Usually small sawtooth pattern

[Dean Hickerson]

The idea for this pattern came from the "Very Low Expansion Factor?" discussion, but I think it deserves it's own thread.

In every sawtooth pattern that I've seen before, the population is usually large, in the sense that for any positive number P, the density of the set of times when the population is less than P is zero. (P.S., May 11, 2016: No, that's not true. For the quadratic sawtooth the population is small for long periods of time. The set of such times does not have an asymptotic density.)

For the sawtooth below, the opposite is true: The density of the set of times when the population exceeds 1581 is zero. Most of the time, the stationary part of the pattern is just a p240 oscillator, whose population fluctuates between 1351 and 1581. But at times around 3840*2^n - 1760, it receives a glider from a caber tosser, which triggers one cycle of an e.f. 7/6 sawtooth. During that time, the population grows and then shrinks; after that the stationary part becomes an oscillator again.

If I've computed correctly, at the times T when the population is maximal, it's about C*T^a, where a = log(7/6)/log(2) ~ 0.22239. (I haven't computed C yet.)

Code: Select all

#C Usually small sawtooth
#C Dean Hickerson, 5/2/2016
x = 339, y = 387, rule = B3/S23
305bo$297bo7b2o$296bobo2b3obobo$297bo3b2o3b3o$298bobob2obobo$302b2ob2o
$297bob5obo$285b2o11b4o$285b2o7$277b2o$277b2o23bo$290bobo6bo$288bobobo
11bo$286b2o10bo2bo3bo$288bo10bo2b3o$299bo3bo$300b2o$301bo10b2o$304bo4b
o2bo$303bobo2bob3o2bo$304b4o4bo2bo$312bo2bo$305bo6bo$310bob2o$305bo29b
o$306b2o19bo7b2o$326bobo2b3obobo$327bo3b2o3b3o$328bobob2obobo$332b2ob
2o$327bob5obo$328b4o12$335b2o$335b2o7$327b2o$327b2o71$105bo$103b3o$
102bo$102b2o3$98b2o$97bobo$99bo6b2o5b2o$106b2o5b2o2$89bo19b2o$88bobo
18b2o$90bo$34b2o$34b2o$55bo31bobo$8b2o43b3o30bo3bo$8b2o42bo33bo4bo$52b
2o28b2o8bo$82b2o3b2o2bo$11b2o59bo16b2o$11b2o57b3o$69bo$8b2o47bo11b2o
11bo$8b2o23bo22b2o24b3o$2o29bo3bo19bo2bo26bo22bo$bo28bo4bo20b2o26b2o
20b3o$bobo31bo63b2o4bo$2b2o20b2o7b2o64bo5b2o$19bo4b2o2bo67b2obo$17b2ob
2o37b2o34bo2bo3bo$17b2ob2o37b3o24b2o8b2o4bo$16b3obo7bob2o25b2o2bo24bob
2o$19b3o10bo12b2o10bo2b2o26b2o$29bo3bo11bobo9bo2bo25bob2o10b2o3b2o$29b
o2bo14bo10b3o25b2o13b5o$29bo2bo2b2o10b2o53b3o$29bo2bo2bobo30b2o3bo29bo
$29bo2b2o2b2o30bo3bobo$28bo3bo2bo33bo3bobo$19b2o10bo2b2o20b2o12bo3bobo
b2o$19b2o7b2o4bo22bo10bob4o2bob2o$54b3o10bobo3bobo$16b2o36bo12bobo2bo
2b2ob2o$16b2o50bo3b2o2bobo25bo$76bobo10b2o14b2o$77bo11b2o13b2o$19b2o
17bo$19b2o15bobo$37b2o85b3o$126bo$41bo56b2o3b2o20bo$42bo57b3o8bobo31bo
$40b3o56bo3bo8b2o31b3o$100bobo9bo35bo$101bo45b2o2$94bo8b2o$94b3o6bo$
97bo6b3o35bo$96b2o8bo29b2o3bobob2o$136b2o2bob3ob2o$141b6o$98b3o44bo$
98b3o8b3o4bo$97bo3bo9bo4b3o$110bo8bo$96b2o3b2o15b2o75b2o$163b2o30b2o$
107b3o53b2o$107bo$102b2o4bo51b2o5b2o23b2o$101bobo56b2o5b2o23b2o$103bo
14b2o3b2o27bobo$118bobobobo28b2o40b2o$119b5o29bo41b2o$103bo11b2o3b3o
46b2o8b2o22b2o$68bo46bobo3bo47b2o8bo23bo$66bobo46bo61bobo21bobo$67b2o
108b2o22b2o2$71bo28b3o66b2o14bo$72bo26bo3bo64bo2bo12b3o$70b3o25bo5bo
63bo2bo12bo2bo$98bo5bo62b2ob2o14b2o$101bo16b3o47bo2bo14bo$99bo3bo13b2o
b2o35b2o10b2o12b2o$100b3o14b2ob2o36bo24b4o$101bo15b5o36bobo23bo2bo$
116b2o3b2o36b2o24bo2$101b2o81bobo$101b2o81b2o2$187b2o$187b2o$116b2o$
117bo$114b3o67b2o$114bo69b2o$120b3o$120b3o$109bo10b3o$109b3o5b3o$112bo
4b3o$111b2o4b3o2$98bo15bo45b2o$96bobo14bobo44b2o2b2o$97b2o10b2o2b2o49b
obo$109b2o54bo$101bo$102bo23b2o34b2o4b3o$95b2o3b3o23bo36bo4b3o$95b2o
13b2o12bobo12bo20b3o5b3o$111b2o11b2o13bobo18bo10b3o$110bo28b2o4bo25b3o
$145b3o23b3o$88bo59bo$87bob2o4bo51b2o$87bo2b2o2b2o$90bo2b2o30b2o23bo$
89b2ob2o31b2o$90bo$91b2o43b2o5b2o$136b2o5b2o$217b3o$85bo54b2o78bo$83b
2o55b2o74bo3bo$84b2o129bobo2bo$213bo2bobo$137b2o74bo3bo$137bo75bo$78b
2o30b2o23bobo18b2o4b3o49b3o$77bobo29bobo23b2o18bo2bo3bob2obo43bo$77bo
33bo42b2o2bo9bo41bobo$76b2o77b2o2bo4bo3bo41b2o$84b2o70b4o4b4o46b2o$84b
2o128bobo$209b2o5bo$87b2o120b2o5b2o$87b2o78b2o$111b2o5b2o47b2o$111b2o
5b2o$84b2o$71b2o11b2o28b2o60bo$71b2o41b2o59bobo$176bo2$74bobo$78b2o11b
2o$74bo5bo10b2o11b4o62b3o$71b2o7bo27bo61bo$71b2o2bob2ob2o5b2o5b2o8bo4b
o62bo4b2o$63b2o10bo2bob2o5b2o5b2o9b2obo59bob2o5bobo$64bo11b4o27bo60bob
o8bo$64bobo9b3o85b2o13b2o$65b2o98bo$81bo80b3o6b2o$82b2o14b2o62bo8b2o$
81b2o16bo$96b3o$96bo8bo$105b2o$104bobo5$82b2o$82b2o$105b2o$79b2o24bo$
79b2o22bobo$103b2o2$82b2o4b2o$82b2o4b2o44bobo$134b2o$135bo$105b2o20bo$
98b2o5b2o19bobo$98b2o14b2o10b2obo29b2o$114b2o10b2ob2o28b2o$93bo32b2obo
45b2o$92bobo31bobo46b2o$93bo6b2o25bo$100bo$101b3o$103bo$129b3o$99b2o
27b2ob2o$99b2o27b2ob2o$128b5o15b3o$127b2o3b2o16bo$102b2o45bo$102b2o2$
99b2o$99b2o30b2o$91b2o$92bo$92bobo$93b2o34b2o$129b2o3$99b2o67bo$99bobo
66b3o$99bo71bo$170b2o6bo$177bobo$106b2o70bo$105bobo$105bob2o63b2o$105b
o2bo50b3o3b2o5b2o$102b2ob2o2bobo46bo2bo3b2o$102b3o5bo22b2o26bo$133bo
27bo$131bobo24bobo21b2o4b2o$126bo4b2o40b2o7b2o4b2o$124bobo46bobo$110b
2o4b2o7b2o40b2o4bo$110b2o4b2o48bobo$166bo$165b2o22bo5b3o$133b2o53bobo
2b2ob2o$126b2o5b2o56bo2bo$126b2o63b2obo$192bobo$121bo70b2o$120bobo$
121bo6b2o$128bo71bo$129b3o66bobo$131bo67b2o2$146bo$146b2o$137b2o2b2o4b
2o56b2o$137b2o2b2o4b3o55bobo$141b2o4b2o58bo$146b2o10bo48b2o$146bo10b3o
39b2o$157b3o39b2o2$155b2o3b2o34b2o$155b2o3b2o34b2o3$158bo40b2o$157bobo
39b2o$156b2o$156b2o$156b3o$157bobo$158b2o!

[Scorbie]

Wow! That's a really original design! That fits the definition of a sawtooth AND it happens to have an ever-increasing-sawtooth-like population graph too!!
I think the sawtooth can be reduced by using a single glider eaten by a c/5 spaceship instead of a 3-glider salvo pushing a block!

Whoops, no. Not really...
Here's the not-quite-working sawtooth, but at least we could add semi-snarks to (make it work first, and then) make the e.f. arbitrarily close to 1, I think!

Code: Select all

x = 245, y = 263, rule = B3/S23
211bo$203bo7b2o$202bobo2b3obobo$203bo3b2o3b3o$204bobob2obobo$208b2ob2o
$203bob5obo$191b2o11b4o$191b2o7$183b2o$183b2o23bo$196bobo6bo$194bobobo
11bo$192b2o10bo2bo3bo$194bo10bo2b3o$205bo3bo$206b2o$207bo10b2o$210bo4b
o2bo$209bobo2bob3o2bo$210b4o4bo2bo$218bo2bo$211bo6bo$216bob2o$211bo29b
o$212b2o19bo7b2o$232bobo2b3obobo$233bo3b2o3b3o$234bobob2obobo$238b2ob
2o$233bob5obo$234b4o12$241b2o$241b2o7$233b2o$233b2o97$14bo$12b3o$11bo$
11b2o2$8bo$8bo3$6b2o3b2o$7b5o$8b3o$9bo7$10bo$11b2o$10b2o$58bo$58b3o$
30b3o28bo$32bo27b2o$4b2o3b2o20bo$6b3o8bobo$5bo3bo8b2o$6bobo9bo$7bo41b
2o5b2o$49b2o5b2o$o8b2o$3o6bo43b2o$3bo6b3o40b2o$2b2o8bo2$108b2o$4b3o69b
o31b2o$4b3o8b3o4bo46b2o4bob2o$3bo3bo9bo4b3o42b2o2bo3bob2o$16bo8bo41bo
2b3o3b3ob2o23b2o$2b2o3b2o15b2o41bo4bo4bobobo23b2o$68b5o4b4o$13b3o54b2o
6b2o28b2o$13bo94b2o$8b2o4bo67b2o8b2o22b2o$7bobo72b2o8bo23bo$9bo14b2o3b
2o59bobo21bobo$24bobobobo59b2o22b2o$25b5o$9bo11b2o3b3o$21bobo3bo78b2o$
21bo$106b2o2$6b3o61b2o35bobo$5bo3bo61bo36bo$4bo5bo60bobo16bo17bo$4bo5b
o61b2o9bo5bo$7bo16b3o57bo4b3o$5bo3bo13b2ob2o54b3o12b2o$6b3o14b2ob2o69b
2o$7bo15b5o$22b2o3b2o71b2o$100b2o$7b2o$7b2o$97b2o$97b2o2$22b2o$23bo$
20b3o$20bo5$81b2o$81bo$79bobo$79b2o2$64b2o$43b4o17b2o$41b2o4b2o$41b2o
5bo$43b2obobo32b2o$48bo25b2o5b2o$44bo3bo25b2o$44bo4bo$46b3o3bo16bo$46b
2o4bo15bobo$52b2o15bo6b2o$54bo21bo$54b3o20b3o$79bo2$57bo$56bob5o$55b2o
5bo$55b2o3bo2bo$63bo$57b2obo2bo$60bo2bo$61b2o$61b2o!

[Dean Hickerson]

I think the sawtooth can be reduced by using a single glider eaten by a c/5 spaceship instead of a 3-glider salvo pushing a block!

Could you describe that in more detail? We could start sending gliders toward a c/5 when we get a signal from the caber tosser, but how would we know when to stop?

[Scorbie]

Whoops... I think I made a mistake somehow... Sorry!
Edit: Sorry for not verifying, but does the idea I suggested above works to make the e.f. arbitrarily close to 1?
I originally thought this has constant population for the most of the time, but no... The glider-activated time range grows more and more.

Now I see that the idea and the design is really original. Great work!!

[chris_c]

I noticed that a p280 stream is capable of opening up the switchable p120 gun and leaving it unaffected thereafter. I wonder if this makes it possible to get rid of the regulator?

Code: Select all

x = 116, y = 144, rule = B3/S23
9bo$9b3o$12bo$11b2o3$16bo$15b2o$2o5b2o6bobo$2o5b2o2$4b2o20bo$4b2o18b2o
$24bobo2$59b2o$26b2o31b2o$25b3o$23b2ob2o$23b2ob2o3b2o23b2o$23b2obo4b2o
23bo$25bo$60bo$59bobo$33b2o8b2o13bo8b2o$33b2o8bo14bo2bo5bo$41bobo13b2o
bo4bobo$41b2o13b3o6b2o$57b2ob2o$57bo2b2o$58b3o$59bo3$21b2o20bobo$22bo
7bobo10b2o$22bobo6b2o11bo$23b2o6bo2$48b2o$48b2o2$51b2o$51b2o3$36b2o10b
2o$36b2o10b2o11$45b3o$45bo$46bo6$81bo11b2o$80bobo10b2o$68bo3bo3b2o2bob
o$66b3o2bobo2bo2b2ob2o$65bo5bobo3bobo$65b2o5bob4o2bob2o$74bo3bobob2o$
73bo3bobo$72bo3bobo$72b2o3bo4$85b2o$85b2o$100b2o10b2o$99bo2bo$100b2obo
7bo3bo$53b2o48bo6bo4bo$53b2o48b2o4bobobo$88b2o18bobobo$89bo16bo4bo$86b
3o17bo3bo$74b2o10bo$74bobo28bo2b2o$76bo27bobo$76b2o26b2o$108b2o$72bo
35bobo$70b3o30b2o5bo$69bo25b2o6b2o5b2o$69b2o23bobo$84bo11bo$82b5o14b2o
$77b2o2bo5bo13bo$78bo2bo2b3o12bobo$78bob2obo15b2o$70b2o4b3o4b4o$70b2o
3bo3b4o3bo3b2o$75b4o4b3o4b2o$61b2o15bob2obo$60bobo12b3o2bo2bo$60bo13bo
5bo2b2o$59b2o14b5o$77bo$64bo26b2o$50b2o5b2o5bobo25bo$51bo5b2o5b2o23b3o
$51bobo35bo$52b2o$56b2o$55bobo27b2o$56bo29bo$52bo33bobo$51bobo22bo10b
2o$50bo3bo19b3o$49bo3bo19bo$48bo3bo20b2o$47bo3bo6b2o48b2o$48bobo8bo48b
2o$49bo9bob2o$60bo2bo$61b2o$76b2o$76b2o4$85bo3b2o$84bobo3bo$83bobo3bo$
79b2obobo3bo$79b2obo2b4obo$83bobo3bobo6b2o$79b2ob2o2bo2bobo6b2o$80bobo
2b2o3bo$68b2o10bobo$68b2o11bo!

EDIT: We would need to make sure that the glider returning from the Cordership always appears at a multiple of lcm(120, 280) = 840 ticks but I don't think that is a problem.

EDIT2: No, I don't even think that the above is necessary. There shouldn't be any conflicts because the p280 stream will already be quiet by the time the next glider from the Cordership comes back.

EDIT3: Replenish the glider in white at any sufficiently large time that is a multiple of 120 in order to trigger the next expansion phase. I don't feel like hooking up the caber tosser for some reason.

Code: Select all

x = 192, y = 218, rule = LifeHistory
105.A$103.3A$102.A$102.2A3$98.2A$99.2A$98.A7.2A5.2A$106.2A5.2A2$89.A
19.2A$90.A18.2A$89.A$34.2A$34.2A$55.A$8.2A43.3A30.2A2.A$8.2A42.A38.A$
52.2A28.2A3.A3.2A$82.2A4.4A$11.2A59.A15.3A$11.2A57.3A$69.A$8.2A46.2A
11.2A11.A$8.2A46.3A23.3A$2A32.A20.A2.A26.A$.A32.3A19.2A26.2A$.A.A31.A
63.2A$2.2A20.2A8.A64.A$18.3A3.2A70.2A.A$17.A3.A37.A.A33.A2.A$61.A24.
3A7.2A$16.A14.A25.2A3.A23.A2.A$17.5A7.4A12.2A9.2A.3A28.A$20.A11.2A11.
A.A9.A28.A2.A$28.3A.2A13.A10.3A25.3A$28.6A.2A10.2A10.A$28.5A.2A.A30.
2A3.A$28.2A.5A.A30.A3.A.A$31.2A2.A33.A3.A.A$19.2A7.2A3.3A20.2A12.A3.A
.A.2A$19.2A13.2A21.A10.A.4A2.A.2A$54.3A10.A.A3.A.A$16.2A36.A12.A.A2.A
2.2A.2A$16.2A50.A3.2A2.A.A$76.A.A10.2A$77.A11.2A$19.2A16.A$19.2A17.2A
$37.2A3$40.A.A$41.2A$41.A15$91.A$90.A.A$89.A3.A$79.A8.A3.A$79.3A5.A3.
A$82.A3.A3.A$81.2A4.A.A$88.A$67.A16.A$68.2A13.A.A$67.2A10.2A2.2A$79.
2A2$70.A.A23.2A$65.2A4.2A23.A$65.2A4.A8.3A11.A.A$82.A11.2A$81.A2$58.
2A$57.A.3A2.2A$58.A2.A.A.A$65.A29.2A$59.2A.3A30.2A$59.2A2.A$61.A3$54.
A$53.A$53.3A2$107.2A$107.A$48.2A30.2A23.A.A$47.A.A31.2A22.2A$47.A32.A
$46.2A$54.2A$54.2A2$57.2A$57.2A$81.2A5.2A$81.2A5.2A$54.2A$41.2A11.2A
28.2A$41.2A41.2A4$45.A3.A11.2A12.2A$50.A10.2A12.3A$41.3A6.A23.A.3A$
41.2A3.3A8.2A5.2A9.A.3A$33.2A10.A5.A5.2A5.2A9.4A$34.A10.A4.A25.2A$34.
A.A9.A2.A$35.2A10.A$52.A$53.A14.2A$51.3A15.A$66.3A$66.A3$141.C$142.C$
127.A12.3C$128.2A28.A15.A$52.2A73.2A25.4A.A12.3A$52.2A100.3A.A.A10.A$
75.2A59.A.A20.A.A9.2A$49.2A24.A54.A.A4.2A21.A$49.2A22.A.A55.2A4.A21.
2A$73.2A56.A27.2A4.A.A$159.2A4.A.A17.A$52.2A4.2A105.A2.A15.3A$52.2A4.
2A106.2A15.A.3A$122.2A58.A3.A$67.2A53.2A57.A3.A$67.2A6.2A103.3A.A$75.
2A104.3A$125.2A55.A$125.2A51.A$63.A113.A.A$62.A.A57.2A53.2A$63.A6.2A
50.2A57.2A$70.A43.2A65.A.A$71.3A41.A60.2A5.A$73.A41.A.A58.2A5.2A$116.
2A2$121.2A.A$121.5A$122.4A$176.2A5.2A$122.3A23.2A26.2A5.A$122.3A20.A
3.A31.A.A$123.A21.4A32.2A$141.A35.2A$139.A.A5.4A26.A.A$140.2A5.A3.A
26.A$133.2A15.2A$133.2A46.2A$181.2A.A$130.2A53.A$130.2A19.2A29.A$152.
2A29.A.2A$151.A33.2A$133.2A$133.2A$138.2A$138.2A7$140.2A$141.A$138.3A
$138.A3$138.2A2.2A$138.2A2.2A9.2A5.2A$137.2A6.A7.2A5.2A$138.A7.A$138.
2A.2A.2A10.2A32.2A$138.2A3.A12.2A32.2A4$133.2A$133.2A2$129.2A5.2A$
129.2A5.2A5$140.2A$141.A$138.3A$138.A!

EDIT4: By the way, the p120 gun is small enough to allow a slightly smaller edge-shooter. I suppose it will reduce the population a bit.

Code: Select all

x = 66, y = 48, rule = LifeHistory
28.A11.2A$27.A.A9.B2AB$19.A3.2A2.A.A9.3B$10.2A6.A.A2.A2.2A.2A9.B.B$9.
B2A2B4.A.A3.A.A2.B8.5B$10.4B5.A.4A2.AB2A6.6B$8.6B7.A3.A.A.2A4.8B$8.5B
7.A2.BA.A2.13B$7.6B6.A.2BA.A5.13B$6.7B6.2A.2BA.B3.15B$7.6B10.4B3.15B$
7.7B10.4B.17B$7.6B4.29B$7.7B2.4BA11B2A13B$7.7B2.4B3A9B2A14B$6.9B.4BAB
A20B3.B2A$6.16BA19B4.A2.A$.B4.20B2.2B2.B3.6B5.2A.A$2AB.19B14.6B7.A$2A
19B14.9B6.2A$.B.17B15.2A4.4B$4.17B15.A5.4B$4.17B12.3A7.2B2A$4.15B.B2A
10.A10.2A2B$4.12B4.BA.A21.BA2B$3.11B9.A10.4B2.B.3B.4B$2.13B8.2A9.4B.
18B$3.12B18.2A5B2A16B$4.10B19.2A5B2A16B$4.9B21.B.22B$4.9B23.B2A21B$4.
9B24.2A7B2.13B$7.5B25.8B6.10B$8.4B27.7B7.7B$8.4B26.10B6.8B$9.4B25.13B
2.A6B2A$10.4B25.12B4A6BAB$11.4B26.9BAB5A6B.B$12.4B25.8B2A6BA6B2A$13.
4B24.9B3ABA3BA5B2A$14.4B24.9B2A2BABA2B.4B$15.4B30.4B.3B.B2.4B$16.4B
30.3B$17.4B30.4B$18.3BA31.2A$19.3BA30.A$20.3AB30.3A$21.4B31.A!

[Dean Hickerson]

Here's the not-quite-working sawtooth, but at least we could add semi-snarks to (make it work first, and then) make the e.f. arbitrarily close to 1, I think!

Here it is with one more semi-snark. This is a sawtooth with expansion factor 256; adding more semi-snarks would make the e.f. larger.

It's not "usually small"; the population is <= 691 for long stretches of time, but the set of such times does not have a limiting density.

Code: Select all

x = 196, y = 182, rule = B3/S23
108b2o$108bo$99bo6bobo$99bobo4b2o$82b2o18b2o11bo$80bo3bo17b2o9bobo$79b
o5bo16b2o8bobo17bo$74b2o2b2obo3bo8bo4bobo9bo2bo16b2o$74b2o3bo5bo9bo3bo
12bobo15b2o$80bo3bo5bo2b3o12b2o3bobo13b3o8b2o$82b2o23bobo5bo4bobo7b2o
8b2o$107bo12b2o9b2o$106b2o13bo10bo$96b2o$95bobo$97bo4bo$100bobo$101b2o
11bo$112b2o$113b2o2$88b3o$77bo12bo10b2o$77b4o8bo11bo$67b2o9b4o10b2o5bo
bo$67b2o9bo2bo9bobo5b2o$72bo5b4o8b3o$72bo4b4o8b3o$77bo12b3o$91bobo$92b
2o31$160bo$159b2o$159bobo15$174bo$173b3o$172bo3bo$171bo2b2o$172bobo$
172bobo$173b2o$174b2o2$184b2o$169b2o13b2o4$166b3ob2obo14bo$166bo2bob3o
13b2o$166b2ob2obo13bo3bo$167b3o3bobo10bo2b3o$42bo124bo2bo2b2o10bo2bo3b
o$42b3o125bo4bobobo11bo$45bo122b3o6bobo6bo$44b2o122bobo18bo$164bo2bo2b
o$163bo2b2o$164b3ob4o$164b2o4bobo$33b2o5b2o128bobo$33b2o5b2o129bo$172b
o$37b2o133b2o$12b2o23b2o133b2o11b4o$12b2o170bob5obo$189b2ob2o$92b2o91b
obob2obobo$4bo55bo31b2o90bo3b2o3b3o$3bobo47b2o4bob2o120bobo2b3obobo$4b
o46b2o2bo3bob2o100b2o19bo7b2o$51bo2b3o3b3ob2o23b2o71bo29bo$51bo4bo4bob
obo23b2o76bob2o$52b5o4b4o97bo6bo$7b2o45b2o6b2o28b2o75bo2bo$7b2o83b2o
67b4o4bo2bo$2b2o62b2o8b2o22b2o58bobo2bob3o2bo$bobo62b2o8bo23bo60bo4bo
2bo$bo72bobo21bobo57bo10b2o$2o13b2o57b2o22b2o57b2o$15bo140bo3bo$8b2o6b
3o126bo10bo2b3o$8b2o8bo71b2o51b2o10bo2bo3bo$145bobobo11bo$90b2o55bobo
6bo$134b2o23bo$54b2o35bobo40b2o$55bo36bo$55bobo16bo17bo$56b2o9bo5bo$
68bo4b3o$66b3o12b2o$81b2o$142b2o$84b2o56b2o11b4o$84b2o68bob5obo$159b2o
b2o$155bobob2obobo$81b2o71bo3b2o3b3o$81b2o70bobo2b3obobo$154bo7b2o$
162bo8$65b2o$65bo$63bobo$63b2o2$48b2o$27b4o17b2o$25b2o4b2o$25b2o5bo$
27b2obobo32b2o$32bo25b2o5b2o$28bo3bo25b2o$28bo4bo$30b3o3bo16bo$30b2o4b
o15bobo$36b2o15bo6b2o$38bo21bo$38b3o20b3o$63bo2$41bo$40bob5o$39b2o5bo$
39b2o3bo2bo$47bo$41b2obo2bo$44bo2bo$45b2o$45b2o!

[Dean Hickerson]

I noticed that a p280 stream is capable of opening up the switchable p120 gun and leaving it unaffected thereafter. I wonder if this makes it possible to get rid of the regulator?
...
EDIT3: Replenish the glider in white at any sufficiently large time that is a multiple of 120 in order to trigger the next expansion phase. I don't feel like hooking up the caber tosser for some reason.
...
EDIT4: By the way, the p120 gun is small enough to allow a slightly smaller edge-shooter. I suppose it will reduce the population a bit.

Very nice! Here's a usually small sawtooth using those ideas. I haven't tried to minimize the initial bounding box yet:

Code: Select all

x = 212, y = 207, rule = B3/S23
72bo11b2o$71bobo10b2o$63bo3b2o2bobo$54b2o6bobo2bo2b2ob2o$54b2o6bobo3bo
bo$63bob4o2bob2o$28b2o35bo3bobob2o$28b2o34bo3bobo$63bo3bobo$63b2o3bo$
31b2o47bo$31b2o46b2o$75b2o$28b2o45bo$28b2o45b3o$20b2o32bo36b2o$21bo32b
3o33bo2bo$21bobo31bo35b2obo$22b2o20b2o8bo39bo$38b3o3b2o48b2o$37bo3bo
37b2o$80bo$36bo14bo25b3o$37b5o7b4o12b2o10bo$40bo11b2o11bobo$48b3ob2o
13bo$48b6ob2o10b2o$48b5ob2obo19b2o5b2o$48b2ob5obo19b2o5b2o$51b2o2bo39b
obo$39b2o7b2o3b3o25b2o11bo2bo$39b2o13b2o25b2o12bo2bob2o$98bo2bo$36b2o
61b2o$36b2o61b2o$104b2o$104b2o$39b2o16bo$39b2o17b2o41b2o5b2o$57b2o42b
2o5b2o3$60bobo$61b2o$61bo35b2o$97bo$98b3o$100bo12$33bo14b2o61bo$30b4o
14b2o60bobo$109bo3bo$99bo8bo3bo$99b3o5bo3bo$33bobo66bo3bo3bo$34bo66b2o
4bobo$32b2o74bo$32bo2bo20b2o29bo16bo$31b2ob2o20b2o30b2o13bobo$87b2o10b
2o2b2o$99b2o2$90bobo23b2o$85b2o4b2o23bo$85b2o4bo8b3o11bobo$102bo11b2o$
101bo2$78b2o$77bob3o2b2o$78bo2bobobo$85bo29b2o$24bobo52b2ob3o30b2o$24b
3o52b2o2bo$24b2o55bo3$27bo46bo$25bobo45bo$3bo21b3o45b3o$4o24bo$24b5o
98b2o$17b3o107bo$68b2o30b2o23bobo$3bobo12b2o47bobo31b2o22b2o$4bo13b2o
47bo32bo$2b2o13bo2bo45b2o$2bo2bo11bo56b2o$b2ob2o10b3o55b2o77bo$16b2o
134b3o$19b2o56b2o72bob3o$18bo2bo55b2o62bo8bo3bo$101b2o5b2o31b3o5bo3bo$
16b2o83b2o5b2o34bo3b3obo$16bo2bo54b2o67b2o4b3o$17b3o41b2o11b2o28b2o44b
o$61b2o41b2o40bo$145bobo$141b2o2b2o$6b2o133b2o$6b2o57bo3bo11b2o12b2o$
70bo10b2o12b3o$61b3o6bo23bob3o$61b2o3b3o8b2o5b2o9bob3o$53b2o10bo5bo5b
2o5b2o9b4o$54bo10bo4bo25b2o$54bobo9bo2bo$14b2o39b2o10bo$14bo57bo$73bo
14b2o$16bobo52b3o15bo$17b2o67b3o$17bo68bo2$131bo$131b2o$130bobo$147bo$
148b2o28bo15bo$72b2o73b2o25b4obo12b3o$72b2o100b3obobo10bo$95b2o59bobo
20bobo9b2o$69b2o24bo54bobo4b2o21bo$69b2o22bobo55b2o4bo21b2o$93b2o56bo
27b2o4bobo$179b2o4bobo17bo$72b2o4b2o105bo2bo15b3o$72b2o4b2o106b2o15bob
3o$142b2o58bo3bo$87b2o53b2o57bo3bo$87b2o6b2o103b3obo$95b2o104b3o$145b
2o55bo$145b2o51bo$83bo113bobo$82bobo57b2o53b2o$83bo6b2o50b2o57b2o$90bo
43b2o65bobo$91b3o41bo60b2o5bo$93bo41bobo58b2o5b2o$136b2o2$141b2obo$
141b5o$142b4o$196b2o5b2o$142b3o23b2o26b2o5bo$142b3o20bo3bo31bobo$143bo
21b4o32b2o$161bo35b2o$159bobo5b4o26bobo$160b2o5bo3bo26bo$153b2o15b2o$
153b2o46b2o$201b2obo$150b2o53bo$150b2o19b2o29bo$98bobo71b2o29bob2o$98b
o2bo69bo33b2o$101b2o8bo41b2o$99bo3b2o5bobo40b2o$101b2o6bob2o45b2o$91b
2o5bo2bo6b2ob2o10b2o33b2o$90bobo5bobo8bob2o10b2o$90bo19bobo$89b2o20bo
4$160b2o$161bo$158b3o$158bo3$59b2o23b2o72b2o2b2o$59b2o23bo73b2o2b2o9b
2o5b2o$50b2o10b2o12b2o4bobo22b2o48b2o6bo7b2o5b2o$50b2o10b3o10bo6b2o21b
o2bo49bo7bo$62b2o10bo15bo13bo11b2o40b2ob2ob2o10b2o32b2o$59b2o13bo13b4o
12bo11b2o40b2o3bo12b2o32b2o$59b2o13bo14bob2o11bo$75bo11bobob3o11bo2bo$
76b2o11bob2o14b2o$84b2o2b4o61b2o$83bobo4bo62b2o$83bo$82b2o65b2o5b2o$
149b2o5b2o5$160b2o$161bo$158b3o$158bo!

[dvgrn]

Here's a usually small sawtooth using those ideas. I haven't tried to minimize the initial bounding box yet...

There's an eater waiting to catch alternate gliders from the suppressing stream, that never gets used because the suppressing stream already has to be p240.

I tried rearranging the three-glider salvo shotgun to reduce the number of p120 guns, but it's not likely to be any use for either population or bounding-box reasons:

Code: Select all

x = 227, y = 242, rule = B3/S23
52bo11b2o$51bobo10b2o$43bo3b2o2bobo$34b2o6bobo2bo2b2ob2o$34b2o6bobo3bo
bo$43bob4o2bob2o$8b2o35bo3bobob2o$8b2o34bo3bobo$43bo3bobo$43b2o3bo$11b
2o$11b2o38bo$52bo3bo$8b2o37b2o3bo4bo$8b2o5b2o30bo3bo2bo2bo$2o13b2o30bo
bo3b4o14b2o53bo$bo12bo33b2o3b2o15bo2bo50b3o$bobo10b3o54b2obo48bo$2b2o
11bobo6b2o48bo48b2o$15b2o7b2o48b2o$17bo41b2o$17bo42bo$19bo37b3o$45b2o
10bo69b2o5b2o$45bobo23b2o54b2o5b2o$47bo23bobo$47b2o22bo58b2o$57b2o5b2o
64b2o$57b2o5b2o59b2o$125b2o$19b2o40b2o61bo2bo$19b2o40b2o44b2o12bo2bob
2o$107b2o11bo2bo$16b2o103bobo$16b2o85b2o5b2o$103b2o5b2o$79b2ob2o$19b2o
57bo5bo$19b2o57bo6bo2b2o$78b3o3bo3b2o$83bo19b2o$103b2o$42bo$43b2o$42b
2o33b2o16bo$77bo16bobo$78b3o14bo19bo$45bobo32bo34b3o$46b2o70bo$46bo50b
obo17bobo$96bo20bobo$96bo2bo18bo$93b2o2bobo$92bobo$92bo22bo$91b2o13b2o
8bo$106bo7b3o16b2o$99b2o6b3o23b2o$99b2o8bo3$113b2o$112bobo$112bo$111b
2o7b2o$120b2o2$128b2obo$128b2ob3o$134bo$128b2ob3o$127bo2b2o$72bo53bobo
$73b2o33bo16bobob2obo$72b2o34b3o15bo2bob2o$111bo17bo$110b2o16b2o$75bob
o47bobo2b2o$76b2o47b2o2bo2bo$76bo53b2o3$125b2o$105b2o18bo$106bo16bobo$
106bobo14b2o10bo$107b2o26b3o$138bo$121b2o14b2o$121b2o$115bo$116bo$115b
2o$108b2o16b2o5b2o$48bo14b2o42bo2b2ob2o11b2o5b2o$45b4o14b2o42bo4b4o29b
o$108b4o4bo13b2o11b2ob2o$112b4o14b2o14b5o$113b2o32bo2bo$48bobo96bo2bo$
49bo57b3o38b2o$47b2o58b2o16bo27b2o$47bo2bo20b2o29bo20b3o27b2o$46b2ob2o
20b2o30b2o6b4o7bo$102b2o8b4o7bo26b2o5b2o$111bob2obo5b2o3b2o21b2o5b2o$
111bobobo8b2o2bo$105bobo4b2o8b2o2b2o$106b2o5bo9bobo$106bo15bo2bo$123b
2o32b2o$157b2o3$166bo$165bobo$153bo12bo$39bobo112b2o$39b3o111b2o$39b2o
$162b2o$162b2o$42bo124b2o$40bobo124bobo$18bo21b3o126bo$15b4o24bo110b2o
13b2o$39b5o111bo$32b3o117b3o6b2o$152bo8b2o$18bobo12b2o$19bo13b2o$17b2o
13bo2bo$17bo2bo11bo99bo$16b2ob2o10b3o99b2o33bo$31b2o99b2o33b3o$34b2o
130bob3o$33bo2bo119bo8bo3bo$134b2o20b3o5bo3bo$31b2o101b2o23bo3b3obo$
31bo2bo123b2o4b3o$32b3o130bo$161bo$160bobo$156b2o2b2o$21b2o133b2o$21b
2o7$29b2o$29bo2$31bobo$32b2o$32bo2$146bo$146b2o$145bobo$162bo$163b2o
28bo15bo$162b2o25b4obo12b3o$189b3obobo10bo$171bobo20bobo9b2o$165bobo4b
2o21bo$166b2o4bo21b2o$166bo27b2o4bobo$194b2o4bobo17bo$200bo2bo15b3o$
201b2o15bob3o$157b2o58bo3bo$157b2o57bo3bo$215b3obo$216b3o$160b2o55bo$
160b2o51bo$212bobo$157b2o53b2o$157b2o57b2o$149b2o65bobo$150bo60b2o5bo$
150bobo58b2o5b2o$151b2o2$156b2obo$156b5o$157b4o$211b2o5b2o$157b3o23b2o
26b2o5bo$157b3o20bo3bo31bobo$158bo21b4o32b2o$176bo35b2o$174bobo5b4o26b
obo$175b2o5bo3bo26bo$168b2o15b2o$168b2o46b2o$216b2obo$165b2o53bo$165b
2o19b2o29bo$113bobo71b2o29bob2o$113bo2bo69bo33b2o$116b2o8bo41b2o$114bo
3b2o5bobo40b2o$116b2o6bob2o45b2o$106b2o5bo2bo6b2ob2o10b2o33b2o$105bobo
5bobo8bob2o10b2o$105bo19bobo$104b2o20bo4$175b2o$176bo$173b3o$173bo3$
74b2o23b2o72b2o2b2o$74b2o23bo73b2o2b2o9b2o5b2o$65b2o10b2o12b2o4bobo22b
2o48b2o6bo7b2o5b2o$65b2o10b3o10bo6b2o21bo2bo49bo7bo$77b2o10bo15bo13bo
11b2o40b2ob2ob2o10b2o32b2o$74b2o13bo13b4o12bo11b2o40b2o3bo12b2o32b2o$
74b2o13bo14bob2o11bo$90bo11bobob3o11bo2bo$91b2o11bob2o14b2o$99b2o2b4o
61b2o$98bobo4bo62b2o$98bo$97b2o65b2o5b2o$164b2o5b2o5$175b2o$176bo$173b
3o$173bo!

[Scorbie]

Here it is with one more semi-snark. This is a sawtooth with expansion factor 256; adding more semi-snarks would make the e.f. larger.

Whoops... My bad...

It's not "usually small"; the population is <= 691 for long stretches of time, but the set of such times does not have a limiting density.

Yeah... I had to learn that the hard way...

Thanks for kindly finishing the pattern and explaining things! Next time I would have to think before posting something stupid

[simsim314]

@Dean It's somewhat trivial modification of low expansion sawtooth, but the result is indeed pretty surprising.

I wonder if there is a way to control the density of the "highs" and "lows"? Say is there a sawtooth which is exactly half of the time in "small" state? If half is hard, at least some number which is not 0 nor 1.

[Dean Hickerson]

I wonder if there is a way to control the density of the "highs" and "lows"? Say is there a sawtooth which is exactly half of the time in "small" state? If half is hard, at least some number which is not 0 nor 1.

I was wondering that too, and I think I've figured out a way to get density between 0 and 1. I'm not sure about 1/2.

The pattern will have two parts, A and B, which use salvos to push and pull blocks on separate diagonals. The pushes and pulls all have the same distance, d.

Part A is just a sqrtgun: After sending out a push salvo, it waits for the return glider. When the glider arrives, A sends out another salvo and emits a glider toward part B. The n'th such glider is sent at time about 4dn^2.

Part B will include some circuitry that counts the gliders from part A (mod m). The n'th glider from A will turn part B on if n==0 (mod m), turn it off if n==1 (mod m), and leave it off if n==2, 3, ..., m-1 (mod m). When B is on, it alternately sends push and pull salvos toward its block, starting and ending with a push salvo. So each group of salvos ends up pushing the block a distance d. (We'll just delete any return gliders.) When B is off, it doesn't send anything.

Warning: In the computation that follows, it's entirely possible that I've made some errors, so someone should check the math.

Suppose the n'th glider from A turns B on, at time 4dn^2, and that the block is kn units from B at that time. (We'll solve for k later.) Then B starts sending salvos, gradually filling the space between it and its block. At time 4d(n+1)^2 ~ 4dn^2 + 8dn, the (n+1)'th glider from A turns B off, and the diagonal between B and its block starts to empty. It takes time 8kn to empty. At this point, B's block has been pushed to distance kn+d.

So from time 4dn^2 to time 4dn^2 + 8dn + 8kn the population is large, with the maximum being some constant times n. The population is small from time 4dn^2 + 8dn + 8kn to time 4d(n+m)^2 ~ 4dn^2 + 8dmn.

Now we just need to solve some equations to figure out the density of 'small' times:

First we solve for k: At time 4d(n+m)^2, B's block is at distance k(n+m), which must equal kn+d. So k=d/m.

Next, during the time from 4dn^2 to d(n+m)^2, the population is 'small' for a total time of about (4dn^2 + 8dmn) - (4dn^2 + 8dn + 8kn) = 8dmn - 8dn - 8kn = 8dn(m^2-m-1)/m. So the fraction of time when the population is small is (8dn(m^2-m-1)/m) / (8dmn) = (m^2-m-1)/m^2.

For m=2, the simplest case to design, the pattern is small 1/4 of the time. For m=3, it's small 5/9 of the time. The fraction gets closer to 1 as m increases.

So we don't get density 1/2 this way. But there are other variations, which I haven't analyzed yet; maybe one of them will work:

First, we could use salvos in B that don't send return gliders. That reduces the time for B's diagonal to empty from 8kn to 4kn, and increases the 'small' time fraction to (2m^2-2m-1)/(2m^2). (We still can't get 1/2 from this.)

Second, we could use different push distances in A and B. We know about 3-glider push salvos for part A with distances 1, 2, 5, and 10. For B we need both push and pull salvos with the same distance; offhand I know of such pairs for distances 1 and 5. Of course we could use larger salvos to get other distances.

Third, we could change the (mod m) behaviour of part B. E.g. the n'th glider could turn B on if n == 0 or 4 (mod 11) and turn it off if n == 2 or 7 (mod 11).

Fourth, maybe someone can think of a different design that gives other fractions.

--------------------------------------------------------------------------------

P.S. (4 hours later): More generally, suppose that A moves its block a distance d and B moves its block a distance e, and that the n'th glider from A turns B on if n == 0 (mod m), turns B off if n == r (mod m), and leaves it alone otherwise. Assume that at least one of B's salvos produces a return glider. Then the fraction of 'small' times is (dm^2-rdm-e)/(dm^2). More simply, the fraction of 'large' times is (rdm+e)/(dm^2). For this to be 1/2, we need e = dm(m-2r)/2. (If neither of B's salvos produces a return glider, then we need e = dm(m-2r).)

Using known salvos, the most practical solution may be d=2, e=5, m=5, r=2. This would use simsim314's push-2 with return glider and pull-5 with return glider, and chris_c's push-5 without return glider. But it's probably worthwhile to look for more salvos, including ones that don't produce return gliders. Here are the block (and blinker) moving salvos that I know about; any additions would be welcome:

Code: Select all

x = 302, y = 281, rule = B3/S23
15b2o18bo138b2o4b2o$16bo19b2o137bo5bo$15bo19b2o137bo5bo$15b2o157b2o4b
2o20bo$176bob2o23b2o$15b2o159b2obo22b2o$16bo149b2obo10b2o$15bo150bob2o
11bo$15b2o33bobo127bo$51b2o127b2o22bobo$15b2o34bo153b2o$16bo188bo3b3o$
15bo164b2o$15b2o163b2o$48bo4b2o$49b2o2b2o$48b2o26$202bobo$203b2o$203bo
$35bo$36b2o$6b2o27b2o139bob2o$7bo168b2obo$6bo167b2o28bobo$6b2o167bo29b
2o$45bobo126bo30bo$6b2o6bob2o28b2o126b2o$7bo6b2obo28bo129bob2o$6bo5b2o
162b2obo$6b2o5bo166b2o25bo$12bo168bo26bo$6b2o4b2o166bo25b3o$7bo5bo34bo
131b2o$6bo5bo36bo126bob2o$6b2o4b2o33b3o126b2obo$214b2o$214b2o2$48b2o$
48b2o20$35bo$36b2o$35b2o3$16b2o$17bo$16bo233bo$16b2o233bo$52bo113bob2o
79b3o$16b2o32bobo113b2obo$8b2obo5bo33b2o111b2o$8bob2o4bo148bo$16b2o
146bo88bo$164b2o12bob2o20bo51b2o$16b2o148bob2o8b2obo21b2o48b2o$17bo34b
o113b2obo6b2o24b2o$16bo36b2o2b2o111b2o5bo$16b2o34b2o3b2o112bo4bo34bobo
44bo$170bo5b2o27bobo4b2o45b2o9bo$170b2o5bo28b2o4bo45b2o11b2o$166bob2o
6bo29bo63b2o$166b2obo6b2o$212b2o$212b2o$276bo$277b2o2b2o$276b2o3b2o20$
167bob2o$167b2obo31bobo$165b2o36b2o$166bo36bo7bobo$35bo129bo46b2o50bo$
2b2obo30b2o127b2o11bob2o30bo52b2o$2bob2o29b2o120b2obo6bob2o7b2obo82b2o
24bobo$6b2o149bob2o6b2obo5b2o113b2o$6bo164b2o4bo113bo$7bo164bo3bo$6b2o
6bob2o153bo4b2o$2b2obo8b2obo153b2o4bo117bo$2bob2o6b2o153bob2o5bo119b2o
$2o11bo153b2obo5b2o36bo80b2o$o11bo202b2o83b2o$bo10b2o35bobo162b2o3b2o
79b2o$2o11bo36b2o167b2o$2b2obo6bo28bo8bo$2bob2o6b2o28b2o$41b2o$50b2o$
50b2o19$35bobo$36b2o$36bo12$158b2o6b2obo$159bo6bob2o$158bo5b2o4b2o$
158b2o4bo5bo$165bo5bo$158b2o4b2o4b2o6bob2o$159bo4bo5bo7b2obo21bo$56bo
101bo6bo5bo4b2o26bo$57b2o99b2o4b2o4b2o5bo24b3o$2b2obo50b2o106bo5bo5bo$
2bob2o152b2o5bo5bo4b2o$6b2o151bo4b2o4b2o5bo$6bo151bo7b2obo6bo$7bo150b
2o6bob2o6b2o$6b2o6bob2o210bobo$2b2obo8b2obo211b2o$2bob2o6b2o215bo$6b2o
5bo42bo165bo$6bo5bo44b2o164b2o$7bo4b2o42b2o164b2o5b2o$6b2o5bo215b2o$2b
2obo6bo$2bob2o6b2o10$71bo$72b2o$71b2o2$75b3o14$203bo$204bo$202b3o7$12b
2obo$12bob2o19bo97b2o6b2obo23b2o6b2obo$16b2o18b2o7bobo86bo6bob2o24bo6b
ob2o$16bo18b2o9b2o85bo5b2o4b2o21bo5b2o4b2o$17bo28bo86b2o4bo5bo22b2o4bo
5bo$16b2o122bo5bo28bo5bo$4b2obo4b2obo117b2o4b2o4b2o21b2o4b2o4b2o$4bob
2o4bob2o29b2o87bo4bo5bo14b2obo5bo4bo5bo57bo$16b2o27b2o86bo6bo5bo13bob
2o4bo6bo5bo48bo5bobo$16bo116b2o4b2o4b2o21b2o4b2o4b2o49bo5b2o$17bo121bo
5bo28bo5bo48b3o$16b2o115b2o5bo5bo21b2o5bo5bo$12b2obo118bo4b2o4b2o22bo
4b2o4b2o$12bob2o117bo7b2obo23bo7b2obo$133b2o6bob2o23b2o6bob2o13$247bob
o$248b2o$248bo4$244bo$245b2o2b2o$244b2o3b2o!

One way to do the counting (mod 5) is to have 2 LWSS guns facing each other, so that their outputs crash and form 2 gliders:

Code: Select all

x = 15, y = 4, rule = B3/S23
o2bo7bo2bo$4bo5bo$o3bo5bo3bo$b4o5b4o!

By deleting a LWSS from one gun or the other, we can change the location of the collisions, thereby incrementing or decrementing a counter, within limits. The output gliders can be used to control what happens next.

[simsim314]

I've also published push3r - together with pretty large amount of mess here.

Code: Select all

x = 31, y = 32, rule = LifeHistory
.C$2.C$3C15$20.C$12.C8.C$10.C.C6.3C$11.2C10$29.2C$29.2C!

Also checked what diogonal operations are available with 2 gliders, and it's pull 1, 3, 4 and pull5 with extra reflecting gliders:

Code: Select all

x = 81, y = 197, rule = LifeHistory
19$26.C$27.2C$26.2C5$28.C$29.C$27.3C4$37.2C$37.2C41$26.C$24.C.C$25.2C
2$31.C$32.C$30.3C11$40.2C$40.2C32$31.C$32.C$30.3C4$31.C$32.C$30.3C6$
40.2C$40.2C21$27.C$28.C$26.3C8$27.C$28.C$26.3C3$36.2C$36.2C!

-----

As for the design - I'm still struggling to understand it.

I was thinking what if we use parabolic sawtooth - but trigger it with returning glider (like your design but with parabolic sawtooth)? Wouldn't it make the "sawtooth teeth" which are linearly growing, being spread out in linearly distant intervals, thus making the system with constant density?

[Dean Hickerson]

I've also published push3r - together with pretty large amount of mess here.

Thanks; I'd missed that. I'm looking through the results now; it looks like we now have 2-glider and 3-glider pushes for all distances from 1 to 10 and pulls for all from 1 to 8. That gives a lot more possibilities for sqrtguns and sawtooths.

I was thinking what if we use parabolic sawtooth - but trigger it with returning glider (like your design but with parabolic sawtooth)? Wouldn't it make the "sawtooth teeth" which are linearly growing, being spread out in linearly distant intervals, thus making the system with constant density?

Excellent idea! With that design, the widths of the teeth depend on the period of the guns used for the tractor beams, so it should give more possibilities for the percentages of 'large population' and 'small population' times.

[Dean Hickerson]

I was thinking what if we use parabolic sawtooth - but trigger it with returning glider (like your design but with parabolic sawtooth)? Wouldn't it make the "sawtooth teeth" which are linearly growing, being spread out in linearly distant intervals, thus making the system with constant density?

It wasn't easy to make this work, but if I've computed correctly, the sawtooth pattern below has small population exactly half the time. This uses every second glider from a sqrtgun 10.1 to trigger a cycle of a p480 parabolic sawtooth (based on the original parabolic sawtooth).

This is intended as a proof of concept; obviously it could be compressed quite a bit, and the old p120 guns should be replaced by Simkin guns. (And if recent experience is any guide, someone will suggest a simpler solution which will make this obsolete.)

Code: Select all

x = 396, y = 667, rule = B3/S23
34b2o11b2o36b2o18b2o$34b2o11b2o35bo2bo17b2o$84bo$84bo$47bo36bobo$46bob
o35bobo$45bo3bo35bo20bo$16b2o27b5o54b2ob2o$16b2o26b2o3b2o$45b5o22b2o8b
2o3b2o14bo5bo$31b2obob2o8b3o23b2o8bo5bo$15b3o29bo55b2obob2o$15b3o13bo
5bo45bo3bo$84b3o$32b2ob2o71bo$34bo11bo58bo2bo$13b2o3b2o28b2o58bo$14b5o
28b3o54b2o$15b3o29b2o55bo$16bo31bo55bobo$47bobo22b3o13bo16b2o$31bo16b
2o21bo3bo10bobo$29b2o4b3o32bo5bo10b2o$30b2o2bo3bo32bo3bo29b2o3b2o$42b
2obob2o23b3o8bo21bo5bo$33bo5bo32b3o7b3o13bo$17bo15b2o3b2o2bo5bo6bo25b
5o12bobo5bo3bo$5b2o11b2o36b2o22b2o3b2o11b2o7b3o$5b2o10b2o24b2ob2o7b2o
24b5o$22bobo20bo35bo3bo$22b2o50b3o5bobo$23bo45bo3b2ob2o5bo$38b2o7b2o
18b2o4b2ob2o$11b2o3b2o20bo8bo20b2o3b5o54bo$13b3o8bobo12b3o6b3o11bobo7b
2o3b2o3b2o23b2o23b3o$12bo3bo8b2o7b2o5bo8bo4b2o6b2o17b2o23b2o26bo$13bob
o9bo9bo19bo7bo70b2o$2b2obob2o5bo20bobo9bo5bobo$36b2o8b2o5b2o$2bo5bo36b
2o13bobo13b2o$44b3o13b2o21bo$3b2ob2o5b2o30b2o3b2o9bo21bobo37b2o5b2o70b
2o$5bo7b2o9b4o18b2o35b2o38b2o5b2o70b2o$19b2o7bo11bo6bo26b2o118bo$19b2o
2b2o3bo12b2o19b4o8b2o51b2o63b3o3b2o5b2o$23b2o2bo12b2o19bo7b2o56b2o62bo
6b2o5b2o$61bo3b2o2b2o16b2o102b2o$62bo2b2o16b2o2b2o2b2o$8bo74b2o2bo2bob
o$2b3o4b2o78b3o47bo10b2o44bo$bo3bo2b2o79b2o46b3o10b2o42bo2bo$137b3o53b
o4bo3b2o$o5bo129bo3bo6b2o5b2o37bo2b2o4b2o$2o3b2o130b4o6b2o5b2o37b3o2b
2o$45bobo89b2obo$45b2o21bo$3bo11bobo16bo11bo21bobo$2bobo11b2o16b3o31b
2o$2bobo11bo20bo116b2o$3bo32b2o115bo2bo18b2o18b2o$25b2o127b2o19b2o$5b
3o17b2o42b2o$5b3o8b3o51bo83bo8bo7b2o5b2o$4bo3bo9bo51bobo8b2o69b2obo6bo
bo6b2o5b2o6bo$17bo6b2obo26bobo14b2o7bobo68bo3bo7bo21bo$3b2o3b2o15bobo
10b3o14b2o22b3o4b2ob3o62bo30b3o$26bo10bo3bo13bo22b3o4bo2b4o57bo3bo$25b
2o52b3o4b2o50b2o8bo4bo5bo$25b2o9bo5bo37bobo55b2o8b3o6b2ob2o$9b2o14b2o
9b2o3b2o38b2o74b2o$8bobo76b2o75b2o$10bo77b2o40bo33bobo$39bo47bo41bobo
34bo$38bobo29bo59bo20b2o13b2o$10bo27bobo11b2o17b2o79bo$40bo11b2o16b2o
77b3o6b2o$40bo108bo8b2o$37bo2bo92b2o$38b2o14b2o77b2o$7b3o44bo32b2o39b
2o$6bo3bo34bo6bobo4b3o25b2o38bobo$5bo5bo33bobo4b2o7bo7bo57bo$5bo5bo16b
2o18b2o10bo9bo55b2o13b2o$8bo17bo3bo17b2o18b3o70bo$6bo3bo9b2o3bo5bo16b
2o84b2o6b3o$7b3o10b2o2b2obo3bo8bo4bobo86b2o8bo$8bo16bo5bo9bo3bo$26bo3b
o5bo2b3o45bo$28b2o58b2o$8b2o77b2o$8b2o46b2o$55bobo$54b3o$54b2o100bo$
57b2o25bobo68bo$44b3o9b3o26b2o68b3o$46bo38bo$45bo$56b2o$56b2o2$26bo8bo
2bo$25bobo10bo22bo$18b2o3b2o3bo5b2o3bo2bo18b2o37bo$18b2o3b2o3bo4bobob
2o3b4o14bobo3b2o33b2o$23b2o3bo14b4o5b2o12b2o32b2o$25bobo5b2o8bo2bo5b2o
$26bo16b4o19bo$42b4o19bobo$42bo22bo2bo$66bo2bo$31bo67bo$29b4o33bo2bo
30bo$20b2o5b4ob2o9b2o21b2o30b3o$18bo2bo3bo3b2ob3o8b2o$17bo7bo3b2ob2o$
9b2o6bo6bo3b5o$9b2o6bo7b3o3bo14bo70bo$18bo2bo24b2o70b2o$20b2o23bobo69b
2o2$33bo$34b2o$33b2o91bo$114bobo8bo$115b2o8b3o$38b2o75bo$38b2o2$25b2o$
23bo2bo$14b2o6bo7b3o3bo$14b2o6bo6bo3b5o$22bo7bo3b2ob2o9b2o$23bo2bo3bo
3b2ob3o8b2o$25b2o5b4ob2o72b2o$34b4o69b2o2b2o2b2o$36bo70bobo2bo2b2o$
108b3o$109b2o24$160bo$161b2o$160b2o3$202b2o$202bo$200bobo$159bo40b2o$
160bo$158b3o4$177bo$178b2o$177b2o5$174bobo$175b2o$175bo4$179b2o$180b2o
$179bo16$328b2o$328b2o3$325b2o$325b2o2$328b2o$328b2o$336b2o$336bo$318b
o15bobo$149b2o166b3o14b2o$150b2o168bo$149bo168b2o$220bo27bo70bo$221b2o
25b3o$220b2o29bo$250b2o4$247b2o3bo$219bo19b2o6b3obob2o$220bo18b2o6b3o
4bo62b2o$218b3o29bo3bo62b2o$243bobo5b3o$243b2o6bo68b2o$320b2o3$266b2o
49b2o$266b2o49b2o2$263b2o5b2o$263b2o5b2o2$294bo$259bo34bobo$257bobo12b
2o8b2o10b2o$258b2o11bo2bo7bo$271bo8bobo$119b2o151bobo5b2o$120b2o150bob
o$119bo153bo$273bo20$93b2o$92b4o9b2o5b2o$91b3obo9b2o5b2o$92b3obo$93b3o
12b2o$94b2o12b2o139b2o$248bobo$248bo$247b2o$85b2o$85b2o192b2o$279b2o$
81b2o5b2o$81b2o5b2o3$348b2o$348b2o$92b2o$93bo$90b3o256bo$90bo257bobo$
347bo3bo$351bo$262b4o$261bo7b2o69b2o6bo2bo$261bo3b2o2b2o70bo6bo2bo$
262bo2b2o74bobo4b3o$342b2o2$368bo$314bo53b3o$313b2o47bo8bo$244bo68bobo
47bo6bobo$244b2o115b3o6bobo$243bobo125bo5$359b2o25b2o$359b2o25b2o2$
356b2o$356b2o$366b2o$365bobo$359b2o4bo$359b2o3b2o7b2o$372bo2bo$372bo$
371b3o7b2obo$371b2o8b2ob3o$374b2o11bo$373bo2bo4b2ob3o$380bo2b2o$371b2o
6bobo$361bo9bo2bo3bobob2obo$361b3o8b3o4bo2bob2o$364bo17bo$363b2o16b2o$
344bo33bobo2b2o$343b2o33b2o2bo2bo$214bo128bobo37b2o$214b2o$213bobo$
317bo$315b3o$314bo$314b2o$383b2o$383b2o3$318b2o5b2o$307bo10b2o5b2o$
307b2o$302b2o2bobo12b2o$301bobo17b2o$301bo$301b2obo63b2o$303b2o63b2o$
298b2o$298b2o2$294b2o5b2o$294b2o5b2o7$184bo$184b2o$183bobo3$297bobo$
297b2o$298bo18$284b2o$284b2o3$128b2o$128b2obo22bo$132bo21b2o$129bo23bo
bo$130bob2o$132b2o$267bobo$136bo130b2o$135bobo130bo$136b2o$132b2o$131b
obo$131bo5b2o$130b2o5b2o18$124bo$124b2o$123bobo3$237bobo$237b2o$238bo
7$298bo$298b3o$301bo$300b2o5$289b2o5b2o11bo$289b2o5b2o9b3o$97b3o10b2o
5b2o188bobo$97b2ob2o8b2o5b2o174b2o12bo$97b2ob2o191b2o$99b2o12b2o$113b
2o2$316b2o$316b2o$90b2o$90b2o221b2o5b2o$313b2o5b2o$86b2o5b2o$86b2o5b2o
4$311bo15b2ob2obo$97b2o213b2o12b2o2b2ob2o$98bo212b2o21bo42bo8b2o$95b3o
228b2o49b3o6b2o$95bo230b2o5b2o45bo$333b2o44b2o13b2o$192b2o5b2o125bo67b
o$192b2o5b2o125b2ob2o2b2o57bobo$327bob2ob2o58b2o$196b2o$196b2o187b2o$
385b2o3$219bo171bo$212b2o4bob2o168bobo$210b2o2bo3bob2o169b2o$210bo2b3o
3b3ob2o$210bo4bo4bobobo147b2o$211b5o4b4o149b2o7b2o$213b2o6b2o149bo9b2o
3$212b2o$212bo$213b3o$215bo4$341bo$342b2o$341b2o10$233b2o$215b2o16b2o
119b2o$215bobo45b2o89bobo$202bobo13bo7b2o35bo92bo$201bo2bo2b2o6bo2bo7b
2o27bo5bobo18b2o72b2o$200b2o5bobo8bo35bobo4b2o18bobo$192b2o4b2o3bo3bo
3bo3bobo16bo7b2o9bo3b2o24bo$174b2o16b2o6b2o5b3ob2o2b2o17bo7b2o9bo3b2o$
174b2o25bo2bo3b2o23bobo17bo3b2o$202bobo27b2ob2o17bobo$191bo39bo5bo17bo
$191bobo40bo$179b2o11bobo7bo15bo12b2o3b2o81b2o8bo$174bo4b2o11bo2bo6b2o
12bobo26bo73b2o6b3o$172b2ob2o15bobo2b2o4b2o12b2o26b3o78bo$191bobo3b2o
4b3o27b4o11bo62b2o13b2o$171bo5bo13bo5b2o4b2o27b2o2bo10b2o38b2o23bo$
202b2o7b2o19b2obo51b2o23bobo$171b2obob2o24bo8bobo36bo62b2o$213bo19b2o
14bobo66b2o$213b2o18bo14bo3bo65b2o$172bo75b5o81bo8b2o$172bo3bo70b2o3b
2o80b3o6b2o$172bo60b2obob2o8b5o34bo49bo$175b2ob2o53bo5bo9b3o34b3o26bo
20b2o13b2o$157b2o20bo54bo3bo11bo35b3o25bobo34bo$157b2o15bo18b2o40b3o
39b3o35bo23bo9bobo$174bo2b2o15bo82bo6b2o3b2o46b5o7b2o$194bobo5bo70bo4b
o5b2o3b2o42b2o5b2o$195b2o4bobo67b3o49b2o14bobo2b3o$169b2o3b2o24bob2o
10b2o54bo52b2o8bo4bo2b2obo$169bo5bo23b2ob2o10b2o54b2o62b2o4bob2o$182bo
17bob2o15bo27b2o37b2o49b5o$157bo12bo3bo5bobo18bobo15bobo26bo18bo69bobo
bo6bo$156b3o12b3o7b2o19bo16b2o14b2o8b3o19bo79bobo$155b5o66b2o7b2o8bo
22bo20b2o48bo8bo$154bobobobo61b2o2b2o2b2o57bo49bo$154b2o3b2o61b2o2bo2b
obo58b3o$228b3o34b2o3b2o20bo46b2o$169b2o7b2o48b2o35bo5bo67b2o$157bo12b
o3b2o2b2o2b2o$156bobo8b3o4bobo2bo2b2o33b2o19b2o26bo3bo$155b2obo8bo7b3o
8bo31bo19bo28b3o$155b3o18b2o8b2o30bobo7bo7bobo88b2o$154bo2bo27bobo31b
2o7b4o4b2o85b2o2b3o2b2o5b2o$154b3o72b4o89b2o4bobo2bo5b2o$153bo3bo10b4o
57bo2bo90bob2obo3bo$152bo5bo8bo7b2o52b4o32b2o57b2o3bo5b2o$153bo3bo3b2o
4bo3b2o2b2o51b4o34bo68b2o$154b3o4b2o5bo2b2o55bo34b3o$263bo2$312b2o$
312b2o$157b2o23bo17b2o$157bo24b3o15b2o106b2o5b2o$185bo122b2o5b2o$158b
2o24b2o75b2o$262b2o$261bo2$319b2o$155b2o3b2o158bo$155bo5bo155b3o$187bo
129bo$156bo3bo25b3o$157b3o25b5o$184b2o3b2o2$294b2o$294bo$186b3o95bo7bo
bo$186b3o92b4o7b2o$160bo112b2o5b4o24b2o$158b2ob2o13b2o95b2o5bo2bo24b2o
$176b2o8b2o92b4o7bo$157bo5bo22b2o93b4o4b2o$214bo69bo5b2o$157b2obob2o
48b4o$211bobob2o$194b2o14bo2bob3o90bo$194b2o15bobob2o90b3o$194b2o11b2o
3b4o8b2o81b3o$194bo11bobo5bo9bobo$173b2obob2o13bobo10bo19bo78b2o3b2o$
193bob2o7b3o19b2o77b2o3b2o$173bo5bo23bo$160b2o41b2o26b2o$160b2o12b2ob
2o15b2o5b3o28b2o$176bo17b2o4bobo28bo75b2o$199bo3bo7b2o$199b5o6bo2bo$
178bo19b2o3b2o5bo99b2o$177bobo19b5o6bo99bo$176bo3bo19b3o7bobo98b3o$
176b5o20bo8bobo100bo$175b2o3b2o29bo$176b5o15b2o$177b3o16bobo$178bo17bo
11b2o3b2o$208bo5bo2$209bo3bo3b2o$210b3o4b2o2$261bo$198b3o58b2o29bo$
197bo3bo58b2o28b2o$178b2o109bobo$178b2o16bo5bo$196b2o3b2o10bo$211b2ob
2o2$199bo10bo5bo$198bobo$198bobo9b2obob2o$200bo$200bo$197bo2bo$198b2o
3$240bo$239b2o$212b2o25bobo$212b2o50b2o$264bo$253b2o7bobo$246bob2o3b3o
6b2o$242bo2bo3bo5b2obo$241b2o2bo4bo4bo2bo30b2o$230b2o8b2o5b4o4b2obo30b
2o$230b2o7b3o7bo3b3o$240b2o11b2o$241b2o26b2o$242bo26b2o$260bo$260b2o7b
o$259bobo6bobo$268bo2bo$269bo2bo2$269bo2bo$269b2o4$241b2o$240bo3bo24b
2o$229b2o8bo5bo7bo15b2o$229b2o8bo3bob2o4bobo27bobo$239bo5bo3b2o22b3o5b
o3bo$240bo3bo4b2o17b2o2bo2bobo7bo$241b2o6b2o15bo2bo2b2o7bo4bo$251bobo
11bo19bo$253bo11bo10b3o2bo3bo3b2o$265bo15bobo5bobo$266bo2bo21bo$268b2o
21b2o!

In general, suppose we use every k'th glider from a sqrtgun with a push of distance d to trigger a cycle of a period P parabolic sawtooth with pushes of distance 1 and pulls of distance 3. The push salvo travels at speed c/4 and the tractor beam pulls the returning block at speed 3c/(P-12), so the total time for the n'th cycle of the parabolic sawtooth is about n/(1/4) + n/(3/(P-12)) = Pn/3. The n'th trigger glider arrives about gen 4d(kn)^2. So the gap between the n'th and (n+1)'th triggers is about 8 d k^2 n, and the fraction of time when the population is 'large' is (Pn/3)/(8 d k^2 n) = P/(24 d k^2). In the pattern above, P=480, k=2, and d=10, so the fraction is 1/2. (I tried but failed to use P=120, k=1, and d=10; with this design there wasn't enough time for the returning block's detector to toggle the gun that releases or suppresses pull salvos.)

--------------------------------------------------------------------------------

P.S.: If we were to replace the sqrtgun in this pattern by a caber tosser, we'd get a usually small sawtooth whose maximum populations grow logarithmically. (It would probably be pretty dull to watch...)

[Dean Hickerson]

This is intended as a proof of concept; obviously it could be compressed quite a bit, and the old p120 guns should be replaced by Simkin guns. (And if recent experience is any guide, someone will suggest a simpler solution which will make this obsolete.)

I thought of a better way. The pattern below has only one moving block, but it uses 2 different salvos: One is a push-10 (with return glider) salvo found by simsim314; the other is a push-0 (without return glider) salvo that I found. When the return glider from a push-10 salvo arrives, it triggers the release of the next push-10, as in previous sqrtguns. The push-0 gliders are controlled by a toggleable gun, which is toggled by 2/3 of the return gliders: One turns on the push-0 stream, the next turns it off, and the next one leaves it off. This leads to a population graph sort of like this; the r's indicate the times of the return gliders:

Code: Select all

                                       ______
           ____                       /      \
          /    \                     /        \
         /      \                   /          \
        /        \                 /            \
... ___/          \_______________/              \________ ...
       r       r        r         r          r

Since each push-10 salvo and return glider takes 80 gens longer than the preceding one, this works well with p240 guns: We don't need a separate mod 3 counter; we just use 3 guns that cross the stream to detect the 3 types of return gliders. (I used p120 guns for that, but half of their output is ignored.)

Here's the pattern; I'll add a more detailed header to this later.

Code: Select all

#C Sawtooth pattern whose population is small half the time
#C Dean Hickerson, 5/7/2016
x = 324, y = 265, rule = B3/S23
242bo$242b3o$245bo$244b2o6bo$251bobo$252bo3$239b2o$239b2o6b2o$247b2o$
22bo$22b3o231b2o$25bo230b2o$24b2o$241b2o$240bobo$240bo$239b2o$13b2o5b
2o$13b2o5b2o$173b2o$17b2o154b2o28bo$17b2o183bobo$202b2obo7b2o$190b2o
10b2ob2o6bobo$190b2o10b2obob3o6bo7b2o$40b2o131bo28bobo2bo2bo2bo2bo7b2o
18b2o5b2o$29b3o8b2o129b2ob2o27bo4b2o6bo27b2o5b2o$27b2ob4o101b2o76bobo$
8b2o17bo2b2o5b2o5b2o44bo11b2o31b2o33bo5bo36b2o33b2o19b2o$8b2o17b3o7b2o
5b2o43bobo10b2o144b2o19b2o$32bo48bo3b2o2bobo78b2obob2o67bo25bo$72b2o6b
obo2bo2b2ob2o39b2o108b3o21b4o$11b2o59b2o6bobo3bobo43b2o107bo23bo3bo$
11b2o19b2o47bob4o2bob2o114b2o32b2o22b3o$32bo11b2o19b2o16bo3bobob2o42b
2o70b2obo56b2o$8b2o35bo19bo16bo3bobo46b2o74bo57bo$8b2o35bobo7bobo5bobo
15bo3bobo55b2o63bo61bo4b2o$2o44b2o7bo3bo3b2o16b2o3bo56bo65bob2o56bo5b
2o$bo57bo81bobo67b2o$bobo51bo4bo63b3o14b2o$2b2o55bo65bo89bo27b2o$55bo
3bo34b2o29b3o86bobo26b2o$55bobo36b2o72b2o3b2o2b2o36b2o47b2o$109b2o57bo
5bo2bo33b2o51bo$108bo2bo98bobo52b3o$109b2obo56bo3bo36bo5b2o49bo$10b3o
49b2o48bo57b3o36b2o5b2o$10b2o50b2o48b2o131bo8b2o$11bobo83b2o146b3o6b2o
$13bo84bo149bo$14b2o79b3o149b2o13b2o$12bobo68b2o10bo28b2o136bo$12b2o5b
2o62bobo38b2o134bobo$19b2o64bo15b2o68b2o87b2o$42b2o41b2o15bo24b2o42b2o
$16b2o24bo59bobo22b2o124b2o$16b2o22bobo60b2o148b2o$40b2o$118b2o4b2o$
19b2o4b2o91b2o4b2o133bo$19b2o4b2o231bobo$223b3o33bo$34b2o65b2o120b3o$
34b2o6b2o57b2o5b2o113b3o$42b2o64b2o116b3o21b2o$226b3o21b2o$114bo64b2o
45b3o$30bo23b2o57bobo18bo11b2o31b2o$29bobo22b2o50b2o6bo18bobo10b2o83bo
$30bo6b2o68bo17bo3b2o2bobo94bobo$37bo66b3o9b2o6bobo2bo2b2ob2o39b2o53b
2o$38b3o63bo11b2o6bobo3bobo43b2o49b2o$40bo84bob4o2bob2o89bobo$127bo3bo
bob2o42b2o45bo5b2o$126bo3bobo47bo44b2o5b2o$125bo3bobo55b2o$125b2o3bo
56bo34bo$39b2o144bobo32b3o$39b2o144b2o32bo$219b2o7b2o5b2o$138b2o40bo
47b2o5b2o$138b2o36bo3bo$153b2o22bo2bo51b2o$152bo2bo21b2ob2o50b2o$153b
2obo21bobo36bo$39b2o65b2o48bo22bo36b3o$38bo2bo2b2o60b2o48b2o58b3o$39b
2o2bobo95b2o19b2o91b2o$41b2o16b2o81bo20bo50b2o3b2o18bo2b2o11b2o$41bo
17bo79b3o72b2o3b2o17b2o2b3o$38b2obo2bo15b3o64b2o10bo28b2o67b3o2b2o8b2o
5b2o$38bob2obobo16bo64bobo38b2o68b2o2b2o8b2o5b2o$42bobo84bo15b2o$39b2o
2bo85b2o15bo24b2o$37b3ob2o103bobo22b2o$36bo110b2o$37b3ob2o205b2o$39bob
2o119b2o4b2o47b2o29bo$162b2o4b2o47b2o30b3o$49b2o200bo$49b2o7b2o$58bo
86b2o$56bobo86b2o5b2o$56b2o94b2o2$158bo81bo$61bo8b2o85bobo80b3o$36b2o
23b3o6b2o78b2o6bo84bo$36b2o26bo86bo90b2o$63b2o13b2o68b3o$78bo69bo$76bo
bo$76b2o$52bo178b2o5bo65bo$51bobo15b2o160b2o4bo64b3o$51bobo15b2o167bo
62bo$52bo186b2o60b2o$53b3o184b3o$55bo19bo162bo3bo$74bobo161b4o63bo8b2o
$75bo161bo67b3o6b2o$237b2o19b2o48bo$237b2o19b2o47b2o13b2o$66b2o254bo$
66b2o187b2o5b2o56bobo$255b2o5b2o56b2o2$313b2o$54bo258b2o$49b3o7b2o5b2o
$49bo2b2o5b2o5b2o184b2o$49b2ob4o196bo66bo$51b3o8b2o254bobo$62b2o255bo
2$239b2o$239b2o69b2o$39b2o269b2o$39b2o2$35b2o5b2o$35b2o5b2o$303b2o5b2o
$303b2o5b2o2$306b2o$46b2o258b2o$47bo$44b3o$44bo$283b2o$283b2o11b4o$
300bo$279b2o5b2o8bo4bo$279b2o5b2o9b2obo$299bo4$290b2o$291bo$288b3o$
288bo3$259b2o5b2o$259b2o5b2o2$169bo7bo85b2o$170bo4bobo85b2o$168b3o5b2o
68b2o$247b2o$246bo$279b2o5b2o$168bo108bo8b2o$169b2o68b2o34b2o4b2o$168b
2o69b2o34bo6b2o6b2o$275bo2b2o2b3o5b2o$276bob2o4$279b2o$279bo$280b3o$
248bo33bo$247bo2bo$241b2o3bo4bo$241b2o4b2o2bo$245b2o2b3o$175b2o$175b2o
3$172b2o13b3o$172b2o15bo78b2o$188bo79b2o$175b2o$168b2o5b2o88b2o5b2o$
168bob2o93b2o5b2o$170b2o$168b2o$166b2o2$166bobo48b3o41b2o$167bo51bo41b
o$218bo43b3o$264bo$249b2o4b2o$249bo5b2o$158b2o35b2o50bobo$157bobo35b2o
50b2o$157bo$156b2o105bo$164b2o26b2o70bo$164b2o26b2o45b2o14b3o6bo$239b
2o14b2o3b3o$167b2o26b2o62bo$167b2o26b2o62bo$260bo$261bo$164b2o$164b2o
3$193b2o2$193b2o$272b2o$194bobo75bobo$178b2o15bo19b2o57bo$177bobo15bo
19b2o57b2o$177bo88b2o$176b2o88b2o$184b2o26b2o25b2o$184b2o26b2o25b2o22b
2o$263b2o$187b2o26b2o$187b2o26b2o$266b2o$266b2o$184b2o$184b2o2$217b3o$
219bo$218bo4$198b2o$197bobo4b3o$197bo6bo2bo$196b2o6bo2bo2$207bo$203bo
3bo$204bobo$205bo3$204b2o$204b2o!

And here's a population graph, starting around generation 5000000:

Code: Select all

x = 554, y = 522, rule = B3/S23
b3o2b5o3bo4b3o$o3bobo6b2o3bo3bo$4bobo7bo3bo2b2o$3bo3b3o4bo3bobobo10bo
170bo179bo$2bo7bo3bo3b2o2bo10bo170bo179bo$bo4bo3bo3bo3bo3bo10bo169b2o
178b2o$5o2b3o3b3o3b3o11bo169b2o178b2o$33bo169b2o178b2o$33bo169bobo177b
obo$33bo169bobo177bobo$33bo169bobo177bobo$33bo169bobo177bobo$33bo169bo
bo177bobo$33bo140b28obobo147b29obobo$33bo140bo26bobobo147bo27bobobo$
33bo140bo26bobobo147bo27bobobo$33bo140bo27b2obo147bo28b2obo$33bo140bo
27b2obo147bo28b2obo$33bo139bo28b2obo147bo28b2obo$33bo139bo28b2obo147bo
28b2obo$33bo139bo28b2obo147bo28b2obo$33bo139bo28b2obo147bo28b2obo$33bo
139bo28b2obo146bo29b2obo$33bo139bo28b2obo146bo29b2obo$33bo139bo28b2o2b
o145bo29b2o2bo$33bo139bo29bo2bo145bo30bo2bo$33bo139bo29bo2bo145bo30bo
2bo$33bo139bo29bo2bo145bo30bo2bo$33bo139bo29bo2bo145bo30bo2bo$33bo139b
o29bo2bo145bo30bo2bo$33bo139bo29bo2bo145bo30bo2bo$33bo138bo30bo2bo145b
o30bo2bo$33bo138bo30bo2bo145bo30bo2bo146bo$33bo138bo30bo2bo145bo30bo2b
o146bo$33bo138bo30bo2bo145bo30bo2bo146bo$33bo138bo33bo145bo33bo146bo$
33bo138bo33bo145bo33bo146bo$33bo138bo33bo144bo34bo145bo$33bo138bo33bo
144bo34bo145bo$33bo138bo33bo144bo34bo145bo$33bo138bo34bo143bo35bo144bo
$33bo138bo34bo143bo35bo144bo$33bo138bo34bo143bo35bo144bo$33bo138bo34bo
143bo35bo144bo$33bo138bo34bo143bo35bo144bo$33bo137bo35bo143bo35bo144bo
$33bo137bo35bo143bo35bo144bo$33bo137bo35bo143bo35bo144bo$33bo137bo35bo
143bo35bo144bo$33bo137bo35bo143bo35bo144bo$33bo137bo35bo143bo35bo144bo
$33bo137bo35bo143bo35bo144bo$33bo137bo35bo143bo35bo144bo$33bo137bo35bo
142bo36bo143bo$33bo137bo35bo142bo36bo143bo$33bo137bo35bo142bo36bo143bo
$33bo137bo35bo142bo36bo143bo$33bo137bo36bo141bo37bo142bo$33bo137bo36bo
141bo37bo142bo$33bo137bo36bo141bo37bo142bo$33bo137bo36bo141bo37bo142bo
$33bo136bo37bo141bo37bo142bo$33bo136bo37bo141bo37bo142bo$33bo136bo37bo
141bo37bo142bo$33bo136bo37bo141bo37bo142bo$33bo136bo37bo141bo37bo142bo
$33bo136bo37bo141bo37bo142bo$33bo136bo37bo141bo37bo142bo$33bo136bo37bo
141bo37bo142bo$33bo136bo37bo141bo37bo142bo$33bo136bo37bo140bo38bo141bo
$33bo136bo37bo140bo38bo141bo$33bo136bo37bo140bo38bo141bo$33bo136bo38bo
139bo39bo140bo$33bo136bo38bo139bo39bo140bo$33bo136bo38bo139bo39bo140bo
$33bo136bo38bo139bo39bo140bo$33bo136bo38bo139bo39bo140bo$33bo135bo39bo
139bo39bo140bo$33bo135bo39bo139bo39bo140bo$33bo135bo39bo139bo39bo140bo
$33bo135bo39bo139bo39bo140bo$33bo135bo39bo139bo39bo140bo$33bo135bo39bo
139bo39bo140bo$33bo135bo39bo139bo39bo140bo$33bo135bo39bo139bo39bo140bo
$33bo135bo39bo138bo40bo139bo$33bo135bo39bo138bo40bo139bo$33bo135bo39bo
138bo40bo139bo$33bo135bo39bo138bo40bo139bo$33bo135bo40bo137bo41bo138bo
$33bo135bo40bo137bo41bo138bo$33bo135bo40bo137bo41bo138bo$33bo135bo40bo
137bo41bo138bo$33bo134bo41bo137bo41bo138bo$33bo134bo41bo137bo41bo138bo
$33bo134bo41bo137bo41bo138bo$33bo134bo41bo137bo41bo138bo$33bo134bo41bo
137bo41bo138bo$33bo134bo41bo137bo41bo138bo$33bo134bo41bo137bo41bo138bo
$33bo134bo41bo137bo41bo138bo$33bo134bo41bo136bo42bo137bo$33bo134bo41bo
136bo42bo137bo$33bo134bo41bo136bo42bo137bo$33bo134bo41bo136bo42bo137bo
$33bo134bo42bo135bo43bo136bo$33bo134bo42bo135bo43bo136bo$33bo134bo42bo
135bo43bo136bo$33bo134bo42bo135bo43bo136bo$33bo134bo42bo135bo43bo136bo
$33bo133bo43bo135bo43bo136bo$33bo133bo43bo135bo43bo136bo$33bo133bo43bo
135bo43bo136bo$33bo133bo43bo135bo43bo136bo$33bo133bo43bo135bo43bo136bo
$33bo133bo43bo135bo43bo136bo$33bo133bo43bo135bo43bo136bo$33bo133bo43bo
135bo43bo136bo$33bo133bo43bo134bo44bo135bo$33bo133bo43bo134bo44bo135bo
$33bo133bo43bo134bo44bo135bo$33bo133bo44bo133bo45bo134bo$33bo133bo44bo
133bo45bo134bo$33bo133bo44bo133bo45bo134bo$33bo133bo44bo133bo45bo134bo
$33bo133bo44bo133bo45bo134bo$33bo132bo45bo133bo45bo134bo$33bo132bo45bo
133bo45bo134bo$33bo132bo45bo133bo45bo134bo$33bo132bo45bo133bo45bo134bo
$33bo132bo45bo133bo45bo134bo$33bo132bo45bo133bo45bo134bo$33bo132bo45bo
133bo45bo134bo$33bo132bo45bo133bo45bo134bo$33bo132bo45bo132bo46bo133bo
$33bo132bo45bo132bo46bo133bo$33bo132bo45bo132bo46bo133bo$33bo132bo45bo
132bo46bo133bo$33b2o131bo46bo131bo47bo132bo$33b2o131bo46bo131bo47bo
132bo$33b2o131bo46bo131bo47bo132bo$33b2o131bo46bo131bo47bo132bo$33b2o
130bo47bo131bo47bo132bo$33b2o130bo47bo131bo47bo132bo$33b2o130bo47bo
131bo47bo132bo$33b2o130bo47bo131bo47bo132bo$33b2o130bo47bo131bo47bo
132bo$33b2o130bo47bo131bo47bo132bo$33b2o130bo47bo131bo47bo132bo$33b2o
130bo47bo131bo47bo132bo$33b2o130bo47bo131bo47bo132bo$33b2o130bo47bo
130bo48bo131bo$33b2o130bo47bo130bo48bo131bo$33b2o130bo47bo130bo48bo
131bo$33bobo129bo48bo129bo49bo130bo$33bobo129bo48bo129bo49bo130bo$33bo
bo129bo48bo129bo49bo130bo$33bobo129bo48bo129bo49bo130bo$33bobo129bo48b
o129bo49bo130bo$33bobo128bo49bo129bo49bo130bo$33bobo128bo49bo129bo49bo
130bo$33bobo128bo49bo129bo49bo130bo$33bobo128bo49bo129bo49bo130bo$33bo
bo128bo49bo129bo49bo130bo$33bobo128bo49bo129bo49bo130bo$33bobo128bo49b
o129bo49bo130bo$33bobo128bo49bo129bo49bo130bo$33bobo128bo49bo128bo50bo
129bo$33bobo128bo49bo128bo50bo129bo$33bobo128bo49bo128bo50bo129bo$33bo
2bo127bo50bo127bo51bo128bo$33bo2bo127bo50bo127bo51bo128bo$33bo2bo127bo
50bo127bo51bo128bo$33bo2bo127bo50bo127bo51bo128bo$33bo2bo127bo50bo127b
o51bo128bo$33bo2bo126bo51bo127bo51bo128bo$33bo2bo126bo51bo127bo51bo
128bo$33bo2bo126bo51bo127bo51bo128bo$33bo2bo126bo51bo127bo51bo128bo$
33bo2bo126bo51bo127bo51bo128bo$33bo2bo126bo51bo127bo51bo128bo$33bo2bo
126bo51bo127bo51bo128bo$33bo2bo126bo51bo127bo51bo128bo$33bo2bo126bo51b
o126bo52bo127bo$33bo2bo126bo51bo126bo52bo127bo$33bo2bo126bo51bo126bo
52bo127bo$33bo2bo126bo51bo126bo52bo127bo$33bo3bo125bo52bo125bo53bo126b
o$33bo3bo125bo52bo125bo53bo126bo$33bo3bo125bo52bo125bo53bo126bo$33bo3b
o125bo52bo125bo53bo126bo$33bo3bo124bo53bo125bo53bo126bo$33bo3bo124bo
53bo125bo53bo126bo$33bo3bo124bo53bo125bo53bo126bo$33bo3bo124bo53bo125b
o53bo126bo$33bo3bo124bo53bo125bo53bo126bo$33bo3bo124bo53bo125bo53bo
126bo$33bo3bo124bo53bo125bo53bo126bo$33bo3bo124bo53bo125bo53bo126bo$
33bo3bo124bo53bo125bo53bo126bo$33bo3bo124bo53bo124bo54bo125bo$33bo3bo
124bo53bo124bo54bo125bo$33bo3bo124bo53bo124bo54bo125bo$33bo4bo123bo54b
o123bo55bo124bo$33bo4bo123bo54bo123bo55bo124bo$33bo4bo123bo54bo123bo
55bo124bo$33bo4bo123bo54bo123bo55bo124bo$33bo4bo123bo54bo123bo55bo124b
o$33bo4bo122bo55bo123bo55bo124bo$33bo4bo122bo55bo123bo55bo124bo$33bo4b
o122bo55bo123bo55bo124bo$33bo4bo122bo55bo123bo55bo124bo$33bo4bo122bo
55bo123bo55bo124bo$33bo4bo122bo55bo123bo55bo124bo$33bo4bo122bo55bo123b
o55bo124bo$33bo4bo122bo55bo123bo55bo124bo$33bo4bo122bo55bo122bo56bo
123bo$33bo4bo122bo55bo122bo56bo123bo$33bo4bo122bo55bo122bo56bo123bo$
33bo4bo122bo55bo122bo56bo123bo$33bo5bo121bo56bo121bo57bo122bo$33bo5bo
121bo56bo121bo57bo122bo$33bo5bo121bo56bo121bo57bo122bo$16b7o10bo5bo
121bo56bo121bo57bo122bo$19bo13bo5bo120bo57bo121bo57bo122bo$18bo14bo5bo
120bo57bo121bo57bo122bo$17bo15bo5bo120bo57bo121bo57bo122bo$16b7o10bo5b
o120bo57bo121bo57bo122bo$33bo5bo120bo57bo121bo57bo122bo$17b5o11bo5bo
120bo57bo121bo57bo122bo$16bo5bo10bo5bo120bo57bo121bo57bo122bo$16bo5bo
10bo5bo120bo57bo121bo57bo122bo$16bo5bo10bo5bo120bo57bo120bo58bo121bo$
17b5o11bo5bo120bo57bo120bo58bo121bo$33bo5bo120bo57bo120bo58bo121bo$33b
o5bo120bo57bo120bo58bo121bo$16bo5bo10bo6bo119bo58bo119bo59bo120bo$16b
7o10bo6bo119bo58bo119bo59bo120bo$16bo5bo10bo6bo119bo58bo119bo59bo120bo
$33bo6bo119bo58bo119bo59bo120bo$33bo6bo119bo58bo119bo59bo120bo$16bo16b
o6bo118bo59bo119bo59bo120bo$16bo16bo6bo118bo59bo119bo59bo120bo$16b7o
10bo6bo118bo59bo119bo59bo120bo$16bo16bo6bo118bo59bo119bo59bo120bo$16bo
16bo6bo118bo59bo119bo59bo120bo$33bo6bo118bo59bo119bo59bo120bo$17b6o10b
o6bo118bo59bo119bo59bo120bo$16bo2bo13bo6bo118bo59bo119bo59bo120bo$16bo
2bo13bo6bo118bo59bo118bo60bo119bo$16bo2bo13bo6bo118bo59bo118bo60bo119b
o$17b6o10bo6bo118bo59bo118bo60bo119bo$33bo7bo117bo60bo117bo61bo118bo$
22bo10bo7bo117bo60bo117bo61bo118bo$22bo10bo7bo117bo60bo117bo61bo118bo$
22bo10bo7bo117bo60bo117bo61bo118bo$22bo10bo7bo117bo60bo117bo61bo118bo$
16b7o10bo7bo116bo61bo117bo61bo118bo$33bo7bo116bo61bo117bo61bo118bo$16b
6o11bo7bo116bo61bo117bo61bo118bo$22bo10bo7bo116bo61bo117bo61bo118bo$
22bo10bo7bo116bo61bo117bo61bo118bo$22bo10bo7bo116bo61bo117bo61bo118bo$
16b6o11bo7bo116bo61bo117bo61bo118bo$33bo7bo116bo61bo117bo61bo118bo$17b
2o14bo7bo116bo61bo116bo62bo117bo$16bo2bo13bo7bo116bo61bo116bo62bo117bo
$16bo2bo13bo7bo116bo61bo116bo62bo117bo$16bo2bo13bo7bo116bo61bo116bo62b
o117bo$16b7o10bo8bo115bo62bo115bo63bo116bo$33bo8bo115bo62bo115bo63bo
116bo$17b5o11bo8bo115bo62bo115bo63bo116bo$16bo5bo10bo8bo115bo62bo115bo
63bo116bo$16bo5bo10bo8bo114bo63bo115bo63bo116bo$16bo5bo10bo8bo114bo63b
o115bo63bo116bo$17b5o11bo8bo114bo63bo115bo63bo116bo$33bo8bo114bo63bo
115bo63bo116bo$17b2o14bo8bo114bo63bo115bo63bo116bo$16bo2bo13bo8bo114bo
63bo115bo63bo116bo$16bo2bo13bo8bo114bo63bo115bo63bo116bo$16bo2bo13bo8b
o114bo63bo115bo63bo116bo$16b7o10bo8bo114bo63bo115bo63bo116bo$33bo8bo
114bo63bo114bo64bo115bo$33bo8bo114bo63bo114bo64bo115bo$33bo8bo114bo63b
o114bo64bo115bo$33bo9bo113bo64bo113bo65bo114bo$33bo9bo113bo64bo113bo
65bo114bo$33bo9bo113bo64bo113bo65bo114bo$33bo9bo113bo64bo113bo65bo114b
o$33bo9bo113bo64bo113bo65bo114bo$33bo9bo112bo65bo113bo65bo114bo$33bo9b
o112bo65bo113bo65bo114bo$33bo9bo112bo65bo113bo65bo114bo$33bo9bo112bo
65bo113bo65bo114bo$33bo9bo112bo65bo113bo65bo114bo$33bo9bo112bo65bo113b
o65bo114bo$33bo9bo112bo65bo113bo65bo114bo$33bo9bo112bo65bo113bo65bo
114bo$33bo9bo112bo65bo112bo66bo113bo$33bo9bo112bo65bo112bo66bo113bo$
33bo9bo112bo65bo112bo66bo113bo$33bo10bo111bo66bo111bo67bo112bo$33bo10b
o111bo66bo111bo67bo112bo$33bo10bo111bo66bo111bo67bo112bo$33bo10bo111bo
66bo111bo67bo112bo$33bo10bo111bo66bo111bo67bo112bo$33bo10bo110bo67bo
111bo67bo112bo$33bo10bo110bo67bo111bo67bo112bo$33bo10bo110bo67bo111bo
67bo112bo$33bo10bo110bo67bo111bo67bo112bo$33bo10bo110bo67bo111bo67bo
112bo$33bo10bo110bo67bo111bo67bo112bo$33bo10bo110bo67bo111bo67bo112bo$
33bo10bo110bo67bo111bo67bo112bo$33bo10bo110bo67bo110bo68bo111bo$33bo
10bo110bo67bo110bo68bo111bo$33bo10bo110bo67bo110bo68bo111bo$33bo10bo
110bo67bo110bo68bo111bo$33bo11bo109bo68bo109bo69bo110bo$33bo11bo109bo
68bo109bo69bo110bo$33bo11bo109bo68bo109bo69bo110bo$33bo11bo109bo68bo
109bo69bo110bo$33bo11bo108bo69bo109bo69bo110bo$33bo11bo108bo69bo109bo
69bo110bo$33bo11bo108bo69bo109bo69bo110bo$33bo11bo108bo69bo109bo69bo
110bo$33bo11bo108bo69bo109bo69bo110bo$33bo11bo108bo69bo109bo69bo110bo$
33bo11bo108bo69bo109bo69bo110bo$33bo11bo108bo69bo109bo69bo110bo$33bo
11bo108bo69bo109bo69bo110bo$33bo11bo108bo69bo108bo70bo109bo$33bo11bo
108bo69bo108bo70bo109bo$33bo11bo108bo69bo108bo70bo109bo$33bo12bo107bo
70bo107bo71bo108bo$33bo12bo107bo70bo107bo71bo108bo$33bo12bo107bo70bo
107bo71bo108bo$33bo12bo107bo70bo107bo71bo108bo$33bo12bo107bo70bo107bo
71bo108bo$33bo12bo106bo71bo107bo71bo108bo$33bo12bo106bo71bo107bo71bo
108bo$33bo12bo106bo71bo107bo71bo108bo$33bo12bo106bo71bo107bo71bo108bo$
33bo12bo106bo71bo107bo71bo108bo$33bo12bo106bo71bo107bo71bo108bo$33bo
12bo106bo71bo107bo71bo108bo$33bo12bo106bo71bo107bo71bo108bo$33bo12bo
106bo71bo106bo72bo107bo$33bo12bo106bo71bo106bo72bo107bo$33bo12bo106bo
71bo106bo72bo107bo$33bo12bo106bo71bo106bo72bo107bo$33bo13bo105bo72bo
105bo73bo106bo$33bo13bo105bo72bo105bo73bo106bo$33bo13bo105bo72bo105bo
73bo106bo$33bo13bo105bo72bo105bo73bo106bo$33bo13bo104bo73bo105bo73bo
106bo$33bo13bo104bo73bo105bo73bo106bo$33bo13bo104bo73bo105bo73bo106bo$
33bo13bo104bo73bo105bo73bo106bo$33bo13bo104bo73bo105bo73bo106bo$33bo
13bo104bo73bo105bo73bo106bo$33bo13bo104bo73bo105bo73bo106bo$33bo13bo
104bo73bo105bo73bo106bo$33bo13bo104bo73bo104bo74bo105bo$33bo13bo104bo
73bo104bo74bo105bo$33bo13bo104bo73bo104bo74bo105bo$33bo13bo104bo73bo
104bo74bo105bo$33bo14bo103bo74bo103bo75bo104bo$33bo14bo103bo74bo103bo
75bo104bo$33bo14bo103bo74bo103bo75bo104bo$33bo14bo103bo74bo103bo75bo
104bo$33bo14bo103bo74bo103bo75bo104bo$33bo14bo102bo75bo103bo75bo104bo$
33bo14bo102bo75bo103bo75bo104bo$33bo14bo102bo75bo103bo75bo104bo$33bo
14bo102bo75bo103bo75bo104bo$33bo14bo102bo75bo103bo75bo104bo$33bo14bo
102bo75bo103bo75bo104bo$33bo14bo102bo75bo103bo75bo104bo$33bo14bo102bo
75bo103bo75bo104bo$33bo14bo102bo75bo102bo76bo103bo$33bo14bo102bo75bo
102bo76bo103bo$33bo14bo102bo75bo102bo76bo103bo$33bo15bo101bo76bo101bo
77bo102bo$33bo15bo101bo76bo101bo77bo102bo$33bo15bo101bo76bo101bo77bo
102bo$33bo15bo101bo76bo101bo77bo102bo$33bo15bo101bo76bo101bo77bo102bo$
33bo15bo100bo77bo101bo77bo102bo$33bo15bo100bo77bo101bo77bo102bo$33bo
15bo100bo77bo101bo77bo102bo$33bo15bo100bo77bo101bo77bo102bo$33bo15bo
100bo77bo101bo77bo102bo$33bo15bo100bo77bo101bo77bo102bo$33bo15bo100bo
77bo101bo77bo102bo$33bo15bo100bo77bo101bo77bo102bo$33bo15bo100bo77bo
100bo78bo101bo$33bo15bo100bo77bo100bo78bo101bo$33bo15bo100bo77bo100bo
78bo101bo$33bo15bo100bo77bo100bo78bo101bo$33bo16bo99bo78bo99bo79bo100b
o$33bo16bo99bo78bo99bo79bo100bo$33bo16bo99bo78bo99bo79bo100bo$33bo16bo
99bo78bo99bo79bo100bo$33bo16bo98bo79bo99bo79bo100bo$33bo16bo98bo79bo
99bo79bo100bo$33bo16bo98bo79bo99bo79bo100bo$33bo16bo98bo79bo99bo79bo
100bo$33bo16bo98bo79bo99bo79bo100bo$33bo16bo98bo79bo99bo79bo100bo$33bo
16bo98bo79bo99bo79bo100bo$33bo16bo98bo79bo99bo79bo100bo$33bo16bo98bo
79bo99bo79bo100bo$33bo16bo98bo79bo98bo80bo99bo$33bo16bo98bo79bo98bo80b
o99bo$33bo16bo98bo79bo98bo80bo99bo$33bo17bo97bo80bo97bo81bo98bo$33bo
17bo97bo80bo97bo81bo98bo$33bo17bo97bo80bo97bo81bo98bo$33bo17bo97bo80bo
97bo81bo98bo$33bo17bo97bo80bo97bo81bo98bo$33bo17bo96bo81bo97bo81bo98bo
$33bo17bo96bo81bo97bo81bo98bo$33bo17bo96bo81bo97bo81bo98bo$33bo17bo96b
o81bo97bo81bo98bo$33bo17bo96bo81bo97bo81bo98bo$33bo17bo96bo81bo97bo81b
o98bo$33bo17bo96bo81bo97bo81bo98bo$33bo17bo96bo81bo97bo81bo98bo$33bo
17bo96bo81bo96bo82bo97bo$33bo17bo96bo81bo96bo82bo97bo$33bo17bo96bo81bo
96bo82bo97bo$33bo18bo95bo82bo95bo83bo96bo$33bo18bo95bo82bo95bo83bo96bo
$33bo18bo95bo82bo95bo83bo96bo$33bo18bo95bo82bo95bo83bo96bo$33bo18bo95b
o82bo95bo83bo96bo$33bo18bo94bo83bo95bo83bo96bo$33bo18bo94bo83bo95bo83b
o96bo$33bo18bo94bo83bo95bo83bo96bo$33bo18bo94bo83bo95bo83bo96bo$33bo
18bo94bo83bo95bo83bo96bo$33bo18bo94bo83bo95bo83bo96bo$33bo18bo94bo83bo
95bo83bo96bo$33bo18bo94bo83bo95bo83bo96bo$33bo18bo94bo83bo94bo84bo95bo
$33bo18bo94bo83bo94bo84bo95bo$33bo18bo94bo83bo94bo84bo95bo$33bo18bo94b
o83bo94bo84bo95bo$33bo19bo93bo84bo93bo85bo94bo$33bo19bo93bo84bo93bo85b
o94bo$33bo19bo93bo84bo93bo85bo94bo$33bo19bo93bo84bo93bo85bo94bo$33bo
19bo92bo85bo93bo85bo94bo$33bo19bo92bo85bo93bo85bo94bo$33bo19bo92bo85bo
93bo85bo94bo$33bo19bo92bo85bo93bo85bo94bo$33bo19bo92bo85bo93bo85bo94bo
$33bo19bo92bo85bo93bo85bo94bo$33bo19bo92bo85bo93bo85bo94bo$33bo19bo92b
o85bo93bo85bo94bo$33bo19bo92bo85bo93bo85bo94bo$33bo19bo92bo85bo92bo86b
o93bo$33bo19bo92bo86bo91bo86bo93bo$33bo19bo92bo86bo91bo86bo93bo$33bo
20bo91bo86bo91bo87bo92bo$33bo20bo91bo86bo91bo87bo92bo$33bo20bo91bo86bo
91bo87bo92bo$33bo20bo91bo86bo91bo87bo92bo$33bo20bo91bo86bo91bo87bo92bo
$33bo20bo90bo87bo91bo87bo92bo$33bo20bo90bo87bo91bo87bo92bo$33bo20bo90b
o87bo58bo32bo87bo92bo$33bo20bo90bo87bo58bo32bo87bo92bo$33bo20bo90bo87b
o58bo32bo87bo92bo$33bo20bo90bo87bo58bo32bo87bo92bo$33bo20bo90bo87bo58b
o32bo87bo92bo$33bo20bo90bo87bo58bo32bo87bo92bo$33bo20bo90bo87bo58bo31b
o88bo91bo$33bo20bo90bo87bo58bo31bo88bo91bo$33bo20bo90bo87bo58bo31bo88b
o91bo$33bo20bo90bo87bo58bo31bo88bo91bo$33bo20bo90bo87bo58b2o30bo88bo
91bo$33bo20bo88bobo87bo58b2o29b2o88bo90b2o$33bo20bo88bobo87bo58b2o29b
2o88bo90b2o$33bo20bo88b3o87bo58b2o29b2o88bo90b2o$33bo20bo29b30o29b2o
88bo29b31o29b2o88bo29b31o30b2o$33bo21bo28bo28bo29b2o89bo28bo29bo29b2o
89bo28bo29bo30b2o$33bo21bo28bo28bo29b2o89bo28bo29bo29b2o89bo28bo29bo
30b2o$33bo21bo27bo29bo29b2o89bo27bo30bo29b2o89bo28bo29bo30b2o$33bo21bo
27bo29bo29bo90bo27bo30bo29bo90bo28bo29bo30bo$33bo21b29o29b31o90b29o30b
29obo90b30o29b30obo$33bo108b2o177bobo178bobo$33bo108b2o178bo180bo$33bo
108b2o178bo180bo$33bo108b2o178bo180bo$33bo108b2o178bo180bo$33bo108b2o
178bo180bo$3bo3b5o2b3o5bo10bo109bo178bo180bo$2b2o3bo5bo3bo3b2o10bo109b
o178bo180bo$3bo3bo5bo3bo2bobo10bo109bo178bo180bo$3bo4b3o3b4obo2bo10bo
109bo178bo180bo$3bo7bo5bob5o9b501o$3bo3bo3bo5bo4bo$2b3o3b3o3b3o5bo8$
12b5o2b3o2b5o3bo3b5o2b3o3b3o164b3o2b5obo3bob5ob4o3b3o2b5o2b3o3b3o2bo3b
o10bo33b3o5bo3b3o4bo5bo4bo164b5o2b3o3b3o4bo3b5o2b3o3b3o$12bo5bo3bobo6b
2o7bobo5bo3bo162bo3bobo5b2o2bobo5bo3bobo3bo3bo5bo3bo3bob2o2bo9bo11bo
21bo3bo3b2o2bo3bo2bobo3b2o5bo163bo5bo3bobo3bo2b2o7bobo5bo3bo$12bo5bo2b
2obo7bo6bo2bo5bo2b2o162bo5bo5bobobobo5bo3bobo3bo3bo5bo3bo3bobobobo9bo
4b4ob5o2b3o2b4o2b5o5bo2bobo2bo2b2obo3bo3bo5bo163bo9bobo3bo3bo6bo2bo5bo
2b2o$13b3o2bobobo2b3o4bo5bo3b4o2bobobo162bo2b2ob3o3bo2b2ob3o3b4o2b5o3b
o5bo3bo3bobo2b2o9bo3bo7bo3bo3bobo3bo10bo2bo2bo2bobobo9bo5bo164b3o5bo3b
4o3bo5bo3b4o2bobobo$16bob2o2bo5bo3bo4bo4bo3bob2o2bo162bo3bobo5bo3bobo
5bo2bo2bo3bo3bo5bo3bo3bobo3bo9bo4b3o4bo3b5obo3bob5o3bo3b5ob2o2bo9bo5bo
167bo3bo7bo3bo4bo4bo3bob2o2bo$12bo3bobo3bobo3bo3bo3bo5bo3bobo3bo162bo
3bobo5bo3bobo5bo3bobo3bo3bo5bo3bo3bobo3bo9bo7bo3bo3bo5bo3bo8bo7bo2bo3b
o9bo5bo163bo3bo2bo8bo3bo3bo5bo3bobo3bo$13b3o3b3o3b3o3b3o2bo6b3o3b3o
164b3o2b5obo3bob5obo3bobo3bo3bo4b3o3b3o2bo3bo10bo2b4o5b2o2b4ob4o8b5o4b
o3b3o9b3o3bo165b3o2b5o2b3o3b3o2bo6b3o3b3o$305bo$305bo!

[simsim314]

Wow, Congrats!

This looks a bit artificial as the shooting gliders salvo is doing "None" operation, on the other hand sawtooth itself is somewhat "artificial" in the sense it only cares about the population graph (nothing has to be functional).

Looks like this design can bring any rational number density (you can chose how many 'skip' and how many 'shoot' operations are done pretty easily, (like by using an array of semi snarks). And we have 0, 1 density sawtooths - so it kinda wraps all the density options.