-1 E-1 E-29 E-57m-5 ,4  :E-9 E7 E7 E11 E-29 E11 E117m-5 ,4  :E-9 E7 E7 E11 E-29 E11 E157m-5 ,4  :E-9 E7 E7 E11 E-29 E3 E157m-5 ,4  :E-9 E7 E7 E11 E-29 E11 E197m-5 ,4  :E-9 E7 E7 E11 E-29 E23 E157m-5 ,4  :E-9 E7 E7 E11 E-29 E23 E197m-5 ,4  :E-9 E7 E7 E11 E-29 E23 E37m-5 ,7  :E-9 E11 E11 E3 E-5 E-21 E197m-5 ,11 :E-9 E-13 E-17 E-33 E-17 E-81 E77m-5 ,11 :E-9 E-13 E-17 E-33 E-17 E-81 E-137m-4 ,-10:E-9 E11 E11 E19 E7 E23 E237m-4 ,-10:E-9 E11 E11 E19 E31 E7 E197m-4 ,-10:E-9 E11 E11 E19 E31 E7 E237m-4 ,-10:E-9 E11 E11 E19 E31 E7 E157m-4 ,6  :E-9 E7 E7 E11 E-29 E-29 E157m-4 ,6  :E-9 E7 E7 E11 E-29 E-29 E197m-4 ,7  :E-9 E-13 E-17 E-5 E-5 E-33 E-297m-4 ,7  :E-9 E-13 E-17 E-5 E-5 E-33 E-497m-4 ,10 :E-9 E11 E11 E-1 E27 E-33 E-97m-3 ,-9 :E-9 E-13 E-13 E-29 E-29 E-13 E-137m-3 ,5  :E-9 E7 E-21 E-13 E-1 E-9 E-17m-3 ,5  :E-9 E7 E-21 E-13 E-1 E-9 E117m-3 ,16 :E-9 E-9 E19 E-1 E-1 E7 E397m-3 ,16 :E-9 E-9 E19 E-1 E-1 E7 E197m-2 ,5  :E-9 E-13 E-13 E-1 E-1 E-29 E-97m-2 ,10 :E-9 E7 E-21 E11 E19 E-5 E117m-2 ,12 :E-9 E-9 E-5 E-17 E-25 E-5 E157m-2 ,17 :E-9 E-1 E15 E-5 E-5 E35 E-217m-2 ,17 :E-9 E-1 E15 E-5 E-5 E-21 E357m-1 ,-1 :E-9 E-29 E39 E59 E39 E-25 E-137m-1 ,-1 :E-9 E-29 E39 E59 E39 E-25 E-177m-1 ,-1 :E-9 E-29 E39 E59 E39 E-25 E-217m-1 ,1  :E-9 E7 E-17 E-25 E11 E3 E-97m-1 ,1  :E-9 E7 E-17 E-25 E11 E3 E-297m-1 ,4  :E-9 E7 E-21 E-21 E11 E-29 E77m-1 ,5  :E-9 E7 E-5 E11 E3 E-5 E-497m-1 ,5  :E-9 E7 E-5 E11 E3 E-5 E-577m-1 ,8  :E-9 E7 E7 E-17 E-65 E3 E-537m-1 ,8  :E-9 E7 E7 E-17 E-65 E3 E-577m-1 ,8  :E-9 E7 E7 E-17 E-65 E3 E-617m-1 ,12 :E-9 E7 E-17 E11 E7 E-1 E117m-1 ,12 :E-9 E7 E-17 E11 E7 E-1 E197m-1 ,28 :E-9 E11 E11 E-1 E27 E-29 E-417m0  ,-10:E-9 E7 E-17 E-29 E-25 E23 E-57m0  ,-10:E-9 E7 E-17 E-29 E-25 E23 E-97m0  ,-10:E-9 E7 E-17 E-29 E-25 E23 E-137m0  ,19 :E-9 E-1 E15 E-5 E-29 E35 E-137m0  ,19 :E-9 E-1 E15 E-5 E-29 E35 E-97m0  ,19 :E-9 E-1 E15 E-5 E-29 E-9 E357m1  ,-2 :E-9 E7 E7 E-13 E-29 E-5 E277m1  ,0  :E-9 E-29 E39 E59 E39 E11 E-97m1  ,0  :E-9 E-29 E39 E59 E39 E11 E-177m1  ,0  :E-9 E-29 E39 E59 E39 E11 E-137m1  ,0  :E-9 E7 E11 E7 E11 E-5 E-297m1  ,0  :E-9 E-13 E-13 E-9 E15 E-1 E-177m1  ,7  :E-9 E-13 E-13 E-9 E3 E3 E-17m1  ,7  :E-9 E-13 E-13 E-9 E3 E19 E157m1  ,7  :E-9 E-13 E-13 E-9 E3 E19 E117m1  ,7  :E-9 E-13 E-13 E-9 E3 E19 E-17m1  ,12 :E-9 E-1 E-1 E19 E27 E-5 E317m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E277m1  ,28 :E-9 E7 E7 E-17 E-13 E-9 E-57m1  ,28 :E-9 E7 E7 E-17 E-13 E-9 E-97m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E317m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E357m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-537m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-577m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-497m2  ,-14:E-9 E7 E-17 E11 E-5 E-33 E-137m2  ,8  :E-9 E-1 E15 E-5 E-17 E35 E-337m2  ,8  :E-9 E-1 E15 E-5 E-17 E35 E-377m2  ,8  :E-9 E-1 E15 E-5 E-17 E35 E-497m2  ,12 :E-9 E-9 E-5 E-17 E-25 E-21 E157m2  ,30 :E-9 E7 E7 E-17 E-65 E3 E-137m2  ,30 :E-9 E7 E7 E-17 E-65 E-13 E37m2  ,30 :E-9 E7 E7 E-17 E-65 E-5 E-57m2  ,30 :E-9 E7 E7 E-17 E-65 E3 E-217m2  ,30 :E-9 E7 E7 E-17 E-65 E-5 E157m2  ,30 :E-9 E7 E7 E-17 E-65 E3 E-177m3  ,-2 :E-9 E-13 E-13 E-9 E-9 E-9 E-137m3  ,-2 :E-9 E-13 E-13 E-9 E-9 E-9 E-177m3  ,8  :E-9 E-9 E-5 E-17 E-25 E-25 E157m3  ,9  :E-9 E-13 E-17 E-21 E-5 E-41 E77m4  ,0  :E-9 E7 E-5 E11 E7 E-29 E-257m4  ,0  :E-9 E7 E-5 E11 E7 E-29 E-137m4  ,9  :E-9 E7 E-17 E-29 E-25 E15 E117m4  ,9  :E-9 E7 E-17 E-29 E-25 E11 E197m4  ,9  :E-9 E7 E-17 E-29 E-25 E23 E157m4  ,9  :E-9 E7 E-17 E-29 E-25 E11 E117m4  ,9  :E-9 E7 E-17 E-29 E-25 E23 E197m4  ,9  :E-9 E7 E-17 E-29 E-25 E23 E237m4  ,14 :E-9 E7 E-5 E-17 E11 E3 E-57m5  ,-2 :E-9 E11 E11 E-1 E19 E-53 E-497m5  ,11 :E-9 E7 E-17 E-29 E-25 E-21 E37m5  ,12 :E-9 E-29 E39 E43 E47 E71 E597m5  ,12 :E-9 E-29 E39 E43 E47 E71 E637m5  ,12 :E-9 E-29 E19 E39 E39 E43 E277m5  ,12 :E-9 E-29 E39 E43 E19 E19 E357m5  ,12 :E-9 E-29 E39 E43 E47 E35 E637m5  ,12 :E-9 E-29 E39 E43 E43 E23 E637m5  ,12 :E-9 E-29 E39 E23 E35 E55 E637m5  ,12 :E-9 E-29 E19 E19 E-1 E19 E637m5  ,12 :E-9 E-29 E39 E59 E39 E11 E37m5  ,12 :E-9 E-29 E39 E59 E39 E11 E-17m5  ,12 :E-9 E-29 E39 E59 E55 E-1 E517m5  ,12 :E-9 E-29 E39 E59 E55 E-1 E477m5  ,12 :E-9 E-29 E39 E59 E55 E-1 E437m5  ,12 :E-9 E-29 E39 E59 E39 E11 E77m5  ,12 :E-9 E-29 E19 E19 E-1 E19 E597m5  ,12 :E-9 E-29 E39 E43 E43 E59 E397m5  ,12 :E-9 E-29 E39 E23 E47 E27 E477m5  ,12 :E-9 E-29 E39 E23 E51 E43 E437m5  ,12 :E-9 E-29 E39 E31 E23 E19 E517m5  ,12 :E-9 E-29 E39 E43 E39 E47 E517m5  ,12 :E-9 E-29 E39 E23 E47 E27 E517m5  ,12 :E-9 E-29 E39 E43 E19 E19 E117m5  ,12 :E-9 E-29 E39 E43 E39 E51 E397m5  ,12 :E-9 E-29 E39 E43 E43 E23 E557m5  ,12 :E-9 E-29 E39 E31 E23 E19 E557m5  ,12 :E-9 E-29 E19 E19 E39 E31 E37m5  ,12 :E-9 E-29 E19 E19 E-1 E19 E557m5  ,12 :E-9 E-29 E19 E19 E39 E31 E237m5  ,12 :E-9 E-29 E39 E23 E35 E55 E397m5  ,12 :E-9 E-29 E39 E23 E35 E55 E557m6  ,-9 :E-9 E-13 E-13 E-9 E19 E23 E37m6  ,-9 :E-9 E-13 E-13 E-9 E19 E23 E-177m6  ,-4 :E-9 E11 E11 E19 E31 E3 E-17m6  ,-4 :E-9 E11 E11 E19 E31 E7 E77m6  ,-1 :E-9 E7 E-17 E-13 E11 E-25 E-97m6  ,7  :E-9 E11 E11 E23 E7 E-29 E397m6  ,7  :E-9 E11 E11 E23 E39 E7 E-297m6  ,7  :E-9 E11 E11 E23 E7 E-29 E437m6  ,7  :E-9 E11 E11 E23 E7 E-29 E477m6  ,12 :E-9 E7 E-21 E-13 E3 E-21 E77m6  ,14 :E-9 E-29 E39 E27 E-25 E27 E357m6  ,14 :E-9 E-29 E39 E43 E-25 E59 E317m6  ,14 :E-9 E-29 E39 E43 E-25 E59 E397m6  ,14 :E-9 E-29 E39 E43 E-25 E39 E397m6  ,14 :E-9 E-29 E39 E59 E-1 E-25 E397m6  ,14 :E-9 E-29 E39 E59 E39 E-25 E37m6  ,14 :E-9 E-29 E39 E59 E39 E-25 E-17m6  ,14 :E-9 E-29 E39 E43 E-25 E39 E357m6  ,14 :E-9 E-29 E39 E59 E-1 E-25 E477m6  ,14 :E-9 E-29 E39 E59 E-1 E-25 E437m6  ,14 :E-9 E-29 E39 E27 E-25 E27 E557m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E77m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-25 E-97m7  ,-8 :E-9 E-29 E-5 E-1 E3 E27 E197m7  ,-8 :E-9 E-29 E-5 E-21 E7 E-1 E-17m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E117m7  ,-8 :E-9 E-29 E-5 E-1 E-1 E-21 E117m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E197m7  ,-8 :E-9 E-29 E-5 E-1 E3 E27 E157m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E-57m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-17 E-177m7  ,-8 :E-9 E-29 E-25 E-25 E-5 E-13 E-417m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E3 E77m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-57m7  ,-8 :E-9 E-29 E-25 E-25 E-45 E19 E-297m7  ,-8 :E-9 E-29 E-25 E-25 E-45 E19 E-337m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-25 E-337m7  ,-8 :E-9 E-29 E-25 E-5 E-5 E-1 E-177m7  ,-8 :E-9 E-29 E-5 E-1 E-1 E-21 E197m7  ,-8 :E-9 E-29 E-25 E-25 E-45 E19 E-257m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E37m7  ,-8 :E-9 E-29 E-5 E-1 E-1 E15 E-57m7  ,-8 :E-9 E-29 E-25 E-25 E-5 E-13 E-217m7  ,-8 :E-9 E-29 E-5 E-1 E3 E-9 E197m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-97m8  ,-6 :E-9 E-29 E-5 E-1 E19 E15 E-57m8  ,-6 :E-9 E-29 E-5 E-17 E-17 E19 E117m8  ,-6 :E-9 E-29 E-5 E-17 E-17 E19 E-97m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-57m8  ,-6 :E-9 E-29 E-5 E-1 E19 E15 E-137m8  ,-3 :E-9 E7 E-5 E3 E-5 E-41 E-177m8  ,6  :E-9 E-1 E-17 E15 E19 E7 E-137m8  ,8  :E-9 E11 E11 E3 E-17 E-41 E-377m8  ,12 :E-9 E11 E11 E-1 E7 E11 E117m9  ,10 :E-9 E-13 E-17 E-21 E-21 E-41 E-177m10 ,-5 :E-9 E-29 E-5 E-1 E19 E39 E-177m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-497m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-417m10 ,2  :E-9 E7 E-5 E11 E-1 E-41 E117m10 ,5  :E-9 E-1 E-17 E3 E19 E-9 E-217m10 ,5  :E-9 E-1 E-17 E3 E19 E-9 E-137m10 ,12 :E-9 E-13 E-17 E-13 E-33 E-33 E-217m11 ,-7 :E-9 E-1 E-17 E-1 E55 E3 E-137m11 ,-7 :E-9 E-1 E-17 E-1 E55 E3 E-217m11 ,3  :E-9 E7 E7 E11 E-29 E11 E-217m11 ,3  :E-9 E7 E7 E11 E-29 E11 E-177m11 ,3  :E-9 E7 E7 E11 E-29 E11 E-137m11 ,4  :E-9 E7 E-5 E3 E23 E3 E-377m11 ,4  :E-9 E7 E-5 E3 E23 E3 E-417m11 ,4  :E-9 E7 E-5 E3 E23 E3 E-457m11 ,26 :E-9 E-29 E-25 E-25 E-45 E19 E277m11 ,26 :E-9 E-29 E-25 E-25 E-45 E19 E317m11 ,26 :E-9 E-29 E-25 E-25 E-45 E19 E357m12 ,0  :E-9 E-1 E-17 E11 E-25 E11 E-217m12 ,0  :E-9 E-1 E-17 E11 E-25 E11 E-257m14 ,22 :E-9 E-9 E19 E-9 E11 E11 E37m15 ,-14:E-9 E-29 E19 E19 E-1 E19 E-177m15 ,-14:E-9 E-29 E19 E19 E-1 E19 E-97m15 ,-14:E-9 E-29 E19 E19 E-1 E19 E-137m17 ,6  :E-9 E11 E11 E23 E-21 E15 E437m17 ,6  :E-9 E11 E11 E23 E-21 E15 E477m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-137m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-177m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-217m20 ,2  :E-9 E-9 E3 E11 E3 E23 E37m21 ,-2 :E-9 E-29 E39 E59 E55 E-1 E-97m21 ,-2 :E-9 E-29 E39 E59 E55 E-1 E-177m21 ,-2 :E-9 E-29 E39 E59 E55 E-1 E-137m24 ,2  :E-9 E11 E11 E23 E-21 E15 E237m24 ,2  :E-9 E11 E11 E23 E7 E-29 E-17m24 ,2  :E-9 E11 E11 E23 E7 E-29 E37m24 ,2  :E-9 E11 E11 E23 E-13 E-21 E-97m24 ,2  :E-9 E11 E11 E23 E-21 E15 E197m24 ,2  :E-9 E11 E11 E23 E7 E-29 E-57m24 ,2  :E-9 E11 E11 E23 E-13 E-29 E117m26 ,3  :E-9 E11 E11 E23 E55 E-21 E-18m-25,13 :E-9 E-13 E-17 E-33 E-17 E11 E-45 E-138m-25,13 :E-9 E-13 E-17 E-33 E-17 E11 E-13 E-458m-25,13 :E-9 E-13 E-17 E-33 E-17 E11 E-45 E38m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E3 E-98m-25,13 :E-9 E-13 E-17 E-33 E-17 E-21 E-41 E-58m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E198m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E118m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E-18m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-58m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E3 E-178m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-98m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-138m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-13 E-178m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E7 E-18m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E7 E78m-25,13 :E-9 E-13 E-17 E-33 E-17 E11 E-13 E-298m-23,14 :E-9 E-13 E-17 E-33 E-17 E-37 E-65 E-138m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E-65 E-18m-23,14 :E-9 E-13 E-17 E-33 E-17 E3 E-65 E-258m-23,14 :E-9 E-13 E-17 E-33 E-17 E-37 E-65 E78m-23,14 :E-9 E-13 E-17 E-33 E-17 E3 E-65 E-298m-23,14 :E-9 E-13 E-17 E-33 E-17 E-21 E-65 E118m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E-65 E158m-18,6  :E-9 E7 E-9 E-41 E-33 E-33 E-25 E-458m-18,6  :E-9 E7 E-9 E-45 E-29 E-37 E-41 E-458m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-25 E-538m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-25 E-498m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-25 E-458m-18,6  :E-9 E7 E-9 E-57 E-29 E-21 E-21 E-418m-18,6  :E-9 E7 E-9 E-57 E-29 E-21 E-21 E-218m-18,6  :E-9 E7 E-9 E-57 E-53 E-61 E-25 E-618m-18,6  :E-9 E7 E-9 E-41 E-33 E-33 E-25 E-378m-16,7  :E-9 E7 E-9 E-57 E-53 E-25 E-37 E-498m-16,7  :E-9 E7 E-9 E-57 E-53 E-25 E-37 E-578m-16,10 :E-9 E-13 E-17 E-21 E-25 E-9 E-61 E-298m-16,11 :E-9 E7 E-9 E-25 E-21 E-89 E-97 E-1018m-16,11 :E-9 E7 E-9 E-25 E-21 E-89 E-101 E-898m-16,11 :E-9 E7 E-9 E-25 E-21 E-89 E-97 E-1058m-15,14 :E-9 E-13 E-17 E-21 E-25 E-9 E-41 E-298m-13,-3 :E-9 E11 E11 E19 E3 E-9 E-13 E278m-13,-3 :E-9 E11 E11 E19 E3 E-9 E-13 E358m-13,4  :E-9 E7 E7 E11 E-29 E-25 E-21 E-498m-13,4  :E-9 E7 E7 E11 E-29 E-25 E-21 E-578m-13,11 :E-9 E7 E-9 E-37 E-29 E-57 E-37 E-298m-12,16 :E-9 E-1 E-17 E-9 E19 E23 E-29 E-138m-12,16 :E-9 E-1 E-17 E-9 E19 E23 E-29 E78m-12,16 :E-9 E-1 E-17 E-9 E19 E19 E-29 E238m-11,-12:E-9 E-13 E-17 E-33 E-53 E-37 E-21 E358m-11,4  :E-9 E7 E-9 E-37 E-41 E-25 E-53 E-378m-11,4  :E-9 E7 E-9 E-37 E-41 E-29 E-53 E-218m-11,4  :E-9 E7 E-9 E-37 E-41 E-29 E-53 E-258m-11,4  :E-9 E7 E-9 E-37 E-41 E-53 E-25 E-378m-11,4  :E-9 E7 E-9 E-29 E-29 E-53 E-53 E-338m-11,4  :E-9 E7 E-9 E-57 E-53 E-61 E-45 E-618m-10,6  :E-9 E7 E-9 E-57 E-53 E-45 E-41 E-498m-10,6  :E-9 E7 E-9 E-57 E-53 E-45 E-41 E-578m-10,9  :E-9 E7 E11 E-29 E-9 E-13 E-41 E198m-10,16 :E-9 E7 E-17 E-29 E-41 E-45 E-9 E-58m-10,16 :E-9 E7 E-17 E-29 E-41 E-45 E-9 E-98m-10,18 :E-9 E7 E-5 E11 E-1 E11 E-45 E198m-10,18 :E-9 E7 E-5 E11 E-1 E11 E-45 E158m-10,18 :E-9 E7 E-5 E11 E-1 E11 E-45 E118m-9 ,-5 :E-9 E7 E-9 E-57 E-29 E-21 E-33 E-418m-9 ,8  :E-9 E-1 E-17 E11 E-25 E-13 E-21 E278m-9 ,8  :E-9 E-1 E-17 E11 E-25 E-13 E-21 E238m-9 ,14 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E358m-9 ,14 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E318m-9 ,14 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E278m-8 ,0  :E-9 E7 E7 E-13 E-13 E-33 E-9 E278m-8 ,3  :E-9 E11 E11 E23 E55 E11 E-21 E-178m-8 ,4  :E-9 E-1 E-17 E11 E-25 E3 E-37 E238m-8 ,4  :E-9 E-1 E-17 E11 E-25 E35 E-37 E238m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E3 E118m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E3 E158m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E3 E78m-7 ,-2 :E-9 E-17 E19 E-5 E11 E31 E-41 E-218m-7 ,-2 :E-9 E-17 E19 E-5 E11 E31 E-41 E-258m-7 ,5  :E-9 E7 E-21 E11 E-1 E7 E31 E198m-7 ,14 :E-9 E11 E11 E-1 E-9 E7 E-45 E-218m-6 ,-5 :E-9 E7 E-5 E-29 E-9 E-29 E-29 E-138m-6 ,-5 :E-9 E7 E-5 E-29 E-9 E-29 E-5 E-138m-6 ,-4 :E-9 E-1 E-5 E7 E3 E-9 E7 E-18m-6 ,5  :E-9 E-1 E-17 E11 E-25 E-13 E-37 E278m-6 ,5  :E-9 E-1 E-17 E11 E-25 E-13 E-37 E238m-6 ,9  :E-9 E7 E-5 E-29 E3 E-1 E7 E118m-6 ,9  :E-9 E7 E-5 E-29 E3 E-1 E11 E118m-6 ,9  :E-9 E7 E-5 E-29 E3 E-1 E-5 E158m-6 ,11 :E-9 E11 E11 E-29 E3 E-1 E-29 E38m-6 ,11 :E-9 E11 E11 E-29 E3 E-1 E-29 E-138m-6 ,11 :E-9 E7 E11 E7 E-29 E-5 E-5 E-178m-6 ,11 :E-9 E-13 E-13 E-1 E-17 E-17 E-21 E-98m-5 ,4  :E-9 E7 E7 E11 E-29 E3 E23 E198m-5 ,4  :E-9 E7 E7 E11 E-29 E3 E23 E358m-5 ,7  :E-9 E11 E11 E3 E-5 E-21 E15 E118m-5 ,7  :E-9 E11 E11 E3 E-5 E-21 E15 E78m-4 ,6  :E-9 E7 E7 E11 E-29 E23 E-29 E38m-4 ,6  :E-9 E7 E7 E11 E-29 E23 E-29 E198m-4 ,6  :E-9 E7 E7 E11 E-29 E23 E-29 E158m-3 ,-9 :E-9 E-13 E-13 E-29 E-29 E-13 E-21 E-98m-3 ,-9 :E-9 E-13 E-13 E-29 E-29 E-13 E-17 E-258m-3 ,-9 :E-9 E-13 E-13 E-29 E-29 E-13 E-17 E-218m-3 ,1  :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-818m-3 ,1  :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-778m-3 ,1  :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-738m-2 ,-19:E-9 E7 E11 E-29 E-9 E7 E-1 E358m-2 ,5  :E-9 E7 E-17 E11 E-9 E-29 E-5 E-298m-2 ,5  :E-9 E7 E-17 E11 E-9 E-29 E-5 E-458m-2 ,5  :E-9 E-9 E-5 E-13 E-17 E-29 E-13 E-618m-2 ,10 :E-9 E7 E-21 E11 E19 E-5 E3 E158m-2 ,10 :E-9 E7 E-21 E11 E19 E7 E-5 E-18m-2 ,10 :E-9 E7 E-21 E11 E19 E7 E-5 E38m-2 ,15 :E-9 E11 E11 E-29 E3 E-1 E7 E-58m-1 ,0  :E-9 E7 E-17 E11 E-1 E-13 E-33 E238m-1 ,0  :E-9 E7 E-17 E11 E-1 E-13 E-33 E38m-1 ,4  :E-9 E7 E-21 E-21 E11 E11 E-29 E158m-1 ,4  :E-9 E7 E-21 E-21 E11 E11 E-29 E118m-1 ,11 :E-9 E11 E11 E-1 E27 E-25 E-33 E-98m-1 ,19 :E-9 E-1 E15 E-5 E-5 E-21 E-49 E358m-1 ,19 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E358m-1 ,19 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E278m-1 ,19 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E318m-1 ,28 :E-9 E11 E11 E-1 E27 E-29 E-33 E-458m0  ,9  :E-9 E7 E-9 E-41 E-21 E-29 E-25 E-498m0  ,9  :E-9 E7 E-9 E-41 E-21 E-29 E-25 E-418m0  ,13 :E-9 E-9 E-5 E-17 E-25 E-5 E-17 E158m0  ,19 :E-9 E-1 E15 E-5 E-9 E11 E-29 E398m0  ,19 :E-9 E-1 E15 E-5 E-5 E35 E-29 E-138m0  ,19 :E-9 E-1 E15 E-5 E-5 E35 E-29 E-98m0  ,19 :E-9 E-1 E15 E-5 E-5 E35 E-29 E-258m0  ,19 :E-9 E-1 E15 E-5 E-9 E11 E-29 E198m1  ,-2 :E-9 E7 E-21 E-13 E-29 E-17 E-5 E-218m1  ,-2 :E-9 E-9 E19 E-5 E27 E-29 E-5 E318m1  ,0  :E-9 E11 E11 E-1 E7 E-13 E23 E-138m1  ,0  :E-9 E11 E11 E-1 E7 E-17 E23 E-58m1  ,0  :E-9 E11 E11 E-1 E7 E-13 E23 E-218m1  ,0  :E-9 E11 E11 E-1 E7 E-1 E23 E-218m1  ,6  :E-9 E7 E-5 E11 E3 E-5 E-1 E-578m1  ,6  :E-9 E7 E-5 E11 E3 E-5 E-1 E-498m1  ,12 :E-9 E-1 E-1 E19 E27 E35 E-5 E438m1  ,12 :E-9 E-1 E-1 E19 E27 E35 E-5 E398m1  ,12 :E-9 E-1 E-1 E19 E27 E39 E-5 E278m1  ,21 :E-9 E-1 E15 E-5 E-29 E-49 E-9 E358m1  ,21 :E-9 E7 E-17 E-33 E-25 E-37 E-21 E78m1  ,21 :E-9 E7 E-17 E-33 E-25 E-37 E-21 E38m1  ,21 :E-9 E7 E-17 E-33 E-25 E-37 E7 E-218m1  ,28 :E-9 E7 E7 E-17 E-13 E-17 E-41 E-338m1  ,28 :E-9 E7 E7 E-17 E-13 E-13 E-25 E78m1  ,28 :E-9 E7 E7 E-17 E-13 E-17 E-41 E-298m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E43 E398m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E43 E318m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E43 E358m2  ,-18:E-9 E-13 E-13 E-9 E-5 E55 E-13 E-178m2  ,-14:E-9 E7 E-17 E11 E-5 E-13 E-25 E-338m2  ,-14:E-9 E7 E-17 E11 E-5 E-13 E-25 E-258m2  ,-14:E-9 E7 E-17 E11 E-5 E-9 E-13 E-338m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-538m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-578m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-618m2  ,-14:E-9 E7 E-17 E11 E-5 E-9 E-9 E-218m2  ,-14:E-9 E7 E-17 E11 E-5 E-9 E-9 E-178m2  ,-14:E-9 E7 E7 E11 E-13 E-5 E-29 E278m2  ,0  :E-9 E7 E7 E-13 E-29 E-5 E-5 E278m2  ,2  :E-9 E11 E11 E-29 E-29 E-29 E19 E78m2  ,12 :E-9 E-13 E-13 E-9 E3 E3 E-17 E-58m2  ,14 :E-9 E-1 E-1 E19 E27 E-5 E-33 E318m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E358m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E318m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E278m2  ,30 :E-9 E7 E7 E-17 E-65 E-13 E-9 E-98m2  ,30 :E-9 E7 E7 E-17 E-65 E-13 E-9 E-58m3  ,0  :E-9 E-1 E15 E-13 E-29 E-21 E-1 E-178m3  ,0  :E-9 E-1 E15 E-13 E-29 E-21 E-1 E-218m3  ,0  :E-9 E-1 E15 E-13 E-29 E-21 E-1 E-258m4  ,-13:E-9 E7 E-17 E11 E-5 E-33 E43 E-138m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E43 E-498m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E43 E-538m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E43 E-578m4  ,-3 :E-9 E11 E11 E-29 E-29 E-29 E19 E38m4  ,0  :E-9 E-13 E-13 E-9 E-9 E-9 E-1 E-138m4  ,0  :E-9 E-13 E-13 E-9 E-9 E-9 E-1 E-178m4  ,9  :E-9 E-1 E15 E-5 E-17 E-1 E35 E-498m4  ,9  :E-9 E-1 E15 E-5 E-17 E-1 E35 E-378m4  ,9  :E-9 E-1 E15 E-5 E-17 E-1 E35 E-338m4  ,9  :E-9 E7 E-17 E-29 E-25 E15 E15 E38m4  ,9  :E-9 E7 E-17 E-29 E-25 E15 E15 E158m4  ,9  :E-9 E7 E-17 E-29 E-25 E11 E7 E78m4  ,10 :E-9 E7 E-17 E11 E7 E-1 E-1 E-178m4  ,11 :E-9 E-1 E15 E-5 E-5 E-5 E-33 E358m5  ,-9 :E-9 E11 E11 E3 E-5 E15 E31 E-18m5  ,1  :E-9 E-13 E-13 E-9 E19 E-9 E15 E-178m5  ,2  :E-9 E-9 E3 E23 E-1 E-1 E7 E198m5  ,2  :E-9 E-9 E3 E23 E-1 E-1 E7 E238m5  ,11 :E-9 E-1 E15 E-5 E-17 E-1 E35 E-218m5  ,11 :E-9 E-1 E15 E-5 E-17 E-1 E-21 E358m5  ,11 :E-9 E7 E-17 E-29 E-25 E-21 E15 E118m5  ,12 :E-9 E-29 E39 E31 E23 E19 E47 E558m5  ,12 :E-9 E-29 E39 E23 E51 E27 E39 E558m5  ,12 :E-9 E-29 E39 E31 E23 E19 E59 E598m5  ,12 :E-9 E-29 E39 E31 E23 E19 E59 E558m5  ,12 :E-9 E-29 E39 E31 E23 E19 E59 E518m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E598m5  ,12 :E-9 E-29 E39 E43 E39 E47 E59 E478m5  ,12 :E-9 E-29 E19 E39 E39 E27 E27 E558m5  ,12 :E-9 E-29 E39 E43 E19 E19 E59 E358m5  ,12 :E-9 E-29 E39 E23 E51 E27 E39 E598m5  ,12 :E-9 E-29 E19 E39 E39 E43 E31 E598m5  ,12 :E-9 E-29 E19 E39 E39 E27 E27 E358m5  ,12 :E-9 E-29 E39 E43 E47 E35 E59 E518m5  ,12 :E-9 E-29 E39 E23 E47 E27 E63 E518m5  ,12 :E-9 E-29 E39 E23 E47 E27 E59 E638m5  ,12 :E-9 E-29 E39 E23 E47 E27 E43 E638m5  ,12 :E-9 E-29 E39 E31 E23 E19 E67 E558m5  ,12 :E-9 E-29 E39 E31 E23 E19 E47 E678m5  ,12 :E-9 E-29 E39 E31 E23 E19 E63 E678m5  ,12 :E-9 E-29 E39 E23 E51 E27 E39 E518m5  ,12 :E-9 E-29 E39 E23 E47 E27 E43 E518m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E198m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E358m5  ,12 :E-9 E-29 E39 E43 E47 E35 E71 E598m5  ,12 :E-9 E-29 E39 E43 E47 E35 E71 E678m5  ,12 :E-9 E-29 E39 E43 E47 E35 E59 E718m5  ,12 :E-9 E-29 E39 E43 E43 E23 E51 E518m5  ,12 :E-9 E-29 E39 E31 E23 E19 E47 E518m5  ,12 :E-9 E-29 E19 E39 E39 E43 E31 E398m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E438m5  ,12 :E-9 E-29 E39 E23 E39 E51 E83 E798m5  ,12 :E-9 E-29 E39 E23 E39 E51 E83 E718m5  ,12 :E-9 E-29 E39 E23 E47 E27 E43 E478m6  ,14 :E-9 E-29 E39 E43 E39 E51 E-25 E398m6  ,14 :E-9 E-29 E39 E23 E47 E27 E-25 E518m6  ,14 :E-9 E-29 E39 E23 E35 E55 E-25 E558m6  ,14 :E-9 E-29 E39 E23 E35 E55 E-25 E398m6  ,14 :E-9 E-29 E39 E31 E23 E19 E-25 E558m6  ,14 :E-9 E-29 E39 E43 E43 E23 E-25 E558m6  ,14 :E-9 E-29 E39 E31 E23 E19 E-25 E518m6  ,14 :E-9 E-29 E39 E23 E47 E27 E-25 E478m6  ,14 :E-9 E-29 E39 E43 E43 E23 E-25 E638m6  ,14 :E-9 E-29 E39 E23 E35 E55 E-25 E638m6  ,14 :E-9 E-29 E39 E43 E-25 E43 E63 E238m6  ,14 :E-9 E-29 E39 E43 E47 E71 E-25 E638m6  ,14 :E-9 E-29 E39 E43 E47 E71 E-25 E598m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E-498m7  ,-8 :E-9 E-29 E-25 E-5 E-5 E-17 E-17 E-98m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E-458m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E-458m7  ,-8 :E-9 E-29 E-25 E-25 E-9 E-33 E-13 E-338m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E-418m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E-41 E158m7  ,-8 :E-9 E-29 E-5 E-1 E3 E-9 E27 E158m7  ,-8 :E-9 E-29 E-5 E-1 E3 E-9 E27 E238m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E-418m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E15 E7 E-418m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E-378m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E-1 E198m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E15 E198m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E15 E-25 E78m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E15 E-25 E-98m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E15 E7 E-258m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-25 E15 E-98m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E-1 E38m7  ,-8 :E-9 E-29 E-5 E-1 E-1 E-21 E7 E78m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E-1 E78m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-98m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-258m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E-41 E-18m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E-1 E-58m7  ,-8 :E-9 E-29 E-25 E-5 E-5 E-17 E-17 E118m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E-1 E-258m7  ,-8 :E-9 E-29 E-25 E-25 E-9 E-33 E-13 E-378m7  ,-7 :E-9 E-13 E-13 E-9 E19 E23 E19 E38m7  ,-7 :E-9 E-13 E-13 E-9 E19 E23 E19 E-178m7  ,-2 :E-9 E-1 E-5 E7 E-1 E-9 E-25 E78m7  ,10 :E-9 E7 E-21 E-13 E3 E3 E27 E-18m7  ,12 :E-9 E7 E-17 E-29 E-25 E-21 E-1 E38m8  ,-6 :E-9 E-29 E-5 E-1 E19 E-1 E-21 E118m8  ,-6 :E-9 E-29 E-5 E-1 E19 E-1 E-21 E198m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-13 E-58m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-13 E78m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-13 E-98m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E7 E19 E-58m8  ,-6 :E-9 E-29 E-5 E-21 E19 E3 E-17 E78m8  ,-6 :E-9 E-29 E-5 E-21 E19 E3 E-17 E38m8  ,-6 :E-9 E-29 E-5 E-21 E15 E-17 E19 E-178m8  ,-6 :E-9 E-29 E-5 E-1 E19 E3 E27 E198m8  ,-6 :E-9 E-29 E-5 E-1 E19 E3 E27 E158m8  ,-3 :E-9 E7 E-5 E3 E-5 E-13 E-41 E-58m8  ,-3 :E-9 E7 E-5 E3 E-5 E-13 E-41 E-98m8  ,11 :E-9 E-29 E39 E31 E47 E27 E23 E438m8  ,11 :E-9 E-29 E39 E31 E47 E27 E23 E518m8  ,14 :E-9 E7 E-17 E11 E7 E19 E-29 E38m8  ,15 :E-9 E-29 E39 E59 E-1 E-25 E-5 E398m8  ,15 :E-9 E-29 E39 E59 E-1 E-25 E-5 E478m8  ,15 :E-9 E-29 E39 E59 E-1 E-25 E-5 E438m9  ,3  :E-9 E-1 E-17 E-9 E19 E3 E-9 E-178m9  ,7  :E-9 E7 E11 E3 E-9 E-33 E31 E-58m10 ,-5 :E-9 E-29 E-5 E-1 E19 E39 E-5 E-58m10 ,-5 :E-9 E-29 E-5 E-1 E19 E39 E-5 E-98m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-45 E-538m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-53 E-538m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-45 E-578m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-45 E-618m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-298m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-458m10 ,12 :E-9 E-13 E-17 E-21 E-21 E-13 E-41 E-178m11 ,-16:E-9 E-29 E39 E31 E23 E19 E59 E-98m11 ,-16:E-9 E-29 E39 E31 E23 E19 E59 E-178m11 ,-16:E-9 E-29 E39 E31 E23 E19 E59 E-138m11 ,4  :E-9 E-1 E-17 E11 E-25 E35 E27 E-218m11 ,4  :E-9 E-1 E-17 E11 E-25 E35 E27 E-258m11 ,22 :E-9 E-1 E15 E-13 E-29 E-21 E-1 E118m11 ,22 :E-9 E-1 E15 E-13 E-29 E-21 E-1 E38m11 ,22 :E-9 E-1 E15 E-13 E-29 E-21 E-1 E78m11 ,22 :E-9 E-1 E15 E-13 E-29 E-21 E23 E278m12 ,0  :E-9 E-1 E-17 E11 E-25 E11 E-45 E-258m12 ,0  :E-9 E-1 E-17 E11 E-25 E11 E-13 E-258m12 ,6  :E-9 E7 E-5 E3 E23 E3 E3 E-378m12 ,6  :E-9 E7 E-5 E3 E23 E3 E3 E-418m12 ,6  :E-9 E7 E-5 E3 E23 E3 E3 E-458m12 ,13 :E-9 E-13 E-17 E-13 E-33 E-33 E7 E-218m13 ,0  :E-9 E7 E11 E3 E-9 E-33 E15 E118m15 ,0  :E-9 E7 E-5 E3 E23 E15 E3 E-498m15 ,0  :E-9 E7 E-5 E3 E23 E15 E-49 E118m15 ,0  :E-9 E7 E-5 E3 E23 E15 E3 E-298m15 ,0  :E-9 E7 E-5 E3 E23 E15 E-49 E38m16 ,-1 :E-9 E7 E-21 E11 E-1 E7 E-29 E198m17 ,-10:E-9 E-29 E39 E23 E51 E27 E39 E-98m17 ,-10:E-9 E-29 E39 E23 E51 E27 E39 E-138m17 ,-10:E-9 E-29 E39 E23 E51 E27 E39 E-178m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-5 E-138m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-5 E-178m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-5 E-98m20 ,2  :E-9 E-9 E3 E11 E3 E23 E-1 E-298m20 ,2  :E-9 E-9 E3 E11 E3 E23 E-1 E-98m21 ,1  :E-9 E-1 E-5 E7 E-5 E-17 E47 E358m23 ,5  :E-9 E-29 E-5 E-21 E-5 E31 E7 E198m24 ,2  :E-9 E7 E-17 E11 E23 E-5 E-9 E-218m24 ,2  :E-9 E11 E11 E23 E-13 E-29 E3 E158m24 ,2  :E-9 E7 E-17 E11 E23 E-5 E-9 E-178m26 ,7  :E-9 E11 E11 E23 E-21 E23 E35 E318m26 ,7  :E-9 E11 E11 E23 E-21 E23 E35 E518m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-138m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-178m28 ,33 :E-9 E-9 E19 E-9 E11 E-1 E-9 E38m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E39m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E15 E119m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E15 E159m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E-65 E119m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E-65 E-19m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E7 E-65 E79m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E7 E-65 E-19m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E-65 E199m-22,16 :E-9 E-13 E-17 E-33 E-17 E-65 E-85 E-9 E159m-22,16 :E-9 E-13 E-17 E-33 E-17 E-65 E-85 E-9 E-19m-18,6  :E-9 E7 E-9 E-57 E-29 E-21 E-13 E-69 E-419m-18,6  :E-9 E7 E-9 E-57 E-29 E-21 E-13 E-69 E-259m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-61 E-25 E-579m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-61 E-25 E-539m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-61 E-25 E-499m-15,4  :E-9 E-9 E3 E23 E-1 E-17 E31 E-41 E359m-11,4  :E-9 E7 E-9 E-25 E-49 E-37 E-49 E-53 E-139m-11,4  :E-9 E7 E7 E-13 E-17 E-5 E-41 E-41 E279m-7 ,-2 :E-9 E-17 E19 E-5 E11 E-5 E-41 E-17 E-419m-7 ,-2 :E-9 E-17 E19 E-5 E11 E-5 E-41 E-17 E-339m-6 ,1  :E-9 E7 E7 E-13 E-13 E-33 E-9 E-5 E279m-6 ,9  :E-9 E7 E-5 E-29 E3 E-1 E23 E-1 E119m-5 ,3  :E-9 E-1 E-17 E11 E-13 E15 E15 E-21 E-579m-5 ,3  :E-9 E-1 E-17 E11 E-13 E15 E15 E-21 E-419m-4 ,-8 :E-9 E7 E-5 E-29 E3 E3 E-1 E3 E279m-4 ,-8 :E-9 E7 E-5 E-29 E3 E3 E-1 E3 E319m-4 ,18 :E-9 E-13 E-13 E-1 E-17 E7 E7 E-33 E-259m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E279m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E319m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E359m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E399m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E439m-3 ,23 :E-9 E-17 E-33 E15 E-1 E-5 E-45 E-5 E199m-3 ,23 :E-9 E-17 E-33 E15 E-1 E-5 E-45 E-5 E279m-1 ,10 :E-9 E7 E7 E-13 E-17 E-5 E-25 E-41 E279m1  ,-16:E-9 E-17 E-33 E15 E15 E23 E-29 E-5 E-179m1  ,-16:E-9 E-17 E-33 E15 E15 E23 E-29 E-5 E-99m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E-499m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E-539m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E-579m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E43 E359m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E43 E399m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E43 E319m2  ,30 :E-9 E7 E7 E-17 E-13 E-17 E-41 E-65 E-339m2  ,30 :E-9 E7 E7 E-17 E-13 E-17 E-41 E-65 E-299m4  ,-13:E-9 E7 E-17 E11 E-5 E-13 E43 E-25 E-339m4  ,-13:E-9 E7 E7 E11 E-13 E-5 E43 E-29 E279m4  ,-13:E-9 E7 E-17 E11 E-5 E-13 E43 E-25 E-259m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E-65 E43 E-539m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E-65 E43 E-619m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E-65 E43 E-579m4  ,31 :E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E279m4  ,31 :E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E319m4  ,31 :E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E359m5  ,12 :E-9 E-29 E39 E31 E23 E19 E67 E47 E359m5  ,12 :E-9 E-29 E39 E31 E23 E19 E67 E47 E519m5  ,12 :E-9 E-29 E39 E23 E47 E27 E63 E43 E479m5  ,12 :E-9 E-29 E39 E23 E47 E27 E63 E43 E319m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E39 E399m5  ,12 :E-9 E-29 E39 E23 E47 E39 E59 E47 E479m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E39 E599m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E39 E479m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E39 E199m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E39 E319m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E39 E399m6  ,14 :E-9 E-29 E39 E23 E47 E27 E43 E-25 E479m6  ,14 :E-9 E-29 E39 E31 E23 E19 E47 E-25 E679m6  ,14 :E-9 E-29 E39 E43 E19 E35 E-25 E3 E439m6  ,14 :E-9 E-29 E39 E31 E23 E19 E47 E-25 E519m6  ,14 :E-9 E-29 E39 E43 E39 E51 E-25 E31 E199m6  ,14 :E-9 E-29 E39 E23 E47 E27 E43 E-25 E639m6  ,14 :E-9 E-29 E39 E43 E39 E51 E-25 E31 E359m6  ,14 :E-9 E-29 E39 E23 E47 E27 E43 E-25 E519m6  ,14 :E-9 E-29 E39 E43 E19 E35 E-25 E3 E599m6  ,14 :E-9 E-29 E39 E43 E47 E35 E71 E-25 E679m6  ,14 :E-9 E-29 E39 E43 E47 E35 E71 E-25 E599m6  ,14 :E-9 E-29 E39 E31 E23 E19 E47 E-25 E559m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-5 E15 E3 E39m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-21 E-419m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-21 E-339m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-5 E-59m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-5 E-259m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-5 E-139m7  ,1  :E-9 E7 E-17 E-33 E11 E19 E3 E-5 E-139m7  ,1  :E-9 E7 E-17 E-33 E11 E19 E3 E-5 E-179m8  ,-6 :E-9 E-29 E-5 E-1 E-25 E-9 E19 E-41 E159m8  ,-6 :E-9 E-29 E-5 E-1 E-25 E-9 E19 E-41 E-19m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E19 E-99m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E19 E-259m8  ,15 :E-9 E-29 E39 E43 E47 E71 E-25 E-5 E639m8  ,15 :E-9 E-29 E39 E43 E47 E71 E-25 E-5 E599m8  ,15 :E-9 E-29 E39 E43 E43 E23 E-25 E-5 E639m8  ,15 :E-9 E-29 E39 E43 E43 E23 E-25 E-5 E559m10 ,-5 :E-9 E-29 E-5 E-1 E19 E3 E27 E39 E199m10 ,-5 :E-9 E-29 E-5 E-1 E19 E3 E27 E39 E159m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-25 E-259m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-25 E-339m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-25 E-459m11 ,2  :E-9 E-1 E-1 E19 E-1 E-9 E-5 E23 E-619m13 ,9  :E-9 E7 E11 E-29 E-5 E11 E7 E-33 E-299m13 ,9  :E-9 E7 E11 E-29 E-5 E11 E7 E-33 E-459m13 ,26 :E-9 E-29 E-25 E-25 E-5 E-45 E-25 E11 E-99m21 ,12 :E-9 E7 E-21 E-13 E3 E3 E3 E27 E-19m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-21 E-139m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-21 E-179m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-21 E-19m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E-9 E-99m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E-9 E-59m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E-29 E-19m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E-29 E-9`

The same filter could also be applied to the larger monochromatic-all collection posted in the same message. But I suppose NewGlue will be able to re-create all of these recipes in fairly short order.

dvgrn
Moderator

Posts: 5620
Joined: May 17th, 2009, 11:00 pm

### Re: David Bell's engineless caterpillar idea revisited

dvgrn wrote:I hadn't followed that line of thought far enough

Lets assume we want to get to speed m/n (where 4m < n) , this means our movement distance D = m * k and our period (the time between read1 and read2) P = n * k, where k is some positive large number. Now without any loss of generality, we can chose our k = 8l. so D = m * 8 * l and P = n * 8 * l. This means all our periods can be presumed dividable by 8, and all our movement distances as well.

Let me prove we can get as close to c/4 as needed.

As we know our SL movement done by converting SL->Glider and Glider->SL. All the conversions/glider reflections take constant time (the same goes for the helix), and we can remain in glider state as long as it's necessary. Glider moves with c/4 so in total if we move N ticks with speed c/4 and some C (which is constant) ticks we don't move, our average speed (which is the caterloopillar speed) would be c/4 * (N / (N + C)), because we can make N as large as needed we can get any speed lower than c/4.

Another nuance that is necessary to mention is that the distance between reading head and the next measuring from bottom of the first and top of the second can also remain constant (meaning our information in a way of SL and not glider remains SL for constant time).

In other words, Our step is the distance that SL travels by one "read" lets call it D. The time it took to move the SL is ~4D because most of the time it was glider. The next reading head will come shortly after the first finished, so the time between the reads (i.e. the period itself) is ~4D.

dvgrn wrote:the "40" constant for 512-spaced recipes

40 = 512 - 4 * 118. To get to zero point just use period 118 * 8. The zero point is very important place as we can't use any tricks regarding skips for movement purposes. c/8, c/16, c/24... etc are always zero points. Fortunately we don't need to use skips but only block movement recipes.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

MonochromaticP1 depth 12 finished with many new SLs and ~250K block movements.

Depth 12 monochromatic P1 WSS search had finished:

Two different but unfortunately same parity LWSS:

`x = 2491, y = 1491, rule = LifeHistory2C998.2C\$2C998.2C75\$80.3C997.3C\$80.C999.C\$81.C999.C118\$1208.3C\$1208.C\$1209.C12\$208.3C\$208.C\$209.C116\$1336.3C\$1336.C\$1337.C12\$336.3C\$336.C\$337.C116\$1464.3C\$1464.C\$1465.C8\$464.3C\$464.C\$465.C116\$1592.3C\$1592.C\$1593.C4\$592.3C\$592.C\$593.C120\$720.3C\$720.C\$721.C4\$1720.3C\$1720.C\$1721.C110\$848.3C\$848.C\$849.C2\$1848.3C\$1848.C\$1849.C116\$1976.3C\$1976.C\$1977.C12\$976.3C\$976.C\$977.C120\$2104.3C\$2104.C\$2105.C16\$1104.3C\$1104.C\$1105.C120\$2232.3C\$2232.C\$1232.3C998.C\$1232.C\$1233.C120\$2360.3C\$2360.C\$2361.C8\$1360.3C\$1360.C\$1361.C120\$2488.3C\$2488.C\$2489.C!`

HWSS started to appear (6 recipes) but no edge shooters, and MWSS has few variants of the same basic edge shooter, obviously having the same parity.

I think I'll switch to monochromatic p2 search. There should be much more than 800 block moves recipes for depth 9, I'm guessing that many of the recipes are not same parity gliders, but could be made with same parity as well.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

simsim314 wrote:I think I'll switch to monochromatic p2 search. There should be much more than 800 block moves recipes for depth 9, I'm guessing that many of the recipes are not same parity gliders, but could be made with same parity as well.

The 820 block moves I posted are all even-parity gliders, according to the "E" prefixes. Quite possibly the old P2 block-move list was from a highly constrained search with Paul Chapman's Glue2 -- lower population limits or bounding box than you're using now.

Of course it's not impossible that I made some other mistake along the way and filtered out too many recipes. I'll be interested to see how many more block moves you turn up; even at P2, the monochromatic restriction still lowers the branching factor pretty significantly.

No need for Schroedinger superimposed-state cleanups for this search, I suppose. That's a pity -- they were fun while they lasted.

simsim314 wrote:40 = 512 - 4 * 118. To get to zero point just use period 118 * 8. The zero point is very important place as we can't use any tricks regarding skips for movement purposes. c/8, c/16, c/24... etc are always zero points. Fortunately we don't need to use skips but only block movement recipes.

Got it -- thanks. I knew something strange was going on there. It was mostly Doppler-effect confusion on my part.

Here's a minor caveat, though. At a zero point, there are a lot fewer adjustment options, but skipping helix cycles can still cause location changes.

Example: you mentioned period 118*8 = 944. This translates into a 590-cell spacing of the read heads -- period 944 = 2*590 - 2*118 due to the Doppler effect... the upship *WSS spacing is then 354 cells, since 944 = 2*354 + 2*118.

At this period, skipping one helix cycle produces an offset of -118 relative to no-skip, and skipping two cycles changes the location by -236 (or +118); you have to skip three cycles to see the zero point. So even at c/8N periods, you still have to worry a little bit about which cycle the trigger glider comes from.

`#C zero point highlighted by four red arrowsx = 1146, y = 4079, rule = 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dvgrn
Moderator

Posts: 5620
Joined: May 17th, 2009, 11:00 pm

### Re: David Bell's engineless caterpillar idea revisited

Yes you right there is no such thing as absolute Zero point, only close to it (due to Doppler effect).

Here are 1043 block moves recipes from depth 8 monochromatic p2 search (I didn't post the full report yet).

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EDIT From what I've seen thus far I guess the *WSS search will need to work with something faster. If not GPU then at least LifeAPI. I could devise even and odd recipes using my 3SL search results, but I do agree that 3SL construction is tedious and pointlessly lengthy, it would be much simpler and elegant to rewrite my Glue python script, to work with LifeAPI.

EDIT2 Depth 9 monochromatic p2 gave 1861 unique locations (attached).

I've also committed mono. p2 search result to the repository.
Attachments
Monochromatic P2 Block Move Depth9.txt

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

Fully adjustable with self destruct even step back spine (20 *WSS):

`x = 195, y = 1141, rule = LifeHistory36.C.C\$39.C\$39.C\$39.C\$36.C2.C\$37.3C15\$31.C.C\$34.C\$30.C3.C\$30.C3.C\$34.C\$31.C2.C\$32.3C184\$115.C.C\$114.C\$114.C\$114.C2.C\$114.3C24\$105.C.C\$104.C\$104.C3.C\$104.C3.C\$104.C\$104.C2.C\$104.3C23\$103.C.C\$106.C\$102.C3.C\$102.C3.C\$106.C\$103.C2.C\$104.3C5\$89.2C\$88.3C\$88.3C\$88.3C\$88.2C.C\$89.3C\$90.C76\$74.2C\$73.3C\$73.2C.C\$74.3C\$75.C76\$31.C.C\$30.C\$30.C3.C\$30.C3.C\$30.C\$30.C2.C\$30.3C55\$41.2C\$41.3C\$41.3C\$40.C.2C\$40.3C\$41.C7\$20.C.C\$19.C\$19.C3.C\$19.C\$19.C2.C\$19.3C31\$.C.C\$C\$C\$C2.C\$3C50\$10.C.C\$9.C\$9.C3.C\$9.C\$9.C2.C\$9.3C70\$39.C.C\$38.C\$38.C3.C\$38.C3.C\$38.C\$38.C2.C\$38.3C50\$26.2C\$25.C2.C\$25.C.C\$26.C28\$73.C.C\$72.C\$72.C3.C\$72.C3.C\$72.C\$72.C2.C\$72.3C10\$192.2C\$191.3C\$191.3C\$191.2C.C\$192.3C\$193.C47\$88.C.C\$87.C\$87.C3.C\$87.C3.C\$87.C\$87.C2.C\$87.3C62\$103.C.C\$102.C\$102.C3.C\$102.C3.C\$102.C\$102.C2.C\$102.3C48\$128.C.C\$127.C\$127.C\$127.C2.C\$127.3C10\$134.C.C\$137.C\$133.C3.C\$137.C\$134.C2.C\$135.3C156\$187.C.C\$186.C\$186.C3.C\$186.C\$186.C2.C\$186.3C2\$192.C\$191.C.C\$191.C.C\$192.C!`

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

To finish the adjustable front/back issue, here is a script that automatically adjusts the step from user input, for backward and forward *WSS spines:

`import golly as g def MakeBackwardSalvo(distance):      backHelixSL = g.parse("bo\$obo\$obo\$bo!", 191, 1137)   backHelixSL2GliderWSS = g.parse("bobo\$o\$o3bo\$o\$o2bo\$3o!", 186, 1130)   backHelixReflect = g.parse("bobo\$o\$o\$o2bo\$3o10\$7bobo\$10bo\$6bo3bo\$10bo\$7bo2bo\$8b3o!", 127, 955)   backHelixGlider2SL = g.parse("b2o\$3o\$3o\$2obo\$b3o\$2bo!", 191, 781)   backErasingReflectorWSS = g.parse("bobo\$o\$o3bo\$o3bo\$o\$o2bo\$3o62\$16bobo\$15bo\$15bo3bo\$15bo3bo\$15bo\$15bo2bo\$15b3o!", 87, 833)   backSL = g.parse("b2o\$o2bo\$obo\$bo!", 25, 734)   backFrontPart = g.parse("74b2o\$73b3o\$73b2obo\$74b3o\$75bo76\$31bobo\$30bo\$30bo3bo\$30bo3bo\$30bo\$30bo2bo\$30b3o55\$41b2o\$41b3o\$41b3o\$40bob2o\$40b3o\$41bo7\$20bobo\$19bo\$19bo3bo\$19bo\$19bo2bo\$19b3o31\$bobo\$o\$o\$o2bo\$3o50\$10bobo\$9bo\$9bo3bo\$9bo\$9bo2bo\$9b3o70\$39bobo\$38bo\$38bo3bo\$38bo3bo\$38bo\$38bo2bo\$38b3o81\$73bobo\$72bo\$72bo3bo\$72bo3bo\$72bo\$72bo2bo\$72b3o!", 0, 360)   backReflectingPart = g.parse("27bobo\$26bo\$26bo\$26bo2bo\$26b3o24\$17bobo\$16bo\$16bo3bo\$16bo3bo\$16bo\$16bo2bo\$16b3o23\$15bobo\$18bo\$14bo3bo\$14bo3bo\$18bo\$15bo2bo\$16b3o5\$b2o\$3o\$3o\$3o\$2obo\$b3o\$2bo!", 88, 210)   backBackPart = g.parse("6bobo\$9bo\$9bo\$9bo\$6bo2bo\$7b3o15\$bobo\$4bo\$o3bo\$o3bo\$4bo\$bo2bo\$2b3o!", 30, 0)      d = (distance - 118) / 2   g.putcells(backHelixSL, d, d * 3)   g.putcells(backHelixSL2GliderWSS, d, d * 3)   g.putcells(backHelixReflect)   g.putcells(backHelixGlider2SL, d, -d * 3)   g.putcells(backErasingReflectorWSS)   g.putcells(backSL, -d, -d)   g.putcells(backFrontPart, -d, -d)   g.putcells(backReflectingPart, 0, -4 * d)   g.putcells(backBackPart, -d, -d * 7)def MakeForwardSalvo(distance):   frontHelixSL = g.parse("6bo\$5bobo\$5bobo\$6bo2\$b2o7b2o\$o2bo5bo2bo\$b2o7b2o2\$6bo\$5bobo\$5bobo\$6bo!", 0, 0)   frontHelixSL2GliderWSS = g.parse("3o\$o2bo\$o\$o3bo\$o\$bobo!", 9, 15)   frontHelixReflect = g.parse("2b3o\$bo2bo\$4bo\$o3bo\$4bo\$bobo8\$9b3o\$8bo2bo\$11bo\$7bo3bo\$7bo3bo\$11bo\$8bobo!", 61, 60)   frontHelixGlider2SL = g.parse("2bo\$b3o\$2obo\$3o\$3o\$b2o!", 4, 126)   frontErasingReflectorWSS = g.parse("2bo\$b3o\$2obo\$3o\$3o\$3o\$b2o59\$14bo\$13b3o\$12b2obo\$12b3o\$12b3o\$12b3o\$13b2o!", 91, 93)   frontSL = g.parse("bo\$obo\$o2bo\$b2o!", 145, 194)   frontFrontPart = g.parse("25bo\$24b3o\$23b2obo\$23b3o\$23b3o\$24b2o68\$37bo\$36b3o\$36bob2o\$37b3o\$37b3o\$37b3o\$37b2o8\$3o\$o2bo\$o\$o3bo\$o\$bobo39\$24bo\$23b3o\$23bob2o\$24b3o\$4b3o17b3o\$3bo2bo17b3o\$6bo17b2o\$2bo3bo\$2bo3bo\$6bo\$3bobo!", 139, 264)   frontReflectingPart = g.parse("7bo\$6b3o\$5b2obo\$5b3o\$5b3o\$5b3o12bo\$6b2o11b3o\$18b2obo\$18b3o\$19b2o14\$2bo\$b3o\$2obo\$3o\$3o\$b2o!", 82, 460)   frontBackPart = g.parse("11b3o\$11bo2bo\$11bo\$11bo3bo\$11bo\$12bobo4\$3o\$o2bo\$o\$o3bo\$o3bo\$o\$bobo!", 145, 542)   frontErasingReflector = g.parse("bo\$3o\$ob2o\$b3o\$b2o!", 122, 488)   d = (distance - 118) / 2   d_3 = int(d / 3)   g.putcells(frontHelixSL, -d, -d)   g.putcells(frontHelixSL2GliderWSS, -d, -d)   g.putcells(frontHelixReflect)   g.putcells(frontHelixGlider2SL, -d, d)   g.putcells(frontErasingReflectorWSS)   g.putcells(frontSL, d, d)   g.putcells(frontFrontPart, d, d)   g.putcells(frontReflectingPart, 0, 2 * d)   g.putcells(frontBackPart, d, 3 * d)   g.putcells(frontErasingReflector, d - d_3, d + 3 * d_3)   operation = g.getstring("Enter even step size: \n F100 - 100 forarward \n B100 - 100 backward", "F100")salvoType = ""if operation[0] == 'B' or operation[0] == 'b':   salvoType = "backward"   try:      step = int(operation.replace("B", "").replace("b", ""))   except:      g.exit("step must be integer")   if operation[0] == 'F' or operation[0] == 'f':   salvoType = "forward"   try:      step = int(operation.replace("F", "").replace("f", ""))   except:      g.exit("step must be integer")if salvoType == "":   g.exit("Couldn't recogine command")   if step % 2 != 0:   g.exit("Step must be even number")if salvoType == "forward":   g.new(operation)   MakeForwardSalvo(step)else:   g.new(operation)   MakeBackwardSalvo(step)g.fit()   `

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

simsim314 wrote:To finish the adjustable front/back issue, here is a script that automatically adjusts the step from user input, for backward and forward *WSS spines...

Looks good! I did a little testing and didn't find anything wrong, except maybe that the script will cheerfully build impossibly short-step spines. Thanks to the new rather slow *WSS+G -> block+G, it doesn't look like any steps shorter than B96 will work. Forward spines could be tightened up a good bit more -- F72 works, but F70 doesn't.

In the script, the default step is 100. Are there subtle limitations that mean that the minimum step should really be 98 or 100, not 96?

dvgrn
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Posts: 5620
Joined: May 17th, 2009, 11:00 pm

### Re: David Bell's engineless caterpillar idea revisited

dvgrn wrote:In the script, the default step is 100. Are there subtle limitations that mean that the minimum step should really be 98 or 100, not 96?

I chose default to clarify the usage (the first time the user run the script as is, and see it working - this makes his life so much easier). I just made sure 100 is working, and it was chosen because it's round number. I was mainly concentrating for large numbers to work.

I'm surprised the minimal back step is so high. I really have issues with the back design, it's somewhat awkward, but nevertheless working. I think some tweaking should make it possible to reduce both spines to ~15 in optimal case after a lot of effort.

I don't have any theory on how to optimize the self destruct, I used pure greedy algorithm (each block will erase maximum it can). For the back spine, the self destruct is 1 to 1 (each *WSS has another *WSS to delete it).

It would be nice to modify the script to make *WSS salvo by input period. Anyway for now I'm switching to write slow salvo LifeAPI *WSS search.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

I've stopped MonochromaticP2 searches as finishing depth 10 took 2G memory and with factor of 4 my RAM will be overflowed.

Check out the depth 10 results from the search.

EDIT The full SL collection of depth 10. A bit surprising, and unfortunately not full eater collection - only 7/8:
Code: Select all
`x = 526, y = 110, rule = B3/S23bo19bo19bo19bo19bo19bo19bo19bo19bo19bo19bo20b2o15bo20b2o19bo19b2o21bo19bo17b2o18b2o18b2o18b2o22b2o20b2o24b2o15b2o9b2o\$2o18bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo18bo2bo13bobo18bobo18bobo18bobo18b3o19bo16bobo17bobo17bobo17bob3o19bo2bo19bo25b2o15b2o10bo\$2o18b2o18bobo17bobo17bobo17bo2bo16bo2bo16bo2bo15bobo17bobo17bobo19bo2bo14bo19b2o20b2o19bobo16bo22bo16b2o18bo19bo19bo4bo18bo2bo20b3o20b2o28bo\$o38b2ob2o17bo19bo19b2obo16b2o18bobo16bo18b2o17bobo21b2o33b2o24b2o18b2o16b2o59bo19b4o16b3obo16b2ob2o24bo19b2o28b2o\$58b3o42bobo36bo56bo56bobo24bobo95b2o23bo17b2o16bo2bo25b2o\$58bo44bo2bo149b2o26bo119bobo35bo2bo\$104b2o298b2o37b2o8\$105bo150b2o144b2o18b2o19b2o23b2o\$42bo61bobo35bo56bo56bobo121b2o19bo2bo16bo2bo17bo2bo22bobo\$o39b3o60bo2bo15bo18bobo16bo19bo17bobo56b2o64b2o56bo19b2obo16b2obo17bo2bo24bo21b2o\$2o19bo17bo41b2o19bob2o15bobo16bo2bo15bobo17bobo17bobo57b2o61bobo36b2o17bo23bob2o14bob2o17b2ob2o22bobo19b2o\$2o18bobo17b3o37bo2bo17bobo16bo2bo16bobo17bobo17bobo17bobo56bobo60bo20b3o15bobo16bobo21bo2bo14bo2bo19bo2bo22b2o21b2o\$bo19b2o19bo38b2o17bo2bo17b2o18bo19bo19b2o18bo58b2o59b2o39b2o17b2o22b2o16b2o20bo2bo45b2o\$101b2o343b2o74bob2o\$522b2obo9\$b3o17b2o16bo64b2o15b2o19b2o37b2o139b2o\$3o17bobo16b3o61bo2bo13bo2bo17bo2bo35bobo139bo\$21bo20bo60bobo14bobo17bo2bo35bobo138bobo\$39b3o59b2obo16bo19b2o37bo139b2o\$39bo60bo2bo\$100bobo\$101bo10\$121b2o18b2o36b2o\$3o17b2o98bo2bo16bo2bo35bobo\$b3o16bobo98bobo17bo2bo35bobo\$21bo100bo19b2o37bo\$101b2o217b2o\$100bo2bo216bo\$101bobo217b3o\$102bob2o217bo\$103bo2bo\$104bobo\$105bo10\$322b2o\$323bo\$320b3o\$320bo17\$320b2o\$320bobo\$322bo\$322b2o17\$320b2o\$321bo\$321bobo\$322b2o!`

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

simsim314 wrote:EDIT The full SL collection of depth 10. A bit surprising, and unfortunately not full eater collection - only 7/8...

Luckily eaters are a lot more useful for Herschel conduits than for engineless Caterpillars. They aren't high on the list of components for 3SL *WSS seeds -- though quite possibly including them would add enough new search space that a 2SL *WSS seed might show up.

Anyway, there's an integral with the missing orientation. In Spartan circuitry it's very often possible to substitute an integral for a standard eater, if it's eating a glider... or substitute a hat if the tail end is being used as a rock -- that orientation of hat also happens to be available.

However, if P2-even slow salvos were going to be used to construct Spartan circuitry, it would be necessary to search a few levels deeper anyway. Not surprisingly, the integral recipes are all variants of each other, and so none of them are really edgy enough to make incremental constructions possible -- or at least not without serious difficulties.

Could maybe do a 2SL *WSS-seed search, stringing together pairs of these P2-even recipes, but only where they actually fit one after the other... but probably the direct LifeAPI search will produce good results just as fast.

dvgrn
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Posts: 5620
Joined: May 17th, 2009, 11:00 pm

### Re: David Bell's engineless caterpillar idea revisited

dvgrn wrote:Could maybe do a 2SL *WSS-seed search, stringing together pairs of these P2-even recipes, but only where they actually fit one after the other... but probably the direct LifeAPI search will produce good results just as fast.

Well writing LifeAPI for 2SL search should be simpler than Glue, but anyway I'm close to finish the Glue. And probably depth 14-15 would be enough for direct Glue, while two SL recipe will cost 20+.

It's interesting to see what SLs can come directly into the "slow salvo basic kit" (talking of conduits). Probably deeper search will yield some new basic components. All the most common SLs with new eating properties like: hat, shillelagh, snake etc. will probably appear with depth 12 in all orientations. Even deeper searches, because of statistical explosion will come up with many more SLs. I'm guessing eater2 is not on that list, but maybe eater2 will be reached with 2 SL search.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

I've added Glue++ (glue on c++ using LifeAPI), to the Glue repository.

It uses OpenMP for parallel threading (comes with gcc and most modern compilers - but you need to add flag -fopenmp).

There is some memory issue that causes the application to take too much memory for some reason. I seem to clean everything correctly and the recipes are kept in a tree with optimized format for memory. So depth 11 was the limit at my machine.

The results are reported in the same library as the exe, and got a lot of false positives. But the report shouldn't miss *WSS if it appeared, so cleaning the results with python script is necessary.

The last layer reported 14K results (with a lot of junk).

It looks like the memory leak fix is crucial to get enough results.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

I've improved the Glue++ by order of magnitude in speed and memory.

Here are some tricks I used:

In target search one should prefer shuffled data, instead of one next to other cell. The shuffled data cleaned much quicker statistically speaking (there are much more neighboring ON cells than two ON cells with some (dx, dy)).

The TargetLocator could be cheated by some random "*WSS like" pattern that appeared quickly and disappeared again. Making extra check after 4 generation makes the chances much lower for false positives.

Having tree of glider locations can be unpredictable, so storing the tree inside flat vector makes it much more controllable.

This one is dvgrn inspired trick: I clean the hash table of existing pattern when it gets too large. This will cause some of the patterns to repeat, but saves memory and time (from some point the request for the hash table becomes the most intensive operation). I've picked the value to be large enough so the quality will not deteriorate quickly.

Another trick is to limit the population. This is both quality and performance improvement. The more messy the pattern is the less chances edgy *WSS will come out of it, and the less chances it will repeat again so hashing it is useless. So limiting the population will allow to save on memory and improves quality.

Now after those introductions, what previously took about 5 hours and took 2G is now taking half hour and takes 100M, reporting better quality results.

NOTE Memory is still major limitation, as I didn't implemented other dvgrn's trick to search with higher depths, inside some high quality results of lower depth.
---

Switching to python parser now.

EDIT I've introduced few key features:

1. Save and load the data of each search depth. Now other slow salvo searches are possible using the same search tree just by loading the tree.

2. Every 500 results are reported, so even if something went wrong, the last run results will be available.

3. The most important is the option to search for edge shooters but without updating the search tree, thus getting one search depth deeper without paying any price for it. Similar to dvgrn's proposal to search inside limited depth, only with depth = 1.

As the memory playing less of an issue, the run time starts to play. Hopefully finding all the edge shooters in the scope of the run.

-My calculations show that finding all options for HWSS will take 4 days of run. Also maybe working with LWSS and MWSS and with what was found from the HWSS will be good enough.
Last edited by simsim314 on July 4th, 2015, 6:54 am, edited 1 time in total.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

Some initial results (after day of run):

`x = 28436, y = 115128, rule = 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$13.2C18.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C4876\$233.2C998.2C998.2C\$233.2C998.2C998.2C95\$333.3C997.3C997.3C\$333.C999.C999.C\$334.C999.C999.C2\$23.2C.C.2C.C\$23.C.2C.C.2C2\$13.2C5.2C11.2C\$13.C6.C12.C\$14.C6.C12.C\$13.2C5.2C11.2C2\$13.2C5.2C11.2C\$13.C6.C12.C\$14.C6.C12.C\$13.2C5.2C11.2C2\$23.2C.C.2C.C\$23.C.2C.C.2C2\$13.2C5.2C11.2C\$13.C6.C12.C\$14.C6.C12.C\$13.2C5.2C11.2C2\$13.2C5.2C11.2C\$13.C6.C12.C\$14.C6.C12.C\$13.2C5.2C11.2C2\$23.2C.C.2C.C\$23.C.2C.C.2C69\$2433.3C\$2433.C\$2434.C2\$433.3C997.3C\$433.C999.C\$434.C999.C90\$2533.3C\$2533.C\$2534.C8\$533.3C997.3C\$533.C999.C\$534.C999.C84\$2633.3C\$2633.C\$2634.C16\$633.3C997.3C\$633.C999.C\$634.C999.C84\$2733.3C\$2733.C\$2734.C4\$733.3C997.3C\$733.C999.C\$734.C999.C96\$833.3C997.3C\$833.C999.C\$834.C999.C6\$2833.3C\$2833.C\$2834.C76\$2933.3C\$2933.C\$2934.C10\$933.3C997.3C\$933.C999.C\$934.C999.C98\$1033.3C997.3C\$1033.C999.C\$1034.C999.C4\$3033.3C\$3033.C\$3034.C98\$3133.3C\$3133.C\$3134.C4\$1133.3C997.3C\$1133.C999.C\$1134.C999.C80\$3233.3C\$3233.C\$3234.C2\$1233.3C997.3C\$1233.C999.C\$1234.C999.C86\$3333.3C\$3333.C\$3334.C32\$1333.3C997.3C\$1333.C999.C\$1334.C999.C94\$3433.3C\$3433.C\$3434.C3788\$233.2C\$233.2C95\$333.3C\$333.C\$334.C2\$23.2C.C.2C.C\$23.C.2C.C.2C2\$13.2C5.2C11.2C\$13.C6.C12.C\$14.C6.C12.C\$13.2C5.2C11.2C2\$13.2C5.2C11.2C\$13.C6.C12.C\$14.C6.C12.C\$13.2C5.2C11.2C2\$23.2C.C.2C.C\$23.C.2C.C.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C2\$23.2C.C.2C.C\$23.C.2C.C.2C69\$433.3C\$433.C\$434.C98\$533.3C\$533.C\$534.C106\$633.3C\$633.C\$634.C104\$733.3C\$733.C\$734.C98\$833.3C\$833.C\$834.C90\$933.3C\$933.C\$934.C108\$1033.3C\$1033.C\$1034.C98\$1133.3C\$1133.C\$1134.C90\$1233.3C\$1233.C\$1234.C100\$1333.3C\$1333.C\$1334.C106\$1433.3C\$1433.C\$1434.C3884\$3.2C.C.2C.C11.2C.C.2C.C\$3.C.2C.C.2C11.C.2C.C.2C2\$13.2C5.2C11.2C\$13.C6.C12.C\$14.C6.C12.C\$13.2C5.2C11.2C2\$13.2C5.2C11.2C\$13.C6.C12.C\$14.C6.C12.C\$13.2C5.2C11.2C2\$3.2C.C.2C.C\$3.C.2C.C.2C2\$2C18.2C11.2C\$C19.C12.C\$.C19.C12.C\$2C18.2C11.2C2\$2C18.2C11.2C\$C19.C12.C\$.C19.C12.C\$2C18.2C11.2C2\$3.2C.C.2C.C11.2C.C.2C.C\$3.C.2C.C.2C11.C.2C.C.2C4973\$3.2C.C.2C.C\$3.C.2C.C.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C2\$3.2C.C.2C.C\$3.C.2C.C.2C2\$2C31.2C\$C32.C\$.C32.C\$2C31.2C2\$2C31.2C\$C32.C\$.C32.C\$2C31.2C2\$3.2C.C.2C.C\$3.C.2C.C.2C4973\$3.2C.C.2C.C11.2C.C.2C.C\$3.C.2C.C.2C11.C.2C.C.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C2\$3.2C.C.2C.C11.2C.C.2C.C\$3.C.2C.C.2C11.C.2C.C.2C2\$2C18.2C\$C19.C\$.C19.C\$2C18.2C2\$2C18.2C\$C19.C\$.C19.C\$2C18.2C2\$3.2C.C.2C.C11.2C.C.2C.C\$3.C.2C.C.2C11.C.2C.C.2C4973\$3.2C.C.2C.C11.2C.C.2C.C\$3.C.2C.C.2C11.C.2C.C.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C2\$13.2C18.2C\$13.C19.C\$14.C19.C\$13.2C18.2C2\$3.2C.C.2C.C11.2C.C.2C.C\$3.C.2C.C.2C11.C.2C.C.2C2\$2C31.2C\$C32.C\$.C32.C\$2C31.2C2\$2C31.2C\$C32.C\$.C32.C\$2C31.2C2\$3.2C.C.2C.C11.2C.C.2C.C\$3.C.2C.C.2C11.C.2C.C.2C!`

And the recipes:

`-4,2,6,6,2,-4,-6,6,2,6,6,6,2,4,-4,-4,-8,6,14,2,-4,2,6,6,2,-4,-14,-6,6,2,6,-4,2,6,6,2,-4,-6,2,-2,2,6,6,6,2,4,-4,-4,-8,6,14,2,-4,2,6,6,2,-4,-6,6,2,6,-4,2,6,6,2,-4,-14,-6,2,-2,2,6,-4,2,6,6,2,-4,-6,2,0,4,2,6,-4,2,6,6,2,-4,-6,2,0,8,2,6,-4,0,10,-22,-2,8,4,-2,-4,2,8,0,-4,2,6,6,2,-4,-6,6,2,6,-4,-12,-8,-2,-2,2,0,-6,-26,-16,-14,4,-4,-6,-6,2,2,-4,0,-8,-10,2,-2,2,-4,2,2,-8,-10,-8,-16,-16,-20,-6,2,-10,----------------4,-4,10,12,-4,-10,-8,-4,-18,-6,-10,6,6,10,12,12,20,14,4,-12,-16,-14,4,-4,-4,10,12,-10,-10,-4,-8,-4,-18,-6,-10,-4,-4,-2,12,-6,-8,-4,-8,-8,-10,-8,6,-4,-6,-8,-18,-6,-4,28,6,8,0,16,-6,-4,0,8,-6,-22,-8,10,-14,-6,-6,-18,-14,-4,-4,10,12,-10,6,0,10,-6,-8,-14,-16,-4,0,-8,-4,8,-2,6,0,-4,0,6,6,6,-2,0,-20,-12,6,-12,-2,-14,-6,0,14,----------------4,-4,10,-6,-14,4,-2,16,20,16,34,-4,0,-12,-8,8,12,12,12,-6,14,-16,-4,-4,8,2,12,6,-8,22,14,-4,28,10,-4,0,-8,-2,-8,8,14,12,12,-18,-10,2,----------------4,-4,-2,4,0,8,8,4,-8,-14,-8,-4,-4,-8,-12,-10,4,6,10,8,-6,-6,-4,-4,-2,4,0,8,8,4,-8,-14,-8,---------------6,6,2,-6,-6,-18,-20,4,-2,6,0,6,6,2,-6,-6,-18,-20,4,-2,6,-20,0,6,6,2,-6,-6,-18,-20,4,-2,6,-18,0,-4,-4,-6,-2,4,-6,12,12,14,10,18,20,-4,-6,6,0,-8,-18,8,10,-2,-6,8,2,-4,-14,-2,0,-12,-10,20,16,10,18,-4,10,----------------4,-12,-4,6,-12,-8,-2,16,16,0,-4,4,-10,-8,0,-6,-8,-20,-6,10,-4,-6,6,-8,-6,-10,2,-4,-8,-26,6,-4,4,-10,-8,0,-6,-8,-20,-6,10,-4,-4,10,2,4,-8,-18,0,14,8,8,-4,-12,-4,6,-12,-8,-2,16,16,0,-4,0,6,8,-2,-4,-16,-8,-12,0,-18,-4,-12,-4,6,-12,-8,-2,16,16,0,-4,4,-10,-8,0,-6,-8,-20,-6,10,-4,-4,-4,12,10,12,-4,6,10,18,14,-6,----------------4,-4,-8,-20,-20,10,12,-2,12,-2,-4,-4,-8,-20,-20,10,12,-2,12,-26,-2,-4,-4,-8,-20,-20,10,12,-2,12,-2,-4,-4,2,12,-6,-6,0,2,6,8,-4,-4,-4,-8,-20,-20,-26,10,12,-2,12,-2,-4,-4,10,-8,-20,12,-2,-20,12,-2,-4,-4,-8,-20,-20,10,12,-2,12,-26,-2,-4,-4,2,12,-6,-26,-6,0,2,6,8,-4,-4,-4,2,12,-6,-22,-6,0,2,6,8,-4,-4,0,8,-2,-10,-14,-18,-18,4,4,12,-8,-4,0,8,-6,-12,-14,-6,0,6,2,6,2,-4,0,8,-6,-12,-14,-4,0,6,2,6,2,-4,-12,-8,2,6,-12,-24,-12,16,14,12,-6,-4,-14,10,10,8,6,12,10,14,14,8,20,-4,-4,10,-8,-20,12,-2,-20,-26,12,-2,-4,-4,2,12,-6,-18,-6,0,2,6,8,-4,----------------4,-6,6,0,-8,-16,-4,24,20,14,0,-4,-4,10,0,-8,10,-12,-4,-14,24,4,-4,-4,10,0,-8,10,-12,-4,-14,24,4,-4,0,2,6,2,12,10,-8,-20,4,-4,-4,6,6,6,-8,2,-6,-2,16,8,12,22,20,-4,0,10,-2,16,-12,16,10,18,12,12,-14,-4,0,10,-2,16,16,10,18,12,12,-12,-14,-4,0,8,8,-6,14,22,12,6,-10,-2,14,---------------6,6,6,-6,-10,-6,-10,4,4,-4,-6,6,6,14,6,4,-4,0,-2,-10,10,-6,-4,0,8,6,8,-2,6,-12,-10,-6,-8,6,6,6,-2,-6,0,4,8,-4,2,-6,6,6,6,0,8,-10,0,-6,-2,6,-4,-6,6,6,-2,-4,10,14,16,12,4,12,2,-6,6,6,-2,-4,10,14,16,12,4,16,2,-6,6,6,-2,-4,10,14,16,12,6,2,2,-6,6,6,14,2,-4,6,8,8,14,-2,4,-6,6,6,6,-8,-10,-18,-6,4,-18,-16,-4,-6,-4,0,8,6,8,-2,6,-16,-14,-10,-6,-8,-4,0,8,6,8,-2,6,-12,-10,-6,14,-8,-4,0,8,6,8,-2,6,-12,-10,-6,16,-8,-4,0,8,6,8,-2,6,-12,-10,-6,20,-8,6,6,-2,14,8,-4,4,-2,0,10,6,-6,6,6,14,2,-4,12,6,18,14,14,-2,-6,6,6,14,2,-4,12,6,18,14,16,-2,-6,6,6,14,2,-4,12,18,16,18,20,2,-6,6,6,6,-6,-10,-6,-10,4,4,-4,-6,6,6,6,-2,-6,0,4,8,-4,2,6,-6,6,6,6,-2,-6,0,4,8,-4,2,10,-6,6,6,6,-2,-6,0,4,8,-4,2,12,-6,6,6,6,-2,-6,0,4,8,-4,2,14,-6,6,6,6,4,-10,-8,-12,-6,-2,6,-4,-6,6,6,14,6,4,-4,0,-8,-10,6,10,-6,6,6,14,6,4,-4,0,-8,-10,8,10,-6,6,6,14,6,4,-4,0,-2,-10,10,10,-6,6,6,6,-6,2,2,2,-14,0,-4,2,-6,----------------4,-4,-8,-4,4,8,0,-8,-2,-16,-20,-22,----------------4,-6,6,-8,-18,-10,-18,-20,-14,-12,0,-4,-6,6,-8,-18,-10,-18,-20,-14,-10,0,-4,-6,6,-8,-18,-10,-18,-20,-14,-12,-10,0,-4,-6,6,-8,-18,-10,-18,-20,-14,-12,-8,0,-4,-6,6,-8,-18,-10,-18,-20,-14,-12,-4,0,-4,-6,6,-8,-18,-10,-18,-20,-14,-10,-6,0,----------------4,-4,8,-6,10,6,16,14,14,-8,-4,-4,8,10,6,16,14,14,-6,-8,-4,-4,8,10,6,16,20,14,-6,22,-8,-4,-4,8,-6,10,6,16,20,14,22,-8,-4,-4,8,10,6,16,14,14,-6,-8,-4,-4,8,-6,10,6,16,14,14,-8,-4,0,10,-2,-22,2,4,-2,-2,-22,14,4,6,-4,-4,-4,-6,8,10,6,16,14,14,-8,-4,0,10,-2,-22,-22,2,4,-2,-2,14,4,-4,4,-10,6,10,-16,-12,-24,-4,-8,-6,-26,-4,-4,8,10,6,16,20,14,-6,22,-8,-4,-6,-6,-4,-4,-6,8,6,-4,-2,0,6,---------------6,6,10,12,2,-10,-6,2,0,-4,0,10,-------------------------------4,-14,10,10,14,6,4,-2,-10,-4,12,14,-4,-12,-4,6,22,-6,12,-4,16,0,10,4,-4,0,-4,-6,-14,-16,-2,14,4,10,16,14,-4,4,-2,-8,2,6,0,-8,-8,-8,6,-16,----------------4,4,-10,-8,-18,-18,-12,-26,0,-2,-22,-8,----------------------------------------------4,0,2,6,-2,-4,-6,-6,6,-8,14,-4,0,2,6,-2,-4,-6,-6,6,-8,14,-4,-4,-8,-12,-8,4,-18,0,0,-12,-20,10,----------------4,-4,-4,4,10,10,2,12,12,4,6,14,---------------------------------------------------------------------------`

LWSS kit complete.
MWSS kit is half the way (actually more like 25%).

----

I'm running now the last layer of depth 12, without saving the recipe tree (as previous depth took 1.2G RAM with branching factor of 6.7 and only 8G this will suffocate my machine). Now on 20% hopefully after another 2.5 days of run we will get most of the kits.

EDIT Notice not all of them are valid edge shooters, only a large potion. Some of the options posted are invalid. I've used python script to parse and filter the edge shooters. Those are just the results, they have a bit of junk.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

HWSS-less SL->Glider converters (3-4 SLs).

`x = 339, y = 266, rule = LifeHistory130.2C\$129.3C\$129.2C.C\$130.3C\$131.C30\$138.2C\$137.3C\$137.2C.C\$138.3C\$139.C6\$157.C.C\$160.C\$156.C3.C\$160.C\$157.C2.C\$158.3C8\$154.C.C\$157.C\$157.C\$149.2C3.C2.C\$148.C.C4.3C\$150.C121\$216.C.C\$219.C\$215.C3.C\$219.C\$216.C2.C\$217.3C23\$222.C.C\$225.C\$225.C\$222.C2.C\$139.2C82.3C82.2C\$139.3C165.3C\$138.C.2C165.2C.C\$138.3C167.3C\$139.C169.C14\$75.2C\$75.3C\$74.C.2C\$74.3C\$75.C2\$.2C\$.3C\$C.2C\$3C\$.C2\$59.C.C\$58.C58.C.C\$58.C57.C\$58.C2.C54.C\$58.3C55.C2.C196.2C\$116.3C112.2C82.3C\$4.C.C223.3C82.2C.C\$3.C226.2C.C82.3C\$3.C227.3C83.C\$3.C2.C225.C\$3.3C\$18.C.C\$13.2C6.C53.C.C\$12.C2.C.C3.C48.2C6.C54.C.C\$13.C.C5.C47.C2.C.C3.C49.2C6.C198.C.C\$14.C3.C2.C48.C.C5.C48.C2.C.C3.C113.C.C77.2C6.C\$19.3C49.C3.C2.C49.C.C5.C108.2C6.C75.C2.C.C3.C\$76.3C50.C3.C2.C107.C2.C.C3.C76.C.C5.C\$134.3C108.C.C5.C77.C3.C2.C\$246.C3.C2.C82.3C\$251.3C!`

`x = 241, y = 637, rule = LifeHistory53\$41.2C\$40.3C\$40.2C.C\$41.3C\$42.C253\$141.C.C\$144.C\$144.C\$141.C2.C\$142.3C11\$106.2C\$105.3C\$105.2C.C\$106.3C\$107.C14\$114.C.C\$117.C\$117.C\$114.C2.C\$115.3C139\$73.C.C\$72.C\$72.C3.C\$72.C\$72.C2.C\$72.3C23\$67.C.C\$66.C\$66.C\$66.C2.C\$66.3C35\$59.2C\$59.3C\$58.C.2C\$58.3C\$59.C6\$39.C.C\$38.C6.2C\$38.C3.C.C2.C\$38.C5.C.C\$38.C2.C3.C\$38.3C!`

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

Attached are the results from depth 12 run:

LWSS full kit.
MWSS 6/8 are valid (8, 9, 10, 11, 12, 14).
HWSS 2/8 are valid (18, 19)

Another fuller run will finish in about two weeks - meanwhile there is a lot of motivation to find HWSS-less and LWSS emphasized recipes.For now it seems that LWSS + minimal number of MWSS should cost the same, and do the same job. There might be some "bottleneck" I currently miss (especially in the self destruct arena).
Attachments
results_depth11.txt_parsed.txt
WSSMonoSlowSalvoDepth12.rle

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

80% of Depth = 13 run, I think I'll not wait until the end, as it has most of what's needed - and the rest if required should be achieve with the timing adjustment trick.

LWSS: Full kit
MWSS: Full kit
HWSS: 5/8 (6/8 for most practical purposes)

16: Works only if the HWSS has it's own lane.
17: Valid
18: Valid
19: Valid
20: Missing
21: Valid
22: Missing
23: Valid
Attachments
WSS750K.zip
results_750000.txt_parsed.txt

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

simsim314 wrote:80% of Depth = 13 run, I think I'll not wait until the end, as it has most of what's needed - and the rest if required should be achieve with the timing adjustment trick.

Very nice collection! It would be nice to have all the HWSS timings, of course, but these recipes are all a very big improvement in efficiency over 3SL constructions -- might as well use some of the savings on timing-adjustment recipes, and get a complete toolkit that way.

Are you looking again at positive and negative even-step adjustable helices, that maybe aren't so heavy on HWSSes?

dvgrn
Moderator

Posts: 5620
Joined: May 17th, 2009, 11:00 pm

### Re: David Bell's engineless caterpillar idea revisited

dvgrn wrote:Are you looking again at positive and negative even-step adjustable helices, that maybe aren't so heavy on HWSSes?

Probably will. It's not such a problem to use HWSS as to use all HWSS states, and this is only due to heavy use of HWSS. Considering the fact I can choose at what relative step the down and up streams are, there is a lot of flexibility as long as HWSS are at least in 4/8 states. It's also worth mentioning that two HWSS in the same internal state is not an issue at all.

EDIT There is obvious reason to use more LWSS and less HWSS as the LWSS recipes are shorter and cleaner, meaning X1.5-X2 cost factor. Saying that 2 LWSS will cost probably more due to block movement involved as well. Anyway many of the recipes used HWSS assuming nothing wrong with them, sometimes even when LWSS could come instead. So yes replacing the recipes is a small holdback but worth it.

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

After totally HWSS-less 8 *WSS back reader, here is 9 *WSS single HWSS forward reader:

`x = 141, y = 266, rule = LifeHistory19\$62.3A\$57.C3.A2.A\$56.C.C5.A\$55.C2.C.A3.A\$56.2C6.A\$61.A.A8\$44.3A\$44.A2.A\$44.A\$44.A\$45.A.A17\$39.A\$38.3A\$38.A.2A\$39.3A\$39.2A6\$67.A\$66.3A\$66.A.2A\$67.3A\$67.2A60\$108.A\$107.3A\$106.2A.A\$106.3A\$106.3A\$107.2A2\$96.3A\$96.A2.A\$96.A\$96.A3.A\$96.A\$97.A.A12\$91.3A\$90.A2.A\$93.A\$89.A3.A\$93.A\$90.A.A63\$45.3A\$45.A2.A\$45.A\$45.A3.A\$45.A\$46.A.A4\$56.3A\$56.A2.A\$56.A\$56.A3.A\$56.A3.A\$56.A\$57.A.A!`

EDIT Glider + MWSS/LWSS options for self distruct:

`x = 336, y = 627, rule = LifeHistory168.C.C\$167.C\$167.C3.C\$167.C\$167.C2.C\$167.3C\$159.C\$C156.C.C\$.2C155.2C\$2C2\$317.C\$318.2C\$317.2C9\$9.3C\$9.C2.C\$9.C\$9.C\$10.C.C9\$169.C.C\$168.C\$168.C3.C\$168.C\$168.C2.C\$168.3C2\$326.3C\$326.C2.C\$326.C\$326.C3.C\$326.C\$327.C.C5\$158.C.C\$159.2C\$159.C33\$4.C\$5.C\$3.3C5\$318.C\$319.2C\$318.2C22\$327.3C\$327.C2.C\$327.C\$13.3C311.C3.C\$13.C2.C310.C\$13.C314.C.C\$13.C\$14.C.C34\$318.C\$316.C.C\$317.2C20\$13.C\$14.C\$12.3C12\$326.3C\$326.C2.C\$326.C\$326.C3.C\$326.C\$327.C.C9\$22.3C\$22.C2.C\$22.C\$22.C\$23.C.C31\$321.C\$319.C.C\$320.2C11\$329.3C\$329.C2.C\$329.C\$329.C3.C\$329.C\$330.C.C60\$321.C.C\$322.2C\$322.C42\$331.3C\$331.C2.C\$331.C\$331.C3.C\$331.C\$332.C.C55\$315.C.C\$316.2C\$316.C41\$325.3C\$325.C2.C\$325.C\$325.C3.C\$325.C\$326.C.C38\$314.C.C\$315.2C\$315.C33\$324.3C\$324.C2.C\$324.C\$324.C3.C\$324.C\$325.C.C34\$311.C\$312.C\$310.3C33\$320.3C\$320.C2.C\$320.C\$320.C3.C\$320.C\$321.C.C!`

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

### Re: David Bell's engineless caterpillar idea revisited

Fully adjustable front with self destruct, has single HWSS and 19 *WSS in total (posted step 96):

`x = 153, y = 571, rule = LifeHistory6.C\$5.C.C\$5.C.C\$6.C2\$.2C7.2C\$C2.C5.C2.C\$.2C7.2C2\$6.C\$5.C.C\$5.C.C\$6.C3\$9.3C\$9.C2.C\$9.C\$9.C3.C\$9.C\$10.C.C50\$62.3C\$62.C2.C\$62.C\$62.C\$63.C.C2\$54.3C\$53.C2.C\$56.C\$52.C3.C\$56.C\$53.C.C41\$6.C\$5.3C\$4.2C.C\$4.3C\$4.3C\$5.2C44\$96.C\$95.3C\$95.C.2C\$96.3C\$96.2C37\$68.3C\$68.C2.C\$68.C\$68.C3.C\$68.C\$69.C.C9\$133.C\$132.C.C\$132.C2.C\$133.2C50\$142.C\$141.3C\$140.2C.C\$140.3C\$140.3C\$141.2C28\$148.3C\$147.C2.C\$150.C\$150.C\$147.C.C39\$126.3C\$126.C2.C\$126.C\$126.C3.C\$126.C\$127.C.C8\$144.3C\$143.C2.C\$146.C\$146.C\$143.C.C17\$151.C\$150.3C\$149.2C.C\$149.3C\$150.2C6\$123.C\$122.3C\$121.2C.C\$121.3C\$122.2C43\$71.C\$70.3C\$70.C.2C\$71.3C\$71.2C13\$82.C\$81.3C\$81.C.2C\$82.3C\$82.3C\$82.2C2\$92.3C\$91.C2.C\$94.C\$90.C3.C\$94.C\$91.C.C12\$97.3C\$97.C2.C\$97.C\$97.C3.C\$97.C\$98.C.C36\$126.C\$125.3C\$125.C.2C\$126.3C\$126.2C23\$143.3C\$142.C2.C\$145.C\$141.C3.C\$145.C\$142.C.C4\$132.3C\$131.C2.C\$134.C\$130.C3.C\$130.C3.C\$134.C\$131.C.C!`

simsim314

Posts: 1685
Joined: February 10th, 2014, 1:27 pm

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