Home  •  LifeWiki  •  Forums  •  Download Golly

## 4 glider syntheses

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

### Re: 4 glider syntheses

15.1051 (xs15_69ak8zx1256) in six gliders:

`x = 13, y = 24, rule = B3/S232bo\$obo\$b2o3\$5bo\$6bo\$4b3o2\$4bo\$4b2o\$3bobo5\$7bo\$7b2o\$6bobo3bo\$10b2o\$11b2o\$4bo\$4b2o\$3bobo!`

gmc_nxtman

Posts: 1147
Joined: May 26th, 2015, 7:20 pm

### Re: 4 glider syntheses

A few more still lifes in 4 gliders:
xs24_4aab96z255d96
xs20_697ob96z0321
xs13_4aarzx123 (13.217)
xs14_o4s079cz01 (14.14)
xs13_354mp3 (13.213)
xs14_3560uic (14.283)
xs16_39e0ehr (16.138)

`x = 158, y = 211, rule = LifeHistory.A\$2.A151.A\$3A141.A9.A.A\$145.A8.2A\$143.3A\$147.2A\$146.2A\$148.A18\$136.2A\$135.A.A\$59.A77.A\$59.A.A\$59.2A9\$44.2A\$43.2A\$40.2A3.A\$41.2A\$40.A23\$59.A.A94.A\$59.2A93.2A\$60.A94.2A4\$132.A\$122.A.A7.2A\$123.2A6.A.A\$123.A11.3A\$135.A\$136.A13\$26.A.A2.2A\$27.2A.2A\$27.A4.A22\$28.2A\$29.2A\$28.A13\$37.A118.A\$38.A116.A\$36.3A116.3A12\$59.A\$58.A\$58.3A2\$59.A\$58.2A\$58.A.A15\$136.A.A\$137.2A\$137.A\$135.A\$135.2A\$134.A.A2\$31.2A\$32.2A\$31.A\$137.A\$136.2A\$136.A.A18\$16.A\$14.A.A\$15.2A4\$59.A\$59.A.A\$59.2A5\$40.2A\$39.2A\$36.2A3.A\$37.2A\$36.A!`
simeks

Posts: 369
Joined: March 11th, 2015, 12:03 pm
Location: Sweden

### Re: 4 glider syntheses

simeks wrote:A few more still lifes in 4 gliders:...

Great work simeks! Is this the result of a new search program? It does not fit with any search programs that I know of. Is the result here from the same program (if so it has a lot of versatility)?

Goldtiger997

Posts: 523
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 4 glider syntheses

Goldtiger997 wrote:
simeks wrote:A few more still lifes in 4 gliders:...

Great work simeks! Is this the result of a new search program? It does not fit with any search programs that I know of. Is the result here from the same program (if so it has a lot of versatility)?

Thanks! It's not really a search program, but as you correctly guessed, I got curious if that hive/longboat constellation you linked to could be built with 4 gliders.
I threw some code together in about an hour to look for a solution, and then I thought maybe I cound find some new still lifes synthesis with it... My GoLGrid library makes it pretty easy to write something like this, and to identify strict still lifes I already had some code I could borrow from this project.
simeks

Posts: 369
Joined: March 11th, 2015, 12:03 pm
Location: Sweden

### Re: 4 glider syntheses

simeks wrote:Thanks! It's not really a search program, but as you correctly guessed, I got curious if that hive/longboat constellation you linked to could be built with 4 gliders.
I threw some code together in about an hour to look for a solution, and then I thought maybe I cound find some new still lifes synthesis with it... My GoLGrid library makes it pretty easy to write something like this, and to identify strict still lifes I already had some code I could borrow from this project.

Nice work. Here's a thing you may want to try to find a 4-glider replacement using your code. It is the 5-white gliders dvgrn posted at the bottom of this post, and if it is reduced, the loafer synthesis will probably be reduced to 7 gliders!

Goldtiger997

Posts: 523
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 4 glider syntheses

47 new still-lifes synthesized with 4 gliders:

xs10_0cp3z32, 10.10, 5 -> 4
xs10_178ka4, 10.6, 5 -> 4
xs11_08o652z32, 11.32, 5 -> 4
xs11_178b52, 11.34, 5 -> 4
xs11_256o8go, 11.31, 6 -> 4
xs11_32132ac, 11.41, 6 -> 4
xs11_3586246, 11.45, 5 -> 4
xs12_0ggm96z32, 12.73, 5 -> 4
xs12_6530f9, 12.17, 6 -> 4
xs12_xg84213zca1, 12.31, 5 -> 4
xs13_321fgkc, 13.198, 5 -> 4
xs13_4a960ui, 13.27, 5 -> 4
xs13_g88m96z121, 13.154, 5 -> 4
xs13_wggm93z252, 13.66, 6 -> 4
xs14_08o6952z321, 14.583, 5 -> 4
xs14_0g8ob96z23, 14.483, 5 -> 4
xs14_31egm96, 14.161, 5 -> 4
xs14_69akgkczx1, 14.28, 5 -> 4
xs14_8ehjzw1074, 14.469, 5 -> 4
xs14_g4s079cz11, 14.592, 5 -> 4
xs15_0ggca96z1243, 15.971, 7 -> 4
xs15_0ggmp3z346, 15.625, 7 -> 4
xs15_0gilicz346, 15.558, 5 -> 4
xs15_25960uic, 15.118, 5 -> 4
xs15_3lk453z121, 15.472, 5 -> 4
xs15_69aczw6513, 15.550, 5 -> 4
xs15_69aczx3552, 15.970, 5 -> 4
xs15_69ak8zx1256, 15.1051, 8 -> 4
xs15_g8o6996z121, 15.864, 5 -> 4
xs16_08o0ehrz321, 16.1941, 5 -> 4
xs16_0g8o69a4z3421, 16.2765, 5 -> 4
xs16_259e0e952, 16.10, 5 -> 4
xs16_j1u06acz11, 16.728, 6 -> 4
xs17_2ege1ege2
xs17_2ege1t6zx11
xs17_39u0uiz023
xs17_3lk453z3421
xs18_3lk453z3443
xs18_0c88b96z2553
xs19_178jt069a4
xs19_6ikm9a4z3421
xs19_mlhe0e96z1
xs19_mlhe0eicz1
xs20_02596z6511d96
xs20_259mgmiczx66
xs20_69baa4ozw6511
xs24_259aczcid1d93

`x = 941, y = 443, rule = LifeHistory445.A\$443.2A\$444.2A6\$721.A.A\$412.A308.2A\$413.A308.A\$411.3A\$A906.A.A\$.2A904.2A\$2A906.A5\$125.A\$124.A195.A.A\$119.2A3.3A193.2A\$120.2A199.A\$119.A666.A\$426.A360.A\$426.A.A356.3A\$118.2A306.2A\$117.A.A\$119.A819.2A\$21.A.A284.3A627.A.A\$22.2A51.2A190.A40.A112.3A78.A244.A189.A\$22.A53.A189.A.A34.3A3.A113.A79.2A2.2A237.A.A41.A145.A\$27.A46.A92.2A97.2A37.A116.A32.A46.2A2.2A181.A56.A.A41.2A2.3A138.A\$27.A.A44.2A92.A2.A92.2A38.A54.2A.2A90.A.A51.A41.A.2A92.2A41.A.A55.A41.A.A2.A45.2A.2A89.A\$27.2A46.A92.A.A.A92.A94.A.A.A90.2A93.2A.3A90.A2.2A.A36.2A53.3A48.A43.A.A.A89.A\$73.A95.A.A91.A96.A2.A93.2A.A35.A59.A90.A.A.2A90.A95.2A2.A88.A\$73.2A95.A92.2A96.2A94.A.2A36.2A56.2A31.A59.A94.2A98.2A40.A46.2A\$496.2A91.2A4.A94.A192.A.A\$507.A80.2A3.A.A93.2A193.2A\$322.2A182.2A86.2A93.A.A\$321.2A183.A.A381.A\$323.A564.2A\$889.2A\$221.A368.3A\$211.3A5.2A371.A\$213.A6.2A369.A210.3A\$212.A589.A\$803.A\$107.2A109.2A\$108.2A108.A.A663.3A\$107.A110.A667.A\$885.A5\$31.2A687.2A\$31.A.A686.A.A\$31.A688.A\$233.3A\$233.A\$234.A364.2A\$599.A.A\$599.A38\$816.A.A\$816.2A\$817.A6\$214.A\$215.A\$213.3A\$100.A.A\$101.2A\$101.A2\$591.A\$592.A\$25.A.A562.3A\$26.2A577.A\$26.A576.2A\$604.2A\$518.A\$518.A.A168.A206.3A\$518.2A167.A.A201.3A2.A\$363.2A323.2A107.A43.2A50.A3.A\$19.A247.A51.A42.A.A93.2A94.2A240.A43.A.A49.A\$20.A245.A.A50.A.A40.A54.2A38.A2.A41.A51.A.A41.A144.A46.2A4.3A41.A97.2A\$18.3A3.A45.A.2A94.A97.A.A50.2A42.A54.2A37.A.A43.2A51.A39.A.A47.2A3.A90.A.A46.2A46.2A97.A\$23.A46.2A.A70.A.A20.A.A.2A91.2A.A92.3A54.A5.2A30.2A.A43.2A48.4A41.2A47.A.A.A.A89.A2.A.2A41.A50.2A92.2A.A.A\$23.3A47.A.2A59.A7.2A20.A2.A.A52.2A3.3A31.A2.A92.A62.2A32.A94.A.A94.A.A.A90.2A3.A92.A.A92.A2.2A\$73.A2.A59.A.A6.A21.2A2.A53.2A2.A33.A.A57.2A33.A.A63.A29.A.A94.A96.A2.A93.3A52.2A41.A90.A.A\$74.2A60.2A33.2A51.A5.A33.A58.A.A33.A94.2A94.2A97.2A94.A53.2A42.2A89.2A\$315.A7.A175.2A98.3A199.A\$314.2A182.A.A100.A294.A\$141.A172.A.A183.A99.A294.2A\$140.2A753.A.A\$140.A.A3\$424.2A267.2A\$395.2A26.2A269.2A202.2A\$396.2A27.A267.A204.A.A\$395.A502.A\$699.2A\$317.2A379.2A\$316.2A382.A\$318.A2\$201.2A282.2A211.3A\$202.2A282.2A210.A\$13.2A186.A283.A213.A\$12.A.A\$14.A43\$383.A\$381.A.A\$382.2A12\$688.A\$228.A.A455.A.A\$228.2A457.2A\$229.A2\$317.A567.A\$316.A569.2A\$316.3A566.2A\$122.2A578.A\$123.2A2.3A87.2A393.A89.A.A83.A\$11.A4.A105.A4.A88.A.A382.A8.2A84.2A4.2A82.2A\$9.A.A5.2A56.A52.A42.2A45.A47.A285.A46.A.A9.2A34.A47.A.A45.A43.2A\$10.2A4.2A56.A.A93.A.A50.A41.A.A129.A57.2A2.2A90.A.A46.2A44.A.A48.A44.A.A97.2A95.2A\$73.A2.A93.A51.2A42.A.A129.A56.A4.A90.A2.A41.A49.A2.A92.A2.A95.A2.A33.2A58.A.A\$73.3A95.A50.A.A43.A52.2A35.2A36.3A57.4A92.3A39.A.A50.3A50.2A41.2A.A41.A52.A2.A32.A.A58.A\$71.2A95.4A92.4A53.A.A33.A2.A.2A231.2A102.A.A43.A42.2A49.2A.2A35.A55.2A.A.A\$14.2A54.A2.A93.A95.A51.A5.A36.A.A.A.A91.2A96.3A92.3A49.A43.A.A39.A.A48.A.A42.3A50.A2.2A\$13.A.A55.A.A55.2A36.A.A93.A.A47.2A44.A2.A.A90.A.A95.A2.A92.A2.A93.A.A49.2A38.A.A42.A50.A.A\$15.A56.A55.2A38.2A94.2A48.2A46.2A92.A96.2A43.2A50.2A95.2A49.A.A38.A44.A49.2A\$121.3A6.A374.A.A91.2A197.A\$123.A372.A.A7.2A90.A\$122.A302.A71.2A7.A5.A\$317.2A104.2A72.A12.2A\$31.2A284.A.A98.A5.2A85.2A375.3A\$31.A.A170.A112.A101.2A467.A\$31.A172.2A212.2A469.A\$203.A.A4\$799.2A\$798.2A\$534.3A263.A\$534.A\$535.A54\$525.A\$525.A.A\$525.2A4\$15.A.A\$16.2A\$16.A2\$392.A397.A82.A.A\$390.A.A398.2A81.2A\$391.2A397.2A5.A76.A\$705.A89.2A\$107.A.A595.A.A88.2A\$108.2A595.2A93.A\$108.A690.A\$213.A201.3A381.3A\$214.2A199.A\$74.A138.2A93.A107.A230.2A2.2A90.2A2.2A93.2A\$73.A.A233.2A240.2A94.A4.A90.A4.A93.A.A57.A\$73.A2.A45.A139.2A44.2A100.2A46.2A40.2A4.2A43.A.A.2A47.2A42.4A92.4A91.A4.A55.2A\$71.2A.2A40.A4.A140.A.A.2A92.A42.2A6.2A41.2A.A2.A38.A.A3.2A46.A.A47.A.A233.5A57.2A28.2A.2A2.A\$70.A.A44.2A2.3A41.2A3.2A47.A.A42.A.A.A87.2A.A.A.2A39.2A4.A44.A.A.2A40.A5.A44.2A.A49.A42.2A94.2A186.A.A2.A.A\$69.A2.A43.2A46.A2.A.A2.A41.2A3.2A43.A2.2A88.A.A.A.A39.A51.A.A.A93.A.2A52.3A35.A2.A92.A2.A92.3A90.A2.A.A2.A\$69.A.A93.A.A.A.A43.2A3.A41.A.A46.3A43.A.A.A.A92.A2.A93.A55.A37.A.A93.A2.A91.A2.A48.A42.A.A2.2A\$70.A95.2A.2A43.A47.2A49.A44.A3.A94.2A93.2A56.A37.A95.2A93.2A47.2A44.2A\$312.A288.2A286.2A\$211.2A389.2A\$29.A182.2A387.A97.A\$24.A4.A.A179.A485.2A189.2A\$22.A.A4.2A667.2A188.A.A\$23.2A599.2A262.A\$41.2A68.3A509.2A\$41.A.A69.A511.A74.2A\$41.A70.A586.2A\$701.A8\$486.3A\$347.3A138.A\$347.A139.A\$348.A2\$293.2A\$294.2A\$293.A376.2A\$671.2A\$670.A12\$744.2A\$743.A.A\$745.A28\$408.A.A\$409.2A\$409.A9\$600.A.A\$214.A.A383.2A\$215.2A384.A\$215.A3\$203.A111.A.A\$204.2A109.2A330.2A\$203.2A111.A43.2A40.A243.A2.A\$74.A235.A48.A2.A40.2A49.2A95.2A94.A2.A\$19.2A49.2A.A.A145.A.A85.A50.A.A39.2A49.A2.A.2A90.A.3A93.3A\$18.A.A49.A.2A2.A89.2A3.A50.2A3.2A33.2A45.3A49.A92.A.A.A.A89.A4.A\$20.A53.2A89.A2.A.A.A49.A3.2A33.A2.A.2A187.A4.A43.A46.4A.A91.5A\$24.3A44.3A91.2A.A.A.A55.A32.2A.A.A.A90.5A92.4A45.2A49.A90.A4.A\$24.A6.2A37.A2.A94.A.2A92.A.A.A89.A5.A40.3A96.2A47.3A90.A.A.A\$25.A5.A.A36.A.A92.3A93.3A3.A90.2A2.A.A42.A48.2A37.A.A54.A41.2A50.A.A.2A\$31.A39.A93.A95.A49.3A48.2A42.A49.2A38.2A12.A41.2A39.2A5.2A45.A\$121.A4.2A183.A184.A12.A85.A4.A.A\$116.A4.A.A2.A.A183.A196.3A77.2A9.A\$23.3A88.A.A4.2A3.A192.2A267.A.A\$25.A84.A4.2A201.2A270.A\$24.A83.A.A209.A\$109.2A7\$522.2A\$521.2A\$523.A5\$437.3A\$437.A\$438.A!`
simeks

Posts: 369
Joined: March 11th, 2015, 12:03 pm
Location: Sweden

### Re: 4 glider syntheses

simeks wrote:47 new still-lifes synthesized with 4 gliders

Very impressive! I especially like the twin hat synthesis.

I presume that you are finding these by enumerating subsets of 4-glider syntheses. If that's so, are you also finding any new 5-glider syntheses in which 4 gliders form an object and some debris with a fifth glider for cleanup?

I noticed that almost all of these syntheses involve a single glider crashing into a 3-glider collision. One, however, involves the collision of two 2-glider collisions. Is this just a fluke, or are you testing both types of collisions?
-Matthias Merzenich
Sokwe
Moderator

Posts: 1473
Joined: July 9th, 2009, 2:44 pm

### Re: 4 glider syntheses

Sokwe wrote:I presume that you are finding these by enumerating subsets of 4-glider syntheses.

It's a very simple search that ducks the complications of enumerating collisions correctly: It just places 4 gliders, each within one of the boxes below picked at random, at random coordinates and phases, but each headed towards the center.

The sizes shown below are the actual sizes of the boxes used for this search - 64 lanes wide and 160 generations deep:

Then it just runs the pattern until it stabilizes and checks if the result is a single strict still-life. It also imports a list of previously known still-lifes that don't need to be reported as results.

`x = 198, y = 198, rule = LifeHistory33.D130.D\$32.3D128.3D\$31.5D126.5D\$30.7D124.7D\$29.9D122.9D\$28.11D120.11D\$27.13D118.13D\$26.15D116.15D\$25.17D114.17D\$24.19D112.19D\$23.21D110.21D\$22.23D108.23D\$21.25D106.25D\$20.27D104.27D\$19.29D102.29D\$18.31D100.31D\$17.33D98.33D\$16.35D96.35D\$15.37D94.37D\$14.39D92.39D\$13.41D90.41D\$12.43D88.43D\$11.45D86.45D\$10.47D84.47D\$9.49D82.49D\$8.51D80.51D\$7.53D78.53D\$6.55D76.55D\$5.57D74.57D\$4.59D72.59D\$3.61D70.61D\$2.63D68.63D\$.65D66.65D\$67D64.67D\$.67D62.67D\$2.67D60.67D\$3.67D58.67D\$4.67D56.67D\$5.67D54.67D\$6.67D52.67D\$7.67D50.67D\$8.67D48.67D\$9.65D50.65D\$10.63D52.63D\$11.61D54.61D\$12.52DCDC4D56.59D\$13.52D2C3D58.57D\$14.51DC3D60.20DCDC32D\$15.53D62.19D2C32D\$16.51D64.19DC31D\$17.49D66.21DC27D\$18.47D68.20DCDC24D\$19.45D70.19D2C24D\$20.43D72.43D\$21.41D74.41D\$22.39D76.39D\$23.37D78.37D\$24.35D80.35D\$25.33D82.33D\$26.31D84.31D\$27.29D86.29D\$28.27D88.27D\$29.25D90.25D\$30.23D92.23D\$31.21D94.21D\$32.19D96.19D\$33.17D98.17D\$34.15D100.15D\$35.13D102.13D\$36.11D104.11D\$37.9D106.9D\$38.7D108.7D\$39.5D110.5D\$40.3D112.3D\$41.D114.D49\$41.D114.D\$40.3D112.3D\$39.5D110.5D\$38.7D108.7D\$37.9D106.9D\$36.11D104.11D\$35.13D102.13D\$34.15D100.15D\$33.17D98.17D\$32.19D96.19D\$31.21D94.21D\$30.23D92.23D\$29.25D90.25D\$28.27D88.27D\$27.29D86.29D\$26.31D84.31D\$25.33D82.33D\$24.35D80.35D\$23.37D78.37D\$22.39D76.39D\$21.41D74.41D\$20.43D72.43D\$19.45D70.45D\$18.47D68.47D\$17.49D66.49D\$16.51D64.51D\$15.53D62.53D\$14.55D60.55D\$13.57D58.57D\$12.59D56.59D\$11.61D54.61D\$10.63D52.63D\$9.65D50.65D\$8.67D48.67D\$7.67D50.67D\$6.67D52.67D\$5.67D54.67D\$4.67D56.67D\$3.67D58.67D\$2.67D60.67D\$.67D62.67D\$67D64.67D\$.65D66.65D\$2.63D68.63D\$3.61D70.61D\$4.59D72.59D\$5.57D74.57D\$6.55D76.55D\$7.53D78.53D\$8.51D80.51D\$9.49D82.49D\$10.47D84.47D\$11.45D86.45D\$12.43D88.43D\$13.41D90.41D\$14.39D92.39D\$15.3D3C31D94.37D\$16.4DC30D96.35D\$17.2DC30D98.33D\$18.31D100.31D\$19.29D102.29D\$20.27D104.27D\$21.25D106.25D\$22.23D108.23D\$23.21D110.21D\$24.19D112.19D\$25.17D114.17D\$26.15D116.15D\$27.13D118.13D\$28.11D120.11D\$29.9D122.9D\$30.7D124.7D\$31.5D126.5D\$32.3D128.3D\$33.D130.D!`

The search that found 47 new still-lifes repeated this about 130 billion times, which took 10 CPU days (150000 patterns/second).
It was also able to find 179 of the 186 still-lifes previously known to be synthesizable with 4 or less gliders.

Sokwe wrote:If that's so, are you also finding any new 5-glider syntheses in which 4 gliders form an object and some debris with a fifth glider for cleanup?

It would be easy to add this. And to look for oscillators, pseudo still-lifes, non-standard spaceships etc.

Sokwe wrote:I noticed that almost all of these syntheses involve a single glider crashing into a 3-glider collision. One, however, involves the collision of two 2-glider collisions. Is this just a fluke, or are you testing both types of collisions?

As I've described above, all possible types are tested within the limits of the boxes where gliders may be places. My guess is that previous searches haven't looked a lot for collisions where the last glider enters much later than the first three, so that those synthesis that remain to be discovered are mostly of that type.
simeks

Posts: 369
Joined: March 11th, 2015, 12:03 pm
Location: Sweden

### Re: 4 glider syntheses

You might want to not limit the results to stable objects. Ways of getting 4 gliders to result in an oscillator, especially one with a period greater than 2, would be worth knowing.
hkoenig

Posts: 92
Joined: June 20th, 2009, 11:40 am

### Re: 4 glider syntheses

hkoenig wrote:You might want to not limit the results to stable objects. Ways of getting 4 gliders to result in an oscillator, especially one with a period greater than 2, would be worth knowing.

simeks wrote:
Sokwe wrote:If that's so, are you also finding any new 5-glider syntheses in which 4 gliders form an object and some debris with a fifth glider for cleanup?

It would be easy to add this. And to look for oscillators, pseudo still-lifes, non-standard spaceships etc.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

BlinkerSpawn

Posts: 1876
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: 4 glider syntheses

simeks wrote:
Sokwe wrote:I presume that you are finding these by enumerating subsets of 4-glider syntheses.

It's a very simple search that ducks the complications of enumerating collisions correctly: It just places 4 gliders, each within one of the boxes below picked at random, at random coordinates and phases, but each headed towards the center.

The sizes shown below are the actual sizes of the boxes used for this search - 64 lanes wide and 160 generations deep:

Then it just runs the pattern until it stabilizes and checks if the result is a single strict still-life. It also imports a list of previously known still-lifes that don't need to be reported as results.

`x = 198, y = 198, rule = LifeHistory33.D130.D\$32.3D128.3D\$31.5D126.5D\$30.7D124.7D\$29.9D122.9D\$28.11D120.11D\$27.13D118.13D\$26.15D116.15D\$25.17D114.17D\$24.19D112.19D\$23.21D110.21D\$22.23D108.23D\$21.25D106.25D\$20.27D104.27D\$19.29D102.29D\$18.31D100.31D\$17.33D98.33D\$16.35D96.35D\$15.37D94.37D\$14.39D92.39D\$13.41D90.41D\$12.43D88.43D\$11.45D86.45D\$10.47D84.47D\$9.49D82.49D\$8.51D80.51D\$7.53D78.53D\$6.55D76.55D\$5.57D74.57D\$4.59D72.59D\$3.61D70.61D\$2.63D68.63D\$.65D66.65D\$67D64.67D\$.67D62.67D\$2.67D60.67D\$3.67D58.67D\$4.67D56.67D\$5.67D54.67D\$6.67D52.67D\$7.67D50.67D\$8.67D48.67D\$9.65D50.65D\$10.63D52.63D\$11.61D54.61D\$12.52DCDC4D56.59D\$13.52D2C3D58.57D\$14.51DC3D60.20DCDC32D\$15.53D62.19D2C32D\$16.51D64.19DC31D\$17.49D66.21DC27D\$18.47D68.20DCDC24D\$19.45D70.19D2C24D\$20.43D72.43D\$21.41D74.41D\$22.39D76.39D\$23.37D78.37D\$24.35D80.35D\$25.33D82.33D\$26.31D84.31D\$27.29D86.29D\$28.27D88.27D\$29.25D90.25D\$30.23D92.23D\$31.21D94.21D\$32.19D96.19D\$33.17D98.17D\$34.15D100.15D\$35.13D102.13D\$36.11D104.11D\$37.9D106.9D\$38.7D108.7D\$39.5D110.5D\$40.3D112.3D\$41.D114.D49\$41.D114.D\$40.3D112.3D\$39.5D110.5D\$38.7D108.7D\$37.9D106.9D\$36.11D104.11D\$35.13D102.13D\$34.15D100.15D\$33.17D98.17D\$32.19D96.19D\$31.21D94.21D\$30.23D92.23D\$29.25D90.25D\$28.27D88.27D\$27.29D86.29D\$26.31D84.31D\$25.33D82.33D\$24.35D80.35D\$23.37D78.37D\$22.39D76.39D\$21.41D74.41D\$20.43D72.43D\$19.45D70.45D\$18.47D68.47D\$17.49D66.49D\$16.51D64.51D\$15.53D62.53D\$14.55D60.55D\$13.57D58.57D\$12.59D56.59D\$11.61D54.61D\$10.63D52.63D\$9.65D50.65D\$8.67D48.67D\$7.67D50.67D\$6.67D52.67D\$5.67D54.67D\$4.67D56.67D\$3.67D58.67D\$2.67D60.67D\$.67D62.67D\$67D64.67D\$.65D66.65D\$2.63D68.63D\$3.61D70.61D\$4.59D72.59D\$5.57D74.57D\$6.55D76.55D\$7.53D78.53D\$8.51D80.51D\$9.49D82.49D\$10.47D84.47D\$11.45D86.45D\$12.43D88.43D\$13.41D90.41D\$14.39D92.39D\$15.3D3C31D94.37D\$16.4DC30D96.35D\$17.2DC30D98.33D\$18.31D100.31D\$19.29D102.29D\$20.27D104.27D\$21.25D106.25D\$22.23D108.23D\$23.21D110.21D\$24.19D112.19D\$25.17D114.17D\$26.15D116.15D\$27.13D118.13D\$28.11D120.11D\$29.9D122.9D\$30.7D124.7D\$31.5D126.5D\$32.3D128.3D\$33.D130.D!`

The search that found 47 new still-lifes repeated this about 130 billion times, which took 10 CPU days (150000 patterns/second).
It was also able to find 179 of the 186 still-lifes previously known to be synthesizable with 4 or less gliders.
...

This is great! 47 new still life-it's cool!
My SpaceBattle program works about as well.

For 4G synthesis more effectively attack 2G set by two gliders from all possible directions. Because 2G set limited (71) and many of them short-lived, this should dramatically reduce the amount of computation (at least one of the gliders must reacts with 2G).

Bob Shemyakin
BobShemyakin

Posts: 214
Joined: June 15th, 2014, 6:24 am

### Re: 4 glider syntheses

BobShemyakin wrote:For 4G synthesis more effectively attack 2G set by two gliders from all possible directions. Because 2G set limited (71) and many of them short-lived, this should dramatically reduce the amount of computation (at least one of the gliders must reacts with 2G).

Bob Shemyakin

The thing about simeks' program is that it doesn't need to discriminate between 2G + 2G or 2G + G + G or 3G + G collisions; it just places four gliders over and over and over and over.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

BlinkerSpawn

Posts: 1876
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: 4 glider syntheses

BlinkerSpawn wrote:The thing about simeks' program is that it doesn't need to discriminate between 2G + 2G or 2G + G + G or 3G + G collisions; it just places four gliders over and over and over and over.

I think what Bob was trying to get at is that, in most cases, four random gliders in a field will either produce a (posibly also trivial) interaction with 3 gliders with the 4th glider getting away, or two gilders will die or form a simple object/pseudo-object/constellation, and then the other two will hit that. The first cast would be better handled by eliminating it as a total waste of time, as would half of the second. The other half of the second would be better handled by doing two-glider collisions into small stable objects, since that object could be formed in many ways (i.e. two gliders with variable delays, in some cases multiple collisions, and in most cases, multiple input directions).
mniemiec

Posts: 1027
Joined: June 1st, 2013, 12:00 am

### Re: 4 glider syntheses

Alternate 4G synthesis of beehive and dock:

`x = 18, y = 19, rule = B3/S2316bo\$15bo\$15b3o6\$5bo\$6bo\$4b3o2\$4b3o\$4bo\$5bo2\$3o\$2bo\$bo!`

gmc_nxtman

Posts: 1147
Joined: May 26th, 2015, 7:20 pm

### Re: 4 glider syntheses

gmc_nxtman wrote:Alternate 4G synthesis of beehive and dock:

`x = 18, y = 19, rule = B3/S2316bo\$15bo\$15b3o6\$5bo\$6bo\$4b3o2\$4b3o\$4bo\$5bo2\$3o\$2bo\$bo!`

That doesn't look right. Can't that not be rewinded or am I seeing things?
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y

drc

Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

### Re: 4 glider syntheses

drc wrote:
gmc_nxtman wrote:Alternate 4G synthesis of beehive and dock:

`x = 18, y = 19, rule = B3/S2316bo\$15bo\$15b3o6\$5bo\$6bo\$4b3o2\$4b3o\$4bo\$5bo2\$3o\$2bo\$bo!`

That doesn't look right. Can't that not be rewinded or am I seeing things?

Correct; the center gliders would've interacted two generations previously.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

BlinkerSpawn

Posts: 1876
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: 4 glider syntheses

Ouch, that's such a simple mistake that I don't know how I missed it. However, it does allow for this component which can add a dock to a length-1 surface:

`x = 80, y = 19, rule = B3/S2340bo31bo\$41bo31bo\$39b3o29b3o2\$42bobo29bobo\$42b2o30b2o\$bo31bo9bo31bo\$obo14bo14bobo\$bo9bo5bobo13bo\$10bo6b2o46bo\$10b3o51bobo\$40bo24bo6bo\$17b2o21b2o30b2o\$11b3o2b2o21bobo29bobo\$11bo6bo\$12bo\$46b2o30b2o\$45b2o30b2o\$47bo31bo!`

gmc_nxtman

Posts: 1147
Joined: May 26th, 2015, 7:20 pm

### Re: 4 glider syntheses

simeks wrote:47 new still-lifes synthesized with 4 gliders:
...
`x = 941, y = 443, rule = LifeHistory445.A\$443.2A\$444.2A6\$721.A.A\$412.A308.2A\$413.A308.A\$411.3A\$A906.A.A\$.2A904.2A\$2A906.A5\$125.A\$124.A195.A.A\$119.2A3.3A193.2A\$120.2A199.A\$119.A666.A\$426.A360.A\$426.A.A356.3A\$118.2A306.2A\$117.A.A\$119.A819.2A\$21.A.A284.3A627.A.A\$22.2A51.2A190.A40.A112.3A78.A244.A189.A\$22.A53.A189.A.A34.3A3.A113.A79.2A2.2A237.A.A41.A145.A\$27.A46.A92.2A97.2A37.A116.A32.A46.2A2.2A181.A56.A.A41.2A2.3A138.A\$27.A.A44.2A92.A2.A92.2A38.A54.2A.2A90.A.A51.A41.A.2A92.2A41.A.A55.A41.A.A2.A45.2A.2A89.A\$27.2A46.A92.A.A.A92.A94.A.A.A90.2A93.2A.3A90.A2.2A.A36.2A53.3A48.A43.A.A.A89.A\$73.A95.A.A91.A96.A2.A93.2A.A35.A59.A90.A.A.2A90.A95.2A2.A88.A\$73.2A95.A92.2A96.2A94.A.2A36.2A56.2A31.A59.A94.2A98.2A40.A46.2A\$496.2A91.2A4.A94.A192.A.A\$507.A80.2A3.A.A93.2A193.2A\$322.2A182.2A86.2A93.A.A\$321.2A183.A.A381.A\$323.A564.2A\$889.2A\$221.A368.3A\$211.3A5.2A371.A\$213.A6.2A369.A210.3A\$212.A589.A\$803.A\$107.2A109.2A\$108.2A108.A.A663.3A\$107.A110.A667.A\$885.A5\$31.2A687.2A\$31.A.A686.A.A\$31.A688.A\$233.3A\$233.A\$234.A364.2A\$599.A.A\$599.A38\$816.A.A\$816.2A\$817.A6\$214.A\$215.A\$213.3A\$100.A.A\$101.2A\$101.A2\$591.A\$592.A\$25.A.A562.3A\$26.2A577.A\$26.A576.2A\$604.2A\$518.A\$518.A.A168.A206.3A\$518.2A167.A.A201.3A2.A\$363.2A323.2A107.A43.2A50.A3.A\$19.A247.A51.A42.A.A93.2A94.2A240.A43.A.A49.A\$20.A245.A.A50.A.A40.A54.2A38.A2.A41.A51.A.A41.A144.A46.2A4.3A41.A97.2A\$18.3A3.A45.A.2A94.A97.A.A50.2A42.A54.2A37.A.A43.2A51.A39.A.A47.2A3.A90.A.A46.2A46.2A97.A\$23.A46.2A.A70.A.A20.A.A.2A91.2A.A92.3A54.A5.2A30.2A.A43.2A48.4A41.2A47.A.A.A.A89.A2.A.2A41.A50.2A92.2A.A.A\$23.3A47.A.2A59.A7.2A20.A2.A.A52.2A3.3A31.A2.A92.A62.2A32.A94.A.A94.A.A.A90.2A3.A92.A.A92.A2.2A\$73.A2.A59.A.A6.A21.2A2.A53.2A2.A33.A.A57.2A33.A.A63.A29.A.A94.A96.A2.A93.3A52.2A41.A90.A.A\$74.2A60.2A33.2A51.A5.A33.A58.A.A33.A94.2A94.2A97.2A94.A53.2A42.2A89.2A\$315.A7.A175.2A98.3A199.A\$314.2A182.A.A100.A294.A\$141.A172.A.A183.A99.A294.2A\$140.2A753.A.A\$140.A.A3\$424.2A267.2A\$395.2A26.2A269.2A202.2A\$396.2A27.A267.A204.A.A\$395.A502.A\$699.2A\$317.2A379.2A\$316.2A382.A\$318.A2\$201.2A282.2A211.3A\$202.2A282.2A210.A\$13.2A186.A283.A213.A\$12.A.A\$14.A43\$383.A\$381.A.A\$382.2A12\$688.A\$228.A.A455.A.A\$228.2A457.2A\$229.A2\$317.A567.A\$316.A569.2A\$316.3A566.2A\$122.2A578.A\$123.2A2.3A87.2A393.A89.A.A83.A\$11.A4.A105.A4.A88.A.A382.A8.2A84.2A4.2A82.2A\$9.A.A5.2A56.A52.A42.2A45.A47.A285.A46.A.A9.2A34.A47.A.A45.A43.2A\$10.2A4.2A56.A.A93.A.A50.A41.A.A129.A57.2A2.2A90.A.A46.2A44.A.A48.A44.A.A97.2A95.2A\$73.A2.A93.A51.2A42.A.A129.A56.A4.A90.A2.A41.A49.A2.A92.A2.A95.A2.A33.2A58.A.A\$73.3A95.A50.A.A43.A52.2A35.2A36.3A57.4A92.3A39.A.A50.3A50.2A41.2A.A41.A52.A2.A32.A.A58.A\$71.2A95.4A92.4A53.A.A33.A2.A.2A231.2A102.A.A43.A42.2A49.2A.2A35.A55.2A.A.A\$14.2A54.A2.A93.A95.A51.A5.A36.A.A.A.A91.2A96.3A92.3A49.A43.A.A39.A.A48.A.A42.3A50.A2.2A\$13.A.A55.A.A55.2A36.A.A93.A.A47.2A44.A2.A.A90.A.A95.A2.A92.A2.A93.A.A49.2A38.A.A42.A50.A.A\$15.A56.A55.2A38.2A94.2A48.2A46.2A92.A96.2A43.2A50.2A95.2A49.A.A38.A44.A49.2A\$121.3A6.A374.A.A91.2A197.A\$123.A372.A.A7.2A90.A\$122.A302.A71.2A7.A5.A\$317.2A104.2A72.A12.2A\$31.2A284.A.A98.A5.2A85.2A375.3A\$31.A.A170.A112.A101.2A467.A\$31.A172.2A212.2A469.A\$203.A.A4\$799.2A\$798.2A\$534.3A263.A\$534.A\$535.A54\$525.A\$525.A.A\$525.2A4\$15.A.A\$16.2A\$16.A2\$392.A397.A82.A.A\$390.A.A398.2A81.2A\$391.2A397.2A5.A76.A\$705.A89.2A\$107.A.A595.A.A88.2A\$108.2A595.2A93.A\$108.A690.A\$213.A201.3A381.3A\$214.2A199.A\$74.A138.2A93.A107.A230.2A2.2A90.2A2.2A93.2A\$73.A.A233.2A240.2A94.A4.A90.A4.A93.A.A57.A\$73.A2.A45.A139.2A44.2A100.2A46.2A40.2A4.2A43.A.A.2A47.2A42.4A92.4A91.A4.A55.2A\$71.2A.2A40.A4.A140.A.A.2A92.A42.2A6.2A41.2A.A2.A38.A.A3.2A46.A.A47.A.A233.5A57.2A28.2A.2A2.A\$70.A.A44.2A2.3A41.2A3.2A47.A.A42.A.A.A87.2A.A.A.2A39.2A4.A44.A.A.2A40.A5.A44.2A.A49.A42.2A94.2A186.A.A2.A.A\$69.A2.A43.2A46.A2.A.A2.A41.2A3.2A43.A2.2A88.A.A.A.A39.A51.A.A.A93.A.2A52.3A35.A2.A92.A2.A92.3A90.A2.A.A2.A\$69.A.A93.A.A.A.A43.2A3.A41.A.A46.3A43.A.A.A.A92.A2.A93.A55.A37.A.A93.A2.A91.A2.A48.A42.A.A2.2A\$70.A95.2A.2A43.A47.2A49.A44.A3.A94.2A93.2A56.A37.A95.2A93.2A47.2A44.2A\$312.A288.2A286.2A\$211.2A389.2A\$29.A182.2A387.A97.A\$24.A4.A.A179.A485.2A189.2A\$22.A.A4.2A667.2A188.A.A\$23.2A599.2A262.A\$41.2A68.3A509.2A\$41.A.A69.A511.A74.2A\$41.A70.A586.2A\$701.A8\$486.3A\$347.3A138.A\$347.A139.A\$348.A2\$293.2A\$294.2A\$293.A376.2A\$671.2A\$670.A12\$744.2A\$743.A.A\$745.A28\$408.A.A\$409.2A\$409.A9\$600.A.A\$214.A.A383.2A\$215.2A384.A\$215.A3\$203.A111.A.A\$204.2A109.2A330.2A\$203.2A111.A43.2A40.A243.A2.A\$74.A235.A48.A2.A40.2A49.2A95.2A94.A2.A\$19.2A49.2A.A.A145.A.A85.A50.A.A39.2A49.A2.A.2A90.A.3A93.3A\$18.A.A49.A.2A2.A89.2A3.A50.2A3.2A33.2A45.3A49.A92.A.A.A.A89.A4.A\$20.A53.2A89.A2.A.A.A49.A3.2A33.A2.A.2A187.A4.A43.A46.4A.A91.5A\$24.3A44.3A91.2A.A.A.A55.A32.2A.A.A.A90.5A92.4A45.2A49.A90.A4.A\$24.A6.2A37.A2.A94.A.2A92.A.A.A89.A5.A40.3A96.2A47.3A90.A.A.A\$25.A5.A.A36.A.A92.3A93.3A3.A90.2A2.A.A42.A48.2A37.A.A54.A41.2A50.A.A.2A\$31.A39.A93.A95.A49.3A48.2A42.A49.2A38.2A12.A41.2A39.2A5.2A45.A\$121.A4.2A183.A184.A12.A85.A4.A.A\$116.A4.A.A2.A.A183.A196.3A77.2A9.A\$23.3A88.A.A4.2A3.A192.2A267.A.A\$25.A84.A4.2A201.2A270.A\$24.A83.A.A209.A\$109.2A7\$522.2A\$521.2A\$523.A5\$437.3A\$437.A\$438.A!`

Then something a little was 5G. Here are 3 new 5G:
`x = 64, y = 110, rule = B3/S23bo\$2bo\$3o9bobo\$12b2o\$13bo\$61b2o\$14bo47bo\$13bobo45bo\$12bo2bo45b2o\$13b2o42bob2o2bo\$57b2obobo\$61bo5\$4bo\$4b2o\$3bobo32\$obo\$b2o6bobo\$bo7b2o\$10bo2\$11bo\$10bobo\$10bo2bo\$11b2o3\$55bo\$55b3o\$58bo\$57bobo\$56bobo\$56b2o\$b3o\$3bo\$2bo31\$2bo\$obo\$b2o\$54bo\$8bo44bobo\$8bobo43bo\$8b2o4b2o39b3o\$4b2o7bo2bo40b3o\$5b2o6bobo44bo\$4bo9bo44b2o!`

Bob Shemyakin
BobShemyakin

Posts: 214
Joined: June 15th, 2014, 6:24 am

### Re: 4 glider syntheses

LifeWiki's did-you-know section wrote:Did you know that as of 15 August 2017 there are 223 different [strict] still lifes known to be constructible by colliding [at least] four gliders, but it is likely that this list is not complete?

Armed with my Shinjuku database, I wrote a little script to list all these still lifes (and other periodic patterns) synthable in (2, 3, 4) gliders as a mosaic. The results are shown below:
`#C 8 true objects cost 2 gliders:#C xp2_7#C xq4_153#C xs4_33#C xs5_253#C xs6_696#C xs7_178c#C xs7_2596#C xs8_6996#CLL state-numbering gollyx = 43, y = 461, rule = B3/S23o30bobo\$o31b2o\$o31bo4b2o\$36b2o\$38bo61\$3o35bo\$2bo35bobo\$bo32b2o2b2o\$33b2o\$35bo61\$2o30bobo2b3o\$2o31b2o2bo\$33bo4bo61\$b2o30bobo\$obo31b2o\$bo32bo3b3o\$38bo\$39bo61\$bo33bo\$obo30bobo\$obo31b2o\$bo\$37b2o\$36bobo\$38bo61\$2o38bo\$bo37bo\$bobo35b3o\$2b2o30bobo\$35b2o\$35bo61\$b2o33bo\$o2bo30bobo\$bobo31b2o\$2bo36b3o\$39bo\$40bo61\$b2o31bobo3b2o\$o2bo31b2o3bobo\$o2bo31bo4bo\$b2o!`

`#C 18 true objects cost 3 gliders:#C xp2_318c#C xp2_7e#C xp3_co9nas0san9oczgoldlo0oldlogz1047210127401#C xp15_4r4z4r4#C xq4_27dee6#C xq4_27deee6#C xq4_6frc#C xs4_252#C xs6_25a4#C xs6_356#C xs7_25ac#C xs8_25ak8#C xs8_69ic#C xs9_25ako#C xs9_4aar#C xs14_69bqic#C xs14_g88m952z121#C xs16_g88m996z1221#CLL state-numbering gollyx = 52, y = 1184, rule = B3/S232o32bo\$o34b2o3bo\$3bo30b2o3b2o5b3o\$2b2o35bobo4bo\$47bo61\$o35bo\$2o34bobo\$2o34b2o\$bo30bo\$33b2o\$32b2o\$40b3o\$40bo\$41bo61\$2b2o5b2o37bo\$3b2o3b2o37bo\$o2bobobobo2bo34b3o\$3ob2ob2ob3o\$bobobobobobo\$2b3o3b3o2\$2b3o3b3o\$bobobobobobo35bo\$3ob2ob2ob3o33bo\$o2bobobobo2bo33b3o\$3b2o3b2o\$2b2o5b2o32bo\$44b2o\$43b2o61\$bo37b2o\$bo36b2o\$obo32bo4bo\$bo31bobo\$bo32b2o\$bo\$bo\$obo33b3o\$bo34bo\$bo35bo61\$b2o37bo6bo\$2ob3o35bo3b2o\$b5o33b3o4b2o\$2b3o2\$36b3o\$38bo\$37bo61\$b2o34bo\$2ob4o31b2o\$b6o30b2o\$2b4o38b2o\$44bobo\$39b2o3bo\$39bobo\$39bo61\$b2o35bo\$3o35bobo\$2obo34b2o\$b3o\$2bo33bo\$34bobo\$35b2o\$39b2o\$40b2o\$39bo61\$bo31bobo\$obo31b2o\$bo32bo2\$37b2o\$36bobo3b2o\$38bo3bobo\$42bo61\$bo34bo\$obo31bobo\$bobo31b2o\$2bo38b2o\$40bobo\$42bo3\$42b3o\$42bo\$43bo61\$2o31bobo\$obo31b2o\$b2o31bo4\$42b3o\$38bo3bo\$38b2o3bo\$37bobo61\$bo34bo\$obo31bobo\$bobo31b2o\$2b2o35bo\$39b2o3bo\$38bobo2bo\$43b3o61\$bo33bo5bo\$obo33b2o2bo\$bobo31b2o3b3o\$2bobo\$3bo2\$40b2o\$41b2o\$40bo61\$bo40b2o\$obo33bo4b2o\$o2bo33b2o4bo\$bobo32b2o\$2bo2\$35b2o\$34b2o\$36bo61\$bo34bo\$obo34bo\$bobo31b3o\$2bobo\$3b2o\$43bo\$36b2o4bo\$37b2o3b3o\$36bo61\$3bo36b2o\$b3o30bobo3bobo\$o34b2o3bo\$b3o31bo\$3bo2\$41b3o\$41bo\$42bo61\$b2o35bo\$ob3o31bobo4bo\$o4bo31b2o3b2o\$b3obo36bobo\$3b2o2\$48b3o\$48bo\$49bo61\$4b2o41bo\$3bo2bo40bobo\$3bobo41b2o\$b2obo38bo\$o2bo33bobo3b2o\$obo35b2o2bobo\$bo36bo61\$4b2o33bo\$3bo2bo30bobo\$3bo2bo31b2o\$b2ob2o42bobo\$o2bo44b2o\$o2bo45bo\$b2o2\$49b2o\$50b2o\$49bo!`

`#C 225 true objects cost 4 gliders:#C xp2_2a54#C xp2_rhewehr#C xp8_gk2gb3z11#C xs6_39c#C xs6_bd#C xs7_3lo#C xs8_178k8#C xs8_31248c#C xs8_312ko#C xs8_32qk#C xs8_35ac#C xs8_3pm#C xs9_178kc#C xs9_178ko#C xs9_25a84c#C xs9_312453#C xs9_31ego#C xs9_g0g853z11#C xs10_0cp3z32#C xs10_0drz32#C xs10_0j96z32#C xs10_1784ko#C xs10_178ka4#C xs10_178kk8#C xs10_3215ac#C xs10_32qr#C xs10_3542ac#C xs10_358gkc#C xs10_35ako#C xs10_69ar#C xs10_g0s252z11#C xs10_g8o652z01#C xs10_ggka52z1#C xs10_xg853z321#C xs11_08o652z32#C xs11_17842ac#C xs11_178b52#C xs11_178jd#C xs11_178kic#C xs11_2530f9#C xs11_2560ui#C xs11_256o8go#C xs11_2ege13#C xs11_31461ac#C xs11_31eg84c#C xs11_32132ac#C xs11_3586246#C xs11_358gka4#C xs11_69lic#C xs11_g0s253z11#C xs11_g0s453z11#C xs11_g8ka52z11#C xs11_g8o652z11#C xs11_ggka53z1#C xs11_ggm952z1#C xs12_0g8ka52z121#C xs12_0g8o652z121#C xs12_0ggm96z32#C xs12_0ggs252z32#C xs12_178br#C xs12_178c453#C xs12_256o8a6#C xs12_2egm93#C xs12_2egm96#C xs12_31egma#C xs12_32qj4c#C xs12_330f96#C xs12_330fho#C xs12_3hu066#C xs12_641j4czx11#C xs12_6530f9#C xs12_6960ui#C xs12_69iczx113#C xs12_g8o653z11#C xs12_o4q552z01#C xs12_raar#C xs12_xg84213zca1#C xs13_08o696z321#C xs13_0g8ka53z23#C xs13_0ggm952z32#C xs13_0ggs253z32#C xs13_2530f96#C xs13_2530fho#C xs13_2560uic#C xs13_25960ui#C xs13_2eg6p3zx1#C xs13_31ege13#C xs13_31egma4#C xs13_31kmiczw1#C xs13_321fgkc#C xs13_32qb96#C xs13_354mp3#C xs13_356o8a6#C xs13_3hu06a4#C xs13_4a960ui#C xs13_4aarzx123#C xs13_69e0mq#C xs13_djozx352#C xs13_g88m96z121#C xs13_g8ge96z121#C xs13_wggm93z252#C xs14_08o0e96z321#C xs14_08o6952z321#C xs14_0g8421e8z1226#C xs14_0g8ob96z23#C xs14_0gbb8oz123#C xs14_1no3tg#C xs14_31egm93#C xs14_31egm96#C xs14_32qj4ko#C xs14_3560uic#C xs14_39e0e93#C xs14_39e0e96#C xs14_39e0eic#C xs14_3hu0696#C xs14_3hu0okc#C xs14_4a9m88gzx121#C xs14_6960uic#C xs14_6970796#C xs14_69akgkczx1#C xs14_69bo8a6#C xs14_69e0eic#C xs14_69f0f9#C xs14_69la4ozx11#C xs14_6is079c#C xs14_8ehjzw1074#C xs14_c88a53z33#C xs14_g4s079cz11#C xs14_g88b96z123#C xs14_g8o0e96z121#C xs14_g8o69a4z121#C xs14_j1u066z11#C xs14_j1u413z11#C xs14_mmge13z1#C xs14_o4id1e8z01#C xs14_o4s079cz01#C xs14_wggc453z643#C xs15_08o6996z321#C xs15_0at1acz321#C xs15_0g6picz343#C xs15_0ggca96z1243#C xs15_0ggmp3z346#C xs15_0gilicz346#C xs15_0j1u066z121#C xs15_178bqic#C xs15_25960uh3#C xs15_25960uic#C xs15_259e0e93#C xs15_259e0e96#C xs15_259e0eic#C xs15_259e0eio#C xs15_33gv1oo#C xs15_354cgc453#C xs15_3lk453z121#C xs15_3lkm96z01#C xs15_4a9b8oz033#C xs15_4a9raic#C xs15_65123qic#C xs15_65lmzx346#C xs15_69aczw6513#C xs15_69aczx3552#C xs15_69ak8zx1256#C xs15_69bojd#C xs15_bdgmiczw1#C xs15_g8o6996z121#C xs15_j1u06a4z11#C xs15_o4s3pmz01#C xs16_08o0ehrz321#C xs16_08o6hrz643#C xs16_0ca952z2553#C xs16_0g8o69a4z3421#C xs16_259aczx6513#C xs16_259e0e952#C xs16_2lla8cz1221#C xs16_39e0ehr#C xs16_3hu0uh3#C xs16_3lk453z321#C xs16_4a970sia4#C xs16_69960uic#C xs16_69bob96#C xs16_69e0ehr#C xs16_69egmiczx1#C xs16_69f0f96#C xs16_69is079c#C xs16_69is0si6#C xs16_69ngbr#C xs16_c4o0e96z321#C xs16_h7ob96z11#C xs16_j1u0696z11#C xs16_j1u06acz11#C xs17_03lkia4z643#C xs17_0ml2sgz3443#C xs17_2ege1ege2#C xs17_2ege1t6zx11#C xs17_39u0uiz023#C xs17_3lk453z1243#C xs17_3lk453z3421#C xs18_035a4oz69d11#C xs18_0c88b96z2553#C xs18_2egm9a4zx346#C xs18_3lk453z3443#C xs18_69baa4z653#C xs18_69is0si96#C xs18_8ehlmzw12452#C xs18_c4o0ehrz321#C xs18_gbbob96z11#C xs18_gs2ib96z1221#C xs18_rhe0ehr#C xs19_0ml1eoz34611#C xs19_178jt069a4#C xs19_69bo7pic#C xs19_6ikm9a4z3421#C xs19_mlhe0e96z1#C xs19_mlhe0eicz1#C xs20_02596z6511d96#C xs20_259mgmiczx66#C xs20_2egu1rq23#C xs20_2lligz122qq1#C xs20_3lkkl3z32w23#C xs20_697ob96z0321#C xs20_69baa4ozw6511#C xs20_ca9bqicz33#C xs22_69b88cz69d113#C xs24_259aczcid1d93#C xs24_4aab96z255d96#CLL state-numbering gollyx = 99, y = 16862, rule = B3/S232bo36bo\$2o37bobo7b3o\$2b2o31bo3b2o8bo\$bo34bo8b2o3bo\$34b3o7bobo\$46bo61\$2o4b2o32bo18bo\$obo2bobo30bobo18bobo\$2bo2bo33b2o18b2o\$obo2bobo35b2o10b2o\$2o4b2o34bobo10bobo\$44bo10bo61\$4b2o35bobo\$2bob2o31bo3b2o\$bo36bo3bo\$4bo31b3o\$2obo\$2o3\$50b3o\$50bo\$51bo2\$46b2o\$46bobo\$46bo61\$2o43bo\$o43bo\$2bo41b3o\$b2o32bo\$33bobo\$34b2o6b2o\$41b2o\$43bo3\$37b3o\$39bo\$38bo61\$2o30bobo\$o32b2o\$bo31bo\$2o35bobo\$37b2o3b2o\$38bo3bobo\$42bo2\$39b2o\$40b2o\$39bo61\$2o32bo\$o34bo\$bo31b3o9bo\$2bo41bo\$b2o41b3o2\$42bo\$41b2o\$34b3o4bobo\$36bo\$35bo61\$2o33bobo9bo\$bo34b2o7b2o\$bobo32bo9b2o\$2bobo\$3bo2\$38b3o5b3o\$40bo7bo\$39bo7bo61\$2o52bo\$obo51bobo\$3bobo48b2o\$4b2o4\$36bobo\$37b2o8bo\$37bo9bobo\$47b2o3\$47b2o\$46b2o\$48bo61\$2o48bo\$obo47bobo\$3bo46b2o\$4bo30bobo\$3b2o31b2o\$36bo2\$46bobo\$46b2o\$47bo3\$47b2o\$48b2o\$47bo61\$o33bobo14bo\$3o32b2o12b2o\$3bo31bo14b2o\$2bo\$2b2o3\$42b3o3bo\$44bo2b2o\$43bo3bobo61\$2o32bo\$obo32b2o\$bobo30b2o\$2b2o\$46bo\$45b2o6bo\$41bo3bobo4bo\$41b2o9b3o\$40bobo61\$2o31bobo\$obo31b2o6bobo\$2bo31bo7b2o\$bo41bo\$b2o2\$36b3o3b2o\$38bo2b2o\$37bo5bo61\$2o75bo\$bo76bo\$bob2o36bo34b3o\$2bobo35bo\$3bo36b3o37b3o\$35bobo42bo\$36b2o37b2o4bo\$36bo37bobo\$74bo\$73b2o61\$2o34bo\$bo35bo\$bobo31b3o\$2bobo35bobo\$3b2o35b2o\$41bo\$46b3o\$46bo\$47bo2\$43b2o\$42b2o\$44bo61\$bo44bo\$obo42bo\$bo2b2o39b3o\$2b2obo\$41b3o\$36bobo2bo\$37b2o3bo\$37bo\$41bo\$41b2o\$40bobo61\$2o2b2o31bo\$obo2bo32bo\$3b2o31b3o3\$50bo\$49bo\$44bobo2b3o\$44b2o\$45bo3\$45b2o\$44b2o\$46bo61\$2o33bobo\$obo33b2o4bo\$2bo33bo3b2o\$2bobo36b2o\$3b2o3\$37b2o6b3o\$36b2o7bo\$38bo7bo61\$4b2o30bo\$5bo31b2o\$4bo31b2o\$3bo\$obo43b2o\$2o39bo3b2o\$41b2o4bo\$40bobo2\$52b2o\$51b2o\$53bo61\$2b2o30bo\$3bo31b2o\$bo32b2o\$b2o\$2bo55bo\$o55b2o\$2o55b2o2\$60b2o\$60bobo\$60bo20\$76b3o\$76bo\$77bo61\$b2o31bo5bo\$2bo32bo2b2o\$bo31b3o3b2o\$b2o\$2bo39b2o\$o41bobo\$2o40bo6b2o\$49bobo\$49bo61\$b2o37bo\$bobo30bobo2bo\$3bo31b2o2b3o\$2bo32bo\$bo\$o\$2o2\$51b3o\$51bo\$52bo\$40b3o\$42bo\$41bo61\$2o45bo\$bo43b2o\$bob2o31bobo7b2o\$2bo2bo31b2o\$4b2o31bo3\$38b2o\$39b2o3b2o\$38bo4b2o\$45bo61\$2o34bo\$bo2bo32b2o\$bobobo30b2o\$2bobo\$3bo\$37b2o\$37bobo3bo\$37bo4b2o\$42bobo9\$64b2o\$64bobo\$64bo61\$2o34bo\$bo35b2o\$bob2o31b2o\$2bo2bo\$3b2o3\$56bo\$50b3o2b2o\$52bo2bobo\$51bo7\$56b3o\$56bo\$57bo61\$ob2o46bo\$2o2bo32bo3bobo5bo\$3bobo32bo2b2o6b3o\$4b2o30b3o3bo8\$40b2o\$39bobo\$41bo61\$o2bo39bo\$4o37b2o\$42b2o\$2b2o42bobo\$2b2o42b2o\$47bo\$36bo\$34bobo\$35b2o\$39b2o\$38bobo\$40bo61\$2o43bo\$o2b2o39bo\$b2o2bo38b3o\$4b2o\$36bo\$37b2o\$36b2o3\$37b2o\$38b2o\$37bo3\$54b3o\$54bo\$55bo61\$2o41bo\$o40b2o\$bo2b2o30bobo3b2o\$2bo2bo31b2o\$3b2o32bo\$44bo\$43b2o\$43bobo5\$47b2o\$46b2o\$48bo61\$2o35bo\$obo32bobo3bobo\$bobo32b2o3b2o5bo\$2bobo37bo3b2o\$3b2o42b2o2\$36b2o\$37b2o\$36bo61\$bobo30bo\$ob2o31b2o\$o33b2o\$b3o\$3bo37bo\$40bo\$40b3o2\$45b2o\$44b2o\$37b3o6bo\$39bo\$38bo61\$4bo39bo\$3bobo32bo4bo\$2bobo31bobo4b3o\$2bo34b2o\$obo\$2o\$44bo4b2o\$44b2o2b2o\$43bobo4bo61\$4bo31bobo\$3bobo31b2o\$3b2o32bo\$b2o44bobo\$obo44b2o\$bo46bo2\$41b2o\$42b2o3b2o\$41bo4b2o\$48bo61\$4bo33bo\$3bobo30bobo\$2bobo32b2o\$3bo37b3o3bo\$3o40bo2bo\$o41bo3b3o3\$41b2o\$40bobo\$42bo61\$5b2o30bobo\$6bo31b2o5bo\$5bo32bo6bobo\$4bo40b2o\$3bo\$obo\$2o45b2o\$46b2o\$48bo4\$50b2o\$49b2o\$51bo61\$4bo54bo\$3bobo52bo\$3b2o53b3o\$b2o\$2bo\$o\$2o5\$43bo\$43bobo\$43b2o2\$37bo\$38bo6b2o\$36b3o5b2o\$46bo61\$2o37bo\$bo2b2o31bobo8b3o\$bobo2bo31b2o8bo\$2bo2b2o37b2o3bo\$43bobo\$45bo5\$40b2o\$41b2o\$40bo61\$2ob2o50bo\$bobobo48bo\$bo2bo49b3o\$2b2o6\$36bobo\$37b2o\$37bo3bobo\$41b2o\$42bo6\$53b2o\$53bobo\$53bo61\$2ob2o71bo\$bobo70b2o\$bo2bo70b2o\$2bobo\$3bo2\$35bobo\$36b2o\$36bo19\$59bo\$53b3o2b2o\$55bo2bobo\$54bo61\$2o78bo\$bo2bo75bobo\$bobobo36bo37b2o\$2bo2bo35bo\$3b2o36b3o39b3o\$36bobo44bo\$37b2o37b2o6bo\$37bo37bobo\$75bo\$74b2o61\$b2ob2o40bo\$obobo39b2o\$bo2bo40b2o\$4b2o4\$46b2o\$36bobo7bobo\$37b2o2bobo2bo\$37bo3b2o\$42bo61\$bo42bo\$obob2o36b2o\$b2obo38b2o\$4bo\$4b2o3\$41b3o\$36bobo2bo5b2o\$37b2o3bo3b2o\$37bo10bo61\$bo67bobo\$obo66b2o\$b2o67bo\$3b2obo\$3bob2o5\$39bo\$37bobo\$38b2o12\$52bo\$51bo\$51b3o3\$48b2o\$47bobo\$49bo61\$4b2o32bo\$2obobo30bobo\$bobo33b2o6bo\$bobo40bo\$2bo41b3o2\$40b3o\$42bo\$41bo2\$53b3o\$53bo\$54bo61\$2o2bo54bobo\$o2bobo53b2o\$2b2o2bo53bo\$5b2o4\$51bo\$37bobo11bobo\$38b2o2bobo6b2o\$38bo3b2o\$43bo61\$2o35bo\$obo35b2o2bobo\$2bo2b2o30b2o3b2o\$2bobobo36bo\$3bo6\$39b2o\$40b2o\$39bo6\$58b2o\$57b2o\$59bo61\$ob2o35bo\$2ob3o31bobo\$6bo31b2o\$5b2o40b3o\$47bo\$48bo2\$38bo\$39bob3o\$37b3obo\$42bo61\$2o35bo\$o2b2obo31b2o\$bobob2o30b2o\$2bo\$60b2o\$59b2o\$61bo\$56bo\$56b2o\$55bobo\$60b3o\$60bo\$61bo61\$2o37bo\$o4bo31bobo\$bo2bobo31b2o\$2bo2bo37bo\$3b2o36b2o6bo\$42b2o4bo\$48b3o4\$41b3o\$43bo\$42bo61\$b2o33bo\$o2bo33bo\$obobo30b3o14bo\$bo2bo39b3o4bo\$2b2o42bo4b3o\$45bo2\$47b3o\$47bo\$48bo61\$4b2o33bobo\$3bobo33b2o\$2bobo35bo\$2bo\$obo35bo\$2o34bobo\$37b2o3\$46bobo\$36bo9b2o\$37b2o8bo\$36b2o61\$4b2o36bo\$5bo35bo\$2b3o36b3o\$2bo33bobo\$obo34b2o43b2o\$2o35bo43bobo\$75bo5bo\$76bo3b2o\$74b3o4\$76b2o\$77b2o\$76bo61\$4bo49bo\$3bobo48bobo\$2bobo31bobo15b2o\$bobo33b2o8bo\$obo34bo9bobo\$2o45b2o3\$47b2o\$46b2o\$48bo61\$4bo46bo\$3bobo32bo3bobo4b2o\$3b2o31bobo3b2o6b2o\$b2o34b2o4bo\$obo\$2o2\$38b3o\$38bo\$39bo61\$4b2o30bobo\$3bobo31b2o\$2bobo32bo\$3bo\$3o\$o2\$42bo\$40b2o\$41b2o2\$44b2o\$44bobo\$44bo4b3o\$49bo\$50bo61\$3b2o43bo\$2bo2bo32bo7b2o\$2bobo31bobo8b2o\$3bo33b2o\$3o\$o42bo3b2o\$42b2o3bobo\$42bobo2bo61\$5bo37bo\$4bobo35b2o\$3bobo31bobo2bobo\$2bobo33b2o8b2o\$bobo34bo9bobo\$obo45bo\$bo7\$56bo\$55b2o\$55bobo61\$5bo33bo\$4bobo30bobo\$4b2o32b2o\$2b2o\$bobo38b3o\$obo39bo\$bo41bo5\$39b2o\$39bobo\$39bo19b2o\$59bobo\$59bo61\$4bo80bo\$3bobo78bo\$3bobo30bobo45b3o\$4bo32b2o\$b3o33bo\$o\$2o26\$56bo\$57bo2bobo\$55b3o2b2o\$61bo61\$5bo37bo\$4bobo35bo\$3bobo36b3o\$3bo33bobo36bo\$b3o34b2o37bo4b2o\$o37bo36b3o3bobo\$2o79bo\$80b2o2\$76b2o\$77b2o\$76bo61\$2ob2o30bo\$bob2o31b2o\$bo33b2o\$2b3o\$4bo7\$56bo\$45bo8b2o\$45bobo7b2o\$45b2o3\$46b2o\$45b2o\$47bo61\$2o3b2o30bo\$bo4bo31b2o8b2o\$bob3o31b2o9bobo\$2b2o44bo3\$45b3o\$47bo\$46bo7\$53b2o\$53bobo\$53bo61\$bo66bobo\$obo2b2o61b2o\$b2o3bo62bo\$3b3o\$3bo10\$43bo\$37bobo2bo\$38b2o2b3o\$38bo12\$66b2o\$66bobo\$66bo61\$4b2o48bo\$2obobo48bobo\$bobo50b2o\$bo2bo\$2b2o47bo\$49b2o\$50b2o5\$36bobo\$37b2o\$37bo3bobo\$41b2o\$42bo61\$4bo33bo\$2obobo30bobo7bo\$bobobo31b2o5b2o\$bo2bo40b2o\$2b2o4\$38bo4bo\$38b2o2b2o\$37bobo2bobo61\$2o54bo\$obob2o48b2o\$2bobo50b2o\$2bo2bo\$3b2o33bo\$36bobo\$37b2o2\$47b2o\$47bobo\$47bo3\$44b3o\$46bo\$45bo61\$o2bo32bobo\$4o33b2o\$4b2o31bo\$2bo2bo\$2b2o2\$42bo\$40b2o\$41b2o2\$44b2o9b3o\$44bobo8bo\$44bo11bo61\$2ob2o44bo\$2obobo30bobo8b2o\$3bobo31b2o9b2o\$3b2o32bo2\$46bo\$46b2o\$45bobo2\$38b2o\$37bobo\$39bo61\$2ob2o31bobo\$2obo33b2o\$3bo33bo\$3bobo48bo\$4b2o47bo\$53b3o3\$40b3o\$42bo3bo\$41bo3b2o\$45bobo61\$2o44bo\$obob2o39bo\$2bob2o31bo7b3o\$2bo35bo\$b2o33b3o4\$42bo\$36bobo2bo\$37b2o2b3o\$37bo61\$2b2o34bo\$o2bo32bobo\$2o2b2o31b2o\$5bo\$3bo\$3b2o5\$39b3o\$41bo3bo\$40bo3b2o\$44bobo3\$52b3o\$52bo\$53bo61\$b2ob2o32bo\$obobo31bobo\$2o2bo32b2o\$4b2o\$46bo\$44b2o\$45b2o3\$45b2o\$45bobo\$45bo6\$58b2o\$58bobo\$58bo61\$bo46bo\$obob2o41bo\$obobo42b3o\$bo2bo33bo\$4b2o30bobo\$37b2o\$41b2o\$40bobo\$42bo2\$53b2o\$52b2o\$54bo61\$bo46bo\$obo43b2o\$o2bo43b2o\$bobo38bo\$2bo38bo\$3b3o35b3o\$5bo30bobo\$37b2o\$37bo2\$49b2o\$48b2o\$50bo61\$4b2o32bo3bobo4b2o\$3bobo30bobo3b2o5bobo\$3b2o32b2o4bo5bo\$b2o\$obo\$2o\$38b3o\$38bo\$39bo61\$3b2o31bo8bo\$2bo2bo31b2o6bobo\$bob2o31b2o7b2o\$obo\$obo\$bo45b2o\$46b2o\$48bo5\$49bo\$48b2o\$48bobo61\$o2bo41bo\$4o30bobo7bo\$35b2o7b3o\$4o31bo\$o2bo2\$36b2o\$37b2o\$36bo\$43b2o\$42b2o\$44bo61\$7b2o31bo8bo\$6bobo32bo7bobo\$5bo33b3o3b2o2b2o\$4bo39b2o\$3bo42bo\$2bo\$bo\$o\$2o12\$74bo\$73b2o\$73bobo61\$4bo32bo\$3bobo32b2o\$3bobo31b2o4bo\$b2obo37bo\$2bo39b3o\$obo\$2o34b3o\$36bo\$37bo2\$50b2o\$49b2o\$51bo61\$5b2o36bo39bo\$4bobo35bo38b2o\$3bobo36b3o37b2o\$2bobo32bobo\$bobo34b2o37b2o\$bo36bo37bobo3b2o\$2o74bo4bobo\$75b2o6bo61\$4b2o31bobo\$3bo2bo31b2o\$3bobo32bo3bobo\$4bo37b2o\$b3o39bo\$o47bo\$2o45b2o\$47bobo2\$41b3o\$43bo\$42bo61\$5b2o30bobo\$4bobo31b2o\$3bobo32bo\$3bo\$b3o\$o\$2o38b2o\$39bobo3bobo\$41bo3b2o\$46bo7\$58bo\$57b2o\$57bobo61\$b2ob2o44bo\$obobobo42bo\$bo2bobo42b3o\$4b2o4\$37bobo2bobo\$38b2o2b2o\$38bo4bo4\$44bo\$43b2o\$43bobo61\$b2ob2o36bobo4bo\$obobo37b2o5bobo\$bo2bo38bo5b2o\$4bobo\$5b2o\$37bo5bo\$38b2o2b2o\$37b2o3bobo61\$bo36bo\$obob2o33bo\$b2obobo30b3o\$4bobo37bo\$4b2o37bo\$43b3o3\$48b3o\$43b3o2bo\$45bo3bo\$44bo61\$b2o44bobo\$o2bob2o35bo4b2o\$bobobo36bobo3bo\$2bo2bo36b2o\$5b2o31bo\$39bo\$37b3o2b2o\$43b2o\$42bo61\$4b2o42bo\$2obobo40b2o\$bobo33bo9b2o\$bo2bo33bo\$2bobo31b3o\$3bo43b2o\$47bobo\$47bo6\$51b3o\$51bo\$52bo61\$2o3b2o44bobo\$obobobo30bo8bo4b2o\$2bobo33b2o4b2o6bo\$2bobo32b2o6b2o\$3bo2\$44bo\$44b2o\$43bobo61\$2o35bobo\$obob2o32b2o\$2bobobo31bo\$2bo2bo\$3b2o\$53bo\$53bobo\$53b2o4\$50b2o\$51b2o\$50bo4b2o\$55bobo\$55bo61\$2o38bo\$o2b2o35bobo\$2b2obo34b2o\$5bo39bo\$2b3o33bo5bo\$2bo33bobo5b3o\$37b2o2\$41bo\$40b2o\$40bobo61\$ob2o33bobo\$2obo34b2o\$3bob2o31bo\$3bo2bo\$4b2o\$63bo\$61b2o\$62b2o3\$60b2o\$59b2o\$61bo9bo\$70bo\$70b3o61\$o2b2o33bo\$4obo30bobo4bo\$5bo31b2o4b2o4bo\$2b3o37bobo2b2o\$2bo45b2o3\$52b3o\$52bo\$53bo61\$2o2b2o32bo\$o2bobo30bobo\$b3o33b2o\$4bo\$3b2o3\$43bo\$41b2o\$42b2o3\$38b3o\$40bo\$39bo5\$62b2o\$62bobo\$62bo61\$2o44bo\$obo2b2o37b2o\$b2o3bo38b2o\$3b3o33bo\$3bo33bobo\$38b2o2\$41b3o\$43bo8b3o\$42bo9bo\$53bo61\$2o35bobo\$obob2o32b2o\$2bobobo31bo\$2bo2bo\$b2o54bo\$56bo\$56b3o\$46b2o\$47b2o\$46bo7b2o\$54bobo\$54bo61\$2bo34bo\$bobob2o31b2o\$o2bobo31b2o\$b2o2bo\$5b2o13\$79bo\$70bo6b2o\$69bo8b2o\$69b3o\$74b2o\$73b2o\$75bo61\$3bo32bo\$b3o33b2o\$o35b2o\$b3o\$3bo\$3bobo73bo\$4b2o72bo\$78b3o21\$60bo\$60b2o2b3o\$59bobo2bo\$65bo61\$bo49bo\$obob2o44bo\$obobo45b3o\$b2o2bo\$4b2o39bo\$45bobo\$45b2o3\$47b2o\$38bo7b2o\$36bobo9bo\$37b2o61\$2o34bobo9bo\$bo35b2o9bobo\$o36bo10b2o\$obo\$b2o\$3b2o39b3o\$3bobo40bo\$4bo40bo8\$56b2o\$56bobo\$56bo61\$4bo70bo\$3bobo69bobo\$3bobo69b2o\$b2obo\$o2bo\$obo\$bo6\$36bo\$37b2o\$36b2o9\$56bo\$56bobo\$56b2o3\$56b2o\$55b2o\$57bo61\$4bo51bo\$3bobo49bo\$3bobo49b3o\$bob2o\$obo\$obo\$bo5\$36bo\$37b2o\$36b2o\$46bo\$40b2o3b2o\$41b2o2bobo\$40bo61\$5b2o34bo\$4bobo33bo\$4bo35b3o\$5bo\$2b3o33bo\$bo37bo\$obo34b3o\$bo52bobo\$54b2o\$44bo10bo\$42b2o\$43b2o61\$5bo31bobo\$4bobo31b2o3bo\$4bobo31bo4bobo\$b2ob2o37b2o\$2bo\$obo\$2o43b2o\$39b3o2b2o\$41bo4bo\$40bo61\$4b2o59bobo\$3bo2bo30bobo25b2o\$3bobo32b2o26bo\$b2obo33bo\$2bo\$obo\$2o6\$38bobo\$39b2o\$39bo3bobo\$43b2o\$44bo61\$5bo32bobo\$4bobo32b2o\$3bo2bo32bo\$2bo3b2o\$bo\$o\$b3o\$3bo3\$42b3o\$44bo3bo\$43bo3b2o\$47bobo4\$56b2o\$55b2o\$57bo61\$4b2o33bo\$4bobo30bobo\$6bo31b2o\$2b4o\$bobo\$bo51bo\$2o49b2o\$52b2o2\$55b2o\$55bobo\$55bo14\$69b2o\$68b2o\$70bo61\$2b2o36bo\$2b2o36bobo2bo\$40b2o3bobo\$2b4o30bo8b2o\$bo3bo31b2o\$obo33b2o\$b2o\$42b2o\$41b2o\$43bo61\$2ob2o45bo\$bobo46bobo\$bo2bo33bo11b2o\$2bobo31bobo15b2o\$b2ob2o31b2o15bobo\$41b2o11bo\$40bobo\$42bo61\$2o3b2o31bo10bo\$obobobo32b2o7bo\$2bobo33b2o8b3o\$2bo2bo\$3b2o\$39bo4bo\$37bobo3b2o\$38b2o3bobo61\$2o3bo47bo\$obobobo45bo\$2bobobo45b3o\$2bo2bo\$3b2o3\$42bo\$42bobo\$38bo3b2o\$39bo\$37b3o2\$50b2o\$49b2o\$51bo61\$o2bo39b2o\$4o40b2o\$4b2o37bo\$2bo3bo30bobo\$2b2ob2o31b2o6b3o\$38bo7bo\$47bo5\$42b2o\$41b2o\$43bo61\$2o35bobo\$obob2o32b2o\$b2obobo31bo\$4bobo\$4b2o2\$72bo\$62b2o6b2o\$61b2o8b2o\$57b2o4bo\$56bobo\$58bo61\$2o3b2o32bo13bo\$obobobo30bobo13bobo\$2bobo33b2o13b2o\$b2ob2o\$41b2o7b2o\$42b2o5b2o\$41bo9bo61\$2o3bo43bo\$obobobo40b2o\$2bobobo41b2o\$b2ob2o2\$39bo5bo\$37bobo4b2o\$38b2o4bobo3\$38b2o\$39b2o\$38bo61\$2o36bo\$obob2o33bo\$2bobobo30b3o18bo\$b2obobo51bobo\$5bo52b2o2\$48bo\$47bo\$47b3o2\$43b2o\$42bobo\$44bo61\$2o3bo32bo\$obobobo32bo\$2bobobo30b3o\$2bo2bo\$b2o47bo\$49b2o\$45bo3bobo\$45b2o\$44bobo7\$53b3o\$53bo\$54bo61\$2o37bo10bo\$obo34bobo9bo\$2bo2b2o31b2o9b3o\$2bobobo47b3o\$b2ob2o40b2o6bo\$46bobo6bo\$46bo61\$2bo34bobo\$bobo34b2o\$o2bo34bo\$b2ob2o\$3bo2bo\$3bobo\$4bo39bo\$44bobo\$44b2o3\$46b2o\$45b2o\$47bo3\$54b2o\$53b2o\$55bo61\$bo36bobo\$obob2o33b2o\$obobobo32bo\$bo2bobo\$4b2o3\$38bo4bo\$39bo2b2o5bo\$37b3o2bobo3b2o\$48bobo61\$b2ob2o32bo\$obobobo32bo\$obobobo30b3o\$bo3bo40bobo\$46b2o\$47bo2\$49b3o\$49bo\$50bo\$37b3o\$39bo\$38bo61\$bo35bobo\$obo35b2o\$o2bob2o31bo\$b2o3bo\$3b3o\$3bo48bo\$52bobo\$52b2o\$56b2o3b2o\$56bobob2o\$56bo5bo61\$b2o42bo\$obo2b2o30bo7bobo\$o5bo31b2o5b2o\$b5o31b2o\$3bo3\$48b3o\$48bo\$49bo\$45b2o\$44bobo\$46bo61\$bo41bo\$obob2o33bo3bobo\$obobobo30bobo3b2o\$b2obobo31b2o\$5bo\$45b2o\$40b2o3bobo\$39bobo3bo\$41bo61\$b2ob2o38bobo\$obobo39b2o\$obobo40bo\$b2ob2o32bo\$36bobo\$37b2o3bobo\$42b2o\$43bo6\$54b2o\$53b2o\$55bo61\$b2o35bo\$o2bo32bobo4bo\$obobo32b2o3bo\$bobobo36b3o\$2bo2bo\$3b2o34b2o\$39bobo\$39bo\$44b3o\$44bo\$45bo61\$4b2o31bo\$2o2bo33b2o\$obobobo30b2o\$2bo2b2o\$b2o38bo\$40bo\$40b3o6b3o\$49bo\$50bo2\$38b2o\$39b2o\$38bo61\$2b2o61bobo\$bobo61b2o\$bo64bo\$2o\$2b2o\$2bobo\$4bo\$4b2o9\$36bo\$37b2o\$36b2o\$41bo\$40bo\$40b3o4\$40b2o\$41b2o\$40bo61\$4b2o30bo\$3bobo31b2o\$o3bo31b2o\$4o2\$2o\$2o2\$40b3o3bo\$42bo2b2o\$41bo3bobo2\$52bo\$51b2o\$51bobo61\$4b2o39bo\$4bo38b2o\$b2obobo37b2o\$2bo2b2o\$obo\$2o2\$41bo\$41bobo\$41b2o9\$37bobo\$38b2o2bobo\$38bo3b2o\$43bo61\$3b2o31bobo\$3bobo31b2o\$5bo31bo8bo\$b4o40bo\$o44b3o\$obo\$b2o2\$41bo4bo\$41b2o2b2o\$40bobo2bobo61\$5bo32bo12bobo\$4bobo32bo11b2o\$4bobo30b3o12bo\$b2ob2o\$obo\$obo\$bo43bo\$43b2o\$44b2o3\$45bo\$44b2o\$44bobo61\$4bo33bo\$3bobo33bo\$3bo2bo30b3o\$b2ob2o\$obo\$obo\$bo47b3o\$39bo9bo\$39b2o9bo\$38bobo\$43b2o\$43bobo\$43bo61\$2o34bo5bo\$obob2o31b2ob2o\$2bob2o30b2o3b2o\$2bo\$obo\$2o34b2o5b3o\$37b2o4bo\$36bo7bo61\$2o2b2o32bo\$obo2bo30bobo\$2b2o33b2o\$2bo41bo\$obo41b2o\$2o41bobo2\$47b3o\$47bo\$48bo2\$54b2o\$54bobo\$54bo61\$4b2o31bo\$2obobo32bo\$2obo32b3o\$3bo37bobo\$3o38b2o\$o41bo4\$43b2o4b3o\$42bobo4bo\$44bo5bo61\$3b2o36bo5bo\$2bo2bo34bo5bo\$bobobo34b3o3b3o\$o2bob2o\$obo35bo\$bo37bo\$37b3o3b3o\$43bo\$44bo61\$4b2o32bo\$4bo34bo\$b2obobo30b3o\$obo2b2o\$obo\$bo\$83bo\$82bo\$82b3o6\$64bo\$63b2o\$59bo3bobo\$59b2o\$58bobo61\$6b2o32bo\$7bo30bobo\$4b3o32b2o\$4bo\$2b2o\$2bo38b2o\$obo39b2o\$2o39bo2\$46bo\$46b2o\$45bobo\$50b3o\$50bo\$51bo61\$4b2o44bobo\$3bo2bo43b2o\$3bo2bo34bo9bo\$b2ob2o35bobo\$2bo38b2o\$obo35bo\$2o37bo\$37b3o2\$42b2o\$43b2o\$42bo61\$2b2o44bo\$bo2bo42bo\$2bo2bo41b3o\$b2ob2o\$2bo33bo\$obo34b2o\$2o34b2o2\$44bo\$38bo4bo\$38b2o3b3o\$37bobo61\$3bo34bo\$2bobo31bobo\$2bo2bo31b2o\$3bobo\$bob2o46bo\$obo47b2o\$obo47bobo\$bo43b3o\$47bo\$46bo6bo\$52b2o\$52bobo61\$5bo32bo\$4bobo32bo\$3bo2bo30b3o\$3b3o\$b2o\$o2bo\$bobo\$2bo51bo\$53bo\$53b3o3\$52bo\$51b2o4b3o\$51bobo3bo\$58bo61\$4b2o30bobo\$3bobo31b2o5bo\$3bo33bo5bo\$4bo38b3o\$b4o\$o\$obo\$b2o3\$38bo3bobo\$39bo2b2o\$37b3o3bo61\$3bo33bo\$2bobo33bo\$3bobo30b3o\$5bo\$b4o\$o\$obo\$b2o44bo\$46b2o\$46bobo2\$42b3o\$44bo\$43bo10\$59b3o\$59bo\$60bo61\$b2o42bo5bo\$bobob2o37bo4b2o\$3bob2o37b3o3b2o\$3bo\$bobo\$obo34bobo\$bo36b2o4b2o\$38bo6b2o\$44bo61\$2obo33bobo\$bob3o32b2o\$bo4bo31bo4b3o\$2b3obo38bo\$4b2o38bo2\$44bo4b2o\$44b2o3bobo\$43bobo3bo61\$b2o3b2o30bo\$o2bobobo31b2o4b2o\$bobobo32b2o6b2o\$2bo2bo39bo4b2o\$5b2o43bobo\$50bo8\$59b3o\$59bo\$60bo61\$b2o41bo\$o2bob2o35bobo\$bobobobo35b2o\$2bo2bobo\$5b2o39b2o\$47b2o\$46bo2\$40bo\$38bobo\$39b2o5\$43b3o\$45bo\$44bo61\$b2o3b2o30bobo\$o2bobobo31b2o33bo\$bobobo33bo32b2o\$2b2ob2o66b2o21\$54bo\$48bobo2bo\$49b2o2b3o\$49bo61\$b2o3bo33bo\$o2bobobo30bobo\$bobobobo31b2o9bo\$2b2ob2o42bo\$49b3o\$41b2o\$42b2o\$41bo4b2o\$45bobo\$47bo61\$b2o36bo\$o2bob2o33bo\$bobobobo30b3o\$2b2obobo\$6bo3\$55bo\$54bo\$54b3o4\$42b2o4bo\$41bobo3b2o\$43bo3bobo61\$b2o35bobo\$o2bob2o32b2o\$bobobo33bo21bo\$2b2obobo51b2o\$6b2o52b2o4\$47bo3b3o\$47b2o2bo\$46bobo3bo61\$2ob2o34bo11bo\$2obo33bobo10bo\$3bo34b2o10b3o\$3bob2o\$2b2ob2o\$40b3o2bobo\$42bo2b2o\$41bo4bo61\$2o5b2o30bo\$o7bo31b2o\$b3ob3o31b2o11bo\$3bobo45bo\$4bo46b3o4\$52b2o\$51b2o\$53bo37\$96b2o\$96bobo\$96bo61\$2o2b2o72bo\$o4bo71bo\$b4o72b3o2\$b2o\$obo\$bo21\$63bo\$63bobo\$63b2o7\$36bobo\$37b2o\$37bo3bobo\$41b2o\$42bo61\$2o2bo31bobo\$o2bobo31b2o\$b3obo31bo6bo\$4bo39bobo\$b3o40b2o\$bo2\$40bo\$40b2o3b2o\$39bobo3bobo\$45bo61\$2b2o32bobo\$bobo33b2o\$o36bo21bo\$b5o51b2o\$5bo52b2o\$b2o\$b2o\$48b2o\$49b2o\$48bo4b2o\$53bobo\$53bo61\$2b2o36bo\$bob3o34bobo\$o5bo33b2o\$b4obo\$3bobo\$37bo10bobo\$38b2o8b2o\$37b2o10bo\$41b3o\$43bo\$42bo61\$b2obo34bo\$o2b4o33bo\$2o5bo30b3o\$5bobo\$5b2o2\$51bo\$49b2o\$50b2o\$45b3o\$45bo\$46bo4\$60b2o\$59b2o\$61bo61\$b2o42bo\$o2bo40bo\$4o32bobo5b3o\$37b2o\$2b2o33bo\$3bo\$3bobo\$4b2o2\$43bo\$43b2o\$42bobo\$47b3o\$47bo\$48bo61\$bo34bobo\$obo34b2o\$o2bo33bo\$b3o2\$3b3o\$2bo2bo\$2b2o3\$60b3o\$62bo11b2o\$61bo3b2o7bobo\$65bobo6bo\$65bo61\$bo35bobo8bo\$obo35b2o7bo\$o2bo34bo8b3o\$b3o49bo\$52bo\$3b3o46b3o\$3bo2bo\$4b2o44bo\$49b2o\$49bobo61\$bo35bobo\$obo35b2o\$o2bo34bo\$b2obo\$3bo\$3bobo\$4bobo\$5b2o\$47bo3bobo\$47b2o2b2o\$46bobo3bo2\$51bo\$51b2o\$50bobo61\$b2ob2o44bobo\$obobo45b2o\$o4bo45bo\$b3obo31bo\$3b2o33bo\$36b3o9bo\$46b2o\$41b2o4b2o\$41bobo\$41bo61\$2o52bo\$o2b2o48bo\$bobobo47b3o\$2o3bo\$2b3o\$2bo47bo\$49bo\$38bo10b3o\$36bobo\$37b2o3\$37b2o\$38b2o\$37bo61\$4b2o40bo11bobo\$3bo2bo38bo12b2o\$3bo2bo38b3o11bo\$b2ob2o\$obo\$obo\$bo5\$43b2o\$37bobo2b2o\$38b2o4bo\$38bo61\$2o40b3o\$obob2o31bobo2bo\$2bobobo31b2o3bo\$2bo2bo32bo\$obo44b2o\$2o44b2o\$39b2o7bo\$38bobo\$40bo61\$3b2o32bo\$3bobo32bo\$b2o2bo30b3o\$obobo\$obob2o\$bo4\$56bo\$55b2o\$55bobo2\$49bo\$49b2o\$48bobo\$53b2o\$53bobo\$53bo61\$5b2o37bo\$4bobo37bobo\$4bo39b2o\$b2obobo\$2bo2b2o\$obo43b3o\$2o44bo\$37bo9bo\$38b2o\$37b2o\$53b3o\$53bo\$54bo61\$4b2o45bo\$3bobo38bo5bo\$3bo38b2o6b3o\$b2o2bo31bo5b2o\$2bob2o32bo\$2bo33b3o\$obo40b2o\$2o40bobo\$44bo61\$3b2o32bo\$2bo2bo32bo\$bo2bo31b3o\$b3o38b2o\$42bobo\$b3o38bo\$o2bo\$b2o37bo\$40b2o8b2o\$39bobo8bobo\$50bo61\$5bo32bo\$4bobo32b2o\$4bo2bo30b2o\$2b2ob2o\$bobo\$o2bo\$obo\$bo5\$42bo\$40b2o\$41b2o3\$40b2o\$39b2o\$41bo5\$64b2o\$64bobo\$64bo61\$b2o34bobo\$o2bo34b2o\$bo2bo33bo\$2b3o51bo\$56bobo\$4b3o49b2o\$3bo2bo\$3b2o3\$53bo\$53bobo\$53b2o2\$50b2o\$49b2o\$51bo61\$b2o3b2o50bo\$o2bobo2bo48bo\$bobobobo49b3o\$2b2ob2o\$39bo\$40b2o\$39b2o3\$49bo\$49bobo\$49b2o3\$50b2o\$49b2o\$51bo61\$b2o42bo\$o2bo33bo6b2o\$b2o2bo32bo5bobo\$3b3o30b3o\$b2o\$o2bo36b2o\$b2o36bobo\$41bo\$53b2o\$52b2o\$54bo61\$2o3b2o77bo\$obobobo76bo\$2bobo78b3o\$b2obobo\$5b2o16\$37bobo10bo\$38b2o9b2o\$38bo6bo3bobo\$45b2o\$44bobo61\$2o3b2o45bo\$obobobo43b2o\$2bobo46b2o\$2bobo\$b2ob2o2\$39bo\$37bobo9b2o\$38b2o4bo4bobo\$44b2o3bo\$43bobo61\$2o2b2o35bobo\$o4bo35b2o\$b4o31bobo3bo\$37b2o\$b2o34bo\$obo\$2o\$39b2o\$38b2o12b2o\$40bo10b2o\$53bo61\$2b2o35bo\$bobo2b2o32b2o\$o2bobo2bo30b2o\$b2o2bobo35b3o4bo\$5b2o38bo3bo\$44bo4b3o\$54b2o\$53b2o\$55bo61\$b2o37bo\$o2bob2o31bobo\$o2bobobo31b2o4b2o\$b2o2bobo38b2o\$5b2o38bo6bo\$50b2o\$51b2o3\$49b2o\$49bobo\$49bo61\$b2ob2o33bo\$obobobo30bobo\$o5bo31b2o\$b5o41bo\$3bo43bobo\$47b2o3\$39bo7b2o\$39b2o5b2o\$38bobo7bo61\$bo3b2o32bo8bo\$obobobo30bobo8bobo\$obobo33b2o8b2o\$b2obobo36b3o\$5b2o38bo\$44bo2\$47b2o\$46b2o\$48bo61\$bo35bo\$obob2o32b2o\$obobobo30b2o\$b2o3bo\$3b3o43bo\$3bo44b2o\$48bobo\$43b3o\$45bo\$44bo2\$50bo\$49b2o\$49bobo61\$b2ob2o31bobo2bobo6bo\$obobobo31b2o2b2o5b2o\$obobobo31bo4bo6b2o\$b2ob2o3\$43b2o\$44b2o\$43bo61\$bo3b2o32bo\$obo2bo34bo2bobo\$o2bobobo30b3o2b2o\$bobo2b2o36bo\$2b2o3\$50b2o\$49b2o\$46bo4bo\$45b2o\$45bobo61\$bo36bobo\$obo3b2o31b2o\$o2bobobo31bo\$bobobo\$2b2ob2o51bo\$57bo\$57b3o\$62bo\$61b2o\$61bobo\$55b3o\$57bo\$56bo61\$b2ob2o30bo\$obob2o31b2o\$obo33b2o\$bo2b2o\$2b2obo4\$41bo\$41b2o\$40bobo3bo\$46b2o\$45bobo\$50b3o\$50bo\$51bo61\$5bo35bo\$4bobo33bo\$2o2bobo33b3o\$obob2o\$2bo35bo\$obo36bo\$2o35b3o3\$40bo7bobo\$41b2o5b2o\$40b2o7bo61\$2ob2o39bobo\$bobobo38b2o\$bo3bo30bobo6bo\$2b3o32b2o\$obo34bo\$2o45bo\$47bobo\$42b3o2b2o\$42bo\$43bo61\$2o3bo48bo\$obobobo32bo13bo\$2bobobo30bobo13b3o\$2bo2bo32b2o\$obo\$2o\$47bo\$47bobo\$47b2o3\$49b3o\$49bo\$50bo61\$2o46bobo\$obob2o42b2o\$2bobobo30bobo9bo\$2bo2b2o31b2o4bobo\$obo35bo5b2o\$2o43bo3\$43b2o\$44b2o\$43bo61\$b2o36bo\$bo2b2o31bobo\$2b2o2bo31b2o12bo\$5bo45bo\$2b3o46b3o\$2bo37b2o\$obo38b2o\$2o38bo2\$44b2o\$45b2o\$44bo61\$2bo34bo\$bobo34bo\$b2obo31b3o\$4bo43bo\$b2ob2o41bo\$o2bo43b3o\$o2bo36b2o\$b2o37bobo\$40bo2\$36b3o\$38bo\$37bo61\$4bo87bo\$2obobob2o83bobo\$bobobobo84b2o\$bobobobo\$2bo3bo32bo\$40b2o\$39b2o18\$75bo\$73b2o\$74b2o2\$77b2o\$77bobo\$77bo61\$4b2o41bobo\$2obo2bo33bobo4b2o\$bobob2o33b2o6bo\$bobobo35bo\$2bo2bo\$3b2o34bo\$37bobo\$38b2o2\$59b3o\$59bo\$60bo61\$2o36bo\$obob2o30bobo\$2bobo32b2o\$b2obo\$2bob2o\$2bo\$b2o13\$58bo\$56b2o\$57b2o3\$57b2o\$57bobo\$57bo12\$79b3o\$79bo\$80bo61\$2o2b2o30bobo\$o4bo31b2o\$b4o32bo2\$b2o\$o2bo\$bobo\$2bo48bo\$45b3o2b2o\$47bo2bobo\$46bo\$37bo\$37b2o\$36bobo61\$2o2b2o52bobo\$o4bo52b2o\$b4o54bo2\$b2o\$o2bo32bobo\$obo34b2o\$bo35bo\$44bo\$44bobo\$40bo3b2o\$41bo\$39b3o61\$b2o52bo\$bobo50bo\$2bobo49b3o\$3bobo\$5bo\$b4o\$o\$obo\$b2o2\$36bo\$37b2o7bo\$36b2o8bobo\$46b2o3\$46b2o\$45b2o\$47bo61\$4b2o33bo\$4bobo30bobo\$bo4bo31b2o\$b5o2\$b3o\$o2bo\$b2o39\$93bo\$91b2o\$92b2o3\$90b2o\$89b2o\$91bo2\$86b3o\$86bo\$87bo61\$4bo45bo6bo\$2obobo42b2o5b2o\$bobo2bo42b2o5b2o\$bo2b2o\$2b2o34bo\$3bo35bo9b2o\$3bobo31b3o9bobo\$4b2o43bo61\$2o2b2o30bobo\$o4bo31b2o\$b4o32bo2\$b2o\$o2bo\$o2bo\$b2o20\$59bo\$58b2o\$54bo3bobo\$54b2o\$53bobo4\$74b3o\$74bo\$75bo61\$b2o45bo\$ob3o41b2o\$o4bo41b2o\$b4o2\$b2o\$obo40bo\$2o39b2o\$42b2o2\$36bobo\$37b2o4bo\$37bo4b2o\$42bobo61\$bo5bo35bo\$obo3bobo33bo\$o2bobo2bo33b3o\$bobobobo\$2b2ob2o33bo\$41bo\$39b3o16\$40bo3bo\$41bobo\$39b3ob3o61\$2b2o43bo\$bo2bo33bo8bobo\$bob2o34bo7b2o\$2o35b3o11b2o\$2b3o46bobo\$2bo2bo45bo\$3bo2bo\$4b2o\$48bo\$47b2o\$47bobo61\$5b2o34bo\$4bobo33bo\$2o2bo35b3o\$obobobo\$2bo2b2o31bo\$obo36bo\$2o35b3o4\$46bo\$44b2o\$45b2o2\$42bo\$40bobo\$41b2o61\$b2ob2o42bo\$b2obobo35bo3b2o\$6bo35bobo2b2o\$b5o31bo4b2o\$o2bo34b2o\$2o35b2o4\$44bo\$44b2o\$43bobo61\$4b2o31bo\$2b3obo31b2o\$bo4bo30b2o15bo\$bo2b2o46b2o\$2obo49b2o\$o2bo\$b2o39bo\$42b2o\$41bobo2\$45b3o\$45bo\$46bo61\$2o3b2o34bo\$obobobo33bo\$2bobo35b3o\$obobobo\$2o3b2o31bo\$39bo\$37b3o4\$44bo\$42b2o\$43b2o2\$40bo\$38bobo\$39b2o61\$2b2o35bobo\$bo2bo34b2o\$b2obo35bo\$4b2o45bobo\$b2o2bo32bo12b2o\$o2b2o31bobo13bo\$obo34b2o\$b2o\$41b2o\$40bobo\$42bo61\$2ob2o2bo32bobo\$bobo2bobo32b2o\$bo2bobo2bo31bo\$2bobo2b2o\$3b2o6\$69bo\$67b2o\$68b2o3\$57bo\$55b2o\$56b2o3\$55b2o\$55bobo\$55bo61\$b2ob2o32bobo\$obobobo32b2o\$o3bo2bo31bo10bo\$b3obobo41bo\$3bob2o42b3o2\$45b3o\$39b3o5bo\$41bo4bo\$40bo61\$4bo38bo\$2obobo35bobo\$ob2o2bo35b2o\$4b2o\$b3o45bo\$o2bo44bo\$obo39bo5b3o\$bo40bobo\$38bo3b2o\$39bo\$37b3o61\$b2o3bo48bo\$o2bobobo46b2o\$2obobobo41bo4bobo\$3bob2o37bo3b2o\$3o41b2o2bobo\$o37bobo2bobo\$39b2o\$39bo61\$b2o35bo\$o2bob2o32b2o3bo\$2obobobo30b2o3b2o\$3bobobo35bobo\$3o3bo\$o61b2o\$61b2o\$63bo3\$51bo\$50b2o\$50bobo61\$2b2o34bo\$bo2bo34bo\$2bobo32b3o\$3bo\$49bo\$b5o43bobo\$o5bo42b2o\$2o2bobo\$4b2o34bobo\$41b2o\$41bo3bobo\$45b2o\$46bo61\$b2o35bobo\$o2bob2o32b2o\$bobobobo31bo\$2bo4bo\$3b4o2\$3b2o\$3b2o20\$84b2o\$84bobo\$84bo\$61bo\$61b2o\$60bobo2\$64b3o\$64bo\$65bo61\$4b2o2bo30bobo\$2obob4o31b2o11bobo\$bobo36bo12b2o\$bobob2o47bo\$2b2ob2o38b2o\$44bobo\$46bo3\$47b3o\$47bo\$48bo61\$b2o50bobo\$o2bo34bo14b2o\$b2o33bobo15bo\$37b2o\$b4o41bo\$o4bo38b2o\$b4o40b2o2\$3b2o\$3b2o38b2o\$42b2o\$44bo61\$2o2b2o30bobo2bobo\$o4bo31b2o2b2o\$b4o32bo4bo2\$b4o32bo4bo\$o4bo31b2o2b2o\$2o2b2o30bobo2bobo61\$b2ob2o31bobo\$obobobo31b2o\$obo3bo31bo\$bob3o\$3bo\$bobo\$b2o22\$64bo\$62b2o\$63b2o2\$87b2o\$62bo23b2o\$62b2o24bo\$61bobo61\$b2o34bobo\$ob3o33b2o\$o4bo32bo\$b4obo\$6bo\$3b3o\$2bo\$2b2o2\$50b2o\$49bobo\$51bo9b2o\$60b2o\$53bo8bo\$52b2o\$52bobo61\$2b2o34bo\$bob3o33bo\$o5bo30b3o\$5obo\$4b2o\$2o38b2o\$2o39b2o\$40bo6b3o\$47bo\$48bo\$38b3o\$40bo\$39bo61\$b2o34bo\$obo35bo5bo\$o4bo30b3o5bobo\$b5o38b2o\$40bo\$b5o34b2o\$o4bo33bobo\$obo50b3o\$b2o50bo\$54bo61\$b2o34bobo13bo\$o2bo34b2o13bobo\$bo2bo33bo14b2o\$2b3o2\$2b5o\$bo4bo46bo\$obobo46b2o\$obob2o46b2o\$bo\$55b2o\$55bobo\$55bo61\$3b2o33bo\$b3obo30bobo\$o4bo31b2o\$b4o2\$b4o\$o4bo\$b3obo\$3b2o18\$97bo\$96bo\$96b3o10\$82bo\$81b2o\$77bo3bobo\$77b2o\$76bobo!`

I count only 222 strict stills synthable in four. Where's the last one? Or is the LifeWiki count wrong?
Princess of Science, Parcly Taxel

Freywa

Posts: 556
Joined: June 23rd, 2011, 3:20 am
Location: Singapore

### Re: 4 glider syntheses

Freywa wrote:I count only 222 strict stills synthable in four. Where's the last one? Or is the LifeWiki count wrong?

The count could perfectly well be wrong if my source information was wrong somewhere. The math was

223 = 167 + 7 + 47

EDIT: Holy typos, Batman. 223 = 169 + 7 + 47

dvgrn
Moderator

Posts: 5709
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

### Re: 4 glider syntheses

dvgrn wrote:
Freywa wrote:I count only 222 strict stills synthable in four. Where's the last one? Or is the LifeWiki count wrong?

The count could perfectly well be wrong if my source information was wrong somewhere. The math was

223 = 167 + 7 + 47

First of all, that 167 should be 169 – unzipping the .rar shows 172 files, three of which are oscillators.

Second, I did miss a 4G synth of some strict still life, that of mango with block on dock (19-30501-g4-175 Bob 06-25-2015.lif):
`#C >25 -9/-3 0 25 -1/4 4/>xs19_69icw8ozxdd11x = 30, y = 15, rule = B3/S2325b2o\$8bo15bobo\$7bo16bo\$2o5b3o11b2obo\$b2o18b2obob2o\$o5bo18bo2bo\$5b2o19bo2bo\$5bobo19b2o5\$12bo\$11b2o\$11bobo!`

So the count of 223 synthables is correct after all.
Princess of Science, Parcly Taxel

Freywa

Posts: 556
Joined: June 23rd, 2011, 3:20 am
Location: Singapore

### Re: 4 glider syntheses

That count of 223 is no longer true. Arie's 4G search has turned up this gem:
`x = 24, y = 28, rule = B3/S2321bobo\$21b2o\$22bo5\$18bo\$17b2o\$17bobo3\$12b3o\$14bo\$13bo11\$2o\$b2o\$o!`
Princess of Science, Parcly Taxel

Freywa

Posts: 556
Joined: June 23rd, 2011, 3:20 am
Location: Singapore

Previous

Return to Patterns

### Who is online

Users browsing this forum: No registered users and 9 guests