## Miscellaneous Discoveries in Other Cellular Automata

For discussion of other cellular automata.
83bismuth38
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### Re: Miscellaneous Discoveries in Other Cellular Automata

i have taken reply 100. also, to make this legitimate:

Code: Select all

x = 4, y = 3, rule = B2/S34V
obo$3bo$obo!

Code: Select all

x = 5, y = 5, rule = B2/S34H
2bo$4o$bob2o$2b2o$2b3o!


Code: Select all

x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!  No football of any dui mauris said that. wildmyron Posts: 1274 Joined: August 9th, 2013, 12:45 am ### Re: Miscellaneous Discoveries in Other Cellular Automata A p14 oscillator resulting from a dot catalysing a sparky reaction: Code: Select all x = 2, y = 6, rule = B2ck3aq4aek/S02c3j4r o2$o3$bo! The latest version of the 5S Project contains over 221,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki. toroidalet Posts: 1022 Joined: August 7th, 2016, 1:48 pm Location: my computer Contact: ### Re: Miscellaneous Discoveries in Other Cellular Automata 9c/48 diagonal puffer, anyone? Code: Select all x = 19, y = 19, rule = B36n7e/S23 5bo$4bobo$4bobo$5bo$b2o$o2bo$b2o5b3o$7bo2bo$6bo3bo$6bo2bo$6b3o4$16b3o$15bo2bo$14bo3bo$14bo2bo$14b3o!

"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

toroidalet
Posts: 1022
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### Re: Miscellaneous Discoveries in Other Cellular Automata

bump
c/4 ship in B35y/S23, smaller than the one in life:

Code: Select all

x = 9, y = 6, rule = B35y/S23
3o3b3o$3bobo2$4bo$b3ob3o$b2o3b2o!

(well, it's definitely more compact.)
Works in B34e5y7e/S23. Let's see if it becomes natural.
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

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

### Re: Miscellaneous Discoveries in Other Cellular Automata

Switcher:

Code: Select all

x = 114, y = 23, rule = B3/S2-i34n
21b2o49b2o$22bo49bo$22bobo45bobo$23b2o45b2o4$46bo$45bobo$45bo2bo$obo 39b2o2b2o24bo40bo$o2bo37b3o28b3o37b2o$obo39b2o2b2o24bo40bo$45bo2bo$45b obo$46bo4$23b2o45b2o$22bobo45bobo$22bo49bo$21b2o49b2o!

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

A for awesome
Posts: 1904
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### Re: Miscellaneous Discoveries in Other Cellular Automata

Variation on @AbhpzTa's infinite orthogonal speeds rule:

Code: Select all

x = 10, y = 31, rule = B2ci3aer4ai5-c6c/S2-kn3-cenq4-k5eiy6c
bo3bo$ob4o$bo3bo5$bo4bo$ob5o$bo4bo5$bo5bo$ob6o$bo5bo5$bo6bo$ob7o$bo6bo 5$bo7bo$ob8o$bo7bo!

Edit: A close call for an odd-speed rule:

Code: Select all

x = 23, y = 4, rule = B2c3ajr4i5-ay6c7/S123eknqr4etz56ac7
o$o2b19o$b3o18bo$3b19o!  Edit 2: Another interesting close call: Code: Select all x = 41, y = 3, rule = B2ci3acjry4eik5-ajny6c7e8/S123cenr4etz5-ij6ck78 o2b37o$4o36bo$o2b37o!  x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce A for awesome Posts: 1904 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Miscellaneous Discoveries in Other Cellular Automata All speeds of the form c/(2n+1), n > 3: Code: Select all x = 9, y = 31, rule = B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67 o3bo$4o$o3bo5$o4bo$5o$o4bo5$o5bo$6o$o5bo5$o6bo$7o$o6bo5$o7bo$8o$o7bo!  Now every c/n orthogonal speed is known to exist at the minimal period in a 2-state isotropic rule in the range-1 Moore neighborhood. Last edited by A for awesome on July 29th, 2017, 10:52 am, edited 1 time in total. x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Miscellaneous Discoveries in Other Cellular Automata A for awesome wrote:All speeds of the form c/(2n+1): Code: Select all x = 9, y = 31, rule = B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67 o3bo$4o$o3bo5$o4bo$5o$o4bo5$o5bo$6o$o5bo5$o6bo$7o$o6bo5$o7bo$8o$o7bo!  Now every c/n orthogonal speed is known to exist at the minimal period in a 2-state isotropic rule in the range-1 Moore neighborhood. Hah. Muziks collection is dead. Airy Clave White It Nay Code: Select all x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

wwei23
Posts: 939
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### Re: Miscellaneous Discoveries in Other Cellular Automata

Saka wrote:
A for awesome wrote:All speeds of the form c/(2n+1):

Code: Select all

x = 9, y = 31, rule = B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67
o3bo$4o$o3bo5$o4bo$5o$o4bo5$o5bo$6o$o5bo5$o6bo$7o$o6bo5$o7bo$8o$o7bo!

Now every c/n orthogonal speed is known to exist at the minimal period in a 2-state isotropic rule in the range-1 Moore neighborhood.
Wait until Muzik finds out.

muzik
Posts: 3511
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Location: Scotland

### Re: Miscellaneous Discoveries in Other Cellular Automata

A for awesome wrote:All speeds of the form c/(2n+1), n > 3:

Code: Select all

x = 9, y = 31, rule = B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67
o3bo$4o$o3bo5$o4bo$5o$o4bo5$o5bo$6o$o5bo5$o6bo$7o$o6bo5$o7bo$8o$o7bo!

Now every c/n orthogonal speed is known to exist at the minimal period in a 2-state isotropic rule in the range-1 Moore neighborhood.
Well isn't that sexy.

Not only does this decrease the massive mashup ruletable to just 3 rules, it also brings up the question: could a single non-mashup rule which has both the odd and even adjustable speed syringenterprises exist? Optional preferred extras would be having spaceships of speeds c/2, c/3 and c/5, and the ability to search said rule on Catagolue.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

wwei23
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### Re: Miscellaneous Discoveries in Other Cellular Automata

If B34w/S23 explodes, then why doesn't B34w5a/S23 explode?

toroidalet
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### Re: Miscellaneous Discoveries in Other Cellular Automata

wwei23 wrote:If B34w/S23 explodes, then why doesn't B34w5a/S23 explode?
Easy: B34w/S23 contains a dirty replicator:

Code: Select all

x = 9, y = 9, rule = B34w/S23
b3o$o3bo3$7bo$8bo$8bo$8bo$7bo!

In B34w5a/S23 it doesn't replicate.

Code: Select all

x = 9, y = 9, rule = B34w5a/S23
b3o$o3bo3$7bo$8bo$8bo$8bo$7bo!

Same reason why B34w/S236c doesn't explode even though S6c usually makes near-B3/S23 rules explode.

Code: Select all

x = 9, y = 9, rule = B34w/S236c
b3o$o3bo3$7bo$8bo$8bo$8bo$7bo!
Speaking of B34w/S236c, here's a p26:

Code: Select all

x = 18, y = 18, rule = B34w/S236c
6bobo$5b2o2bo$6bobo3$bo$3o2$obo13bo$bo13bobo2$15b3o$16bo3$9bobo$8bo2b
2o$9bobo!  Another p26: Code: Select all x = 12, y = 13, rule = B34w/S236c 3b2o$4bo$bo7bobo$o3bo3bob2o$bobo5bobo$2bo2$2bo$bobo5bobo$o3bo3bob2o$bo
7bobo$4bo$3b2o!


Code: Select all

x = 8, y = 8, rule = B34w/S236c
3o$bo4$7bo$6b2o$7bo!

10c/214 (5c/107) wave:

Code: Select all

x = 120, y = 120, rule = B34w/S236c
bo$2o$bo12$13b3o$14bo11$27bo$26b2o$27bo12$39b3o$40bo11$53bo$52b2o$53bo
12$65b3o$66bo11$79bo$78b2o$79bo12$91b3o$92bo11$105bo$104b2o$105bo12$117b3o$118bo!

p26 in a different rule:

Code: Select all

x = 20, y = 20, rule = B36n/S236c
15bo$7bobo5bo$6b2o2bo$7bobo$18b2o2$2bo$b3o2$bobo13bo$2bo13bobo2$16b3o$
17bo2$2o$10bobo$9bo2b2o$4bo5bobo$4bo!  "Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life." -Terry Pratchett muzik Posts: 3511 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Miscellaneous Discoveries in Other Cellular Automata I would argue that the rule posted actually simulates all speeds c/(2n+1), n > 2, since there exists a c/5 spaceship that looks pretty systematic in a phase different than what was posted above. Code: Select all x = 17, y = 7, rule = B2c3aj4nrt5i6c78_S1c23enr4aet5-iq67 15bo$8bo5bobo$bo5bobo4bobo$obo4bobo5bo$obo5bo6bo$bo6bo6bo$3o4b3o4b3o!  Here are natural c/5, c/7, c/9 and c/13 ships: Code: Select all x = 16, y = 16, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67 obboooboobobbobo$
bobboobbbobbbboo$boobbboobobobbob$
obobbbboobbbbobb$boobooboboooobbb$
bbbboboooobboooo$bobobobboboboobo$
boboobbobboooooo$bbbbbobboooooobo$
obbboooobboooooo$obobbbbooobobboo$
bboooooooobooooo$bbbbooooooobbbbb$
bbbobbobbobooobo$bbobbbboobbbbboo$
bbbbboobbobobooo!

Code: Select all

x = 16, y = 16, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
obobbbbobboobboo$obbooobboooooooo$
bbobboobooobbobb$obbbbbbbobboooob$
booobooboboobobb$bbooobbbboboboob$
obbbobobbboboboo$booooboooboobooo$
obbbobbbbbbooboo$bboboooooobooobb$
oobobobobbbbbboo$obbobobboobbbboo$
oooobboobbboobob$bobboooboboobbbo$
bbboooobbbboooob$obbbbbbooobobobb! Code: Select all x = 16, y = 16, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67 obbbbooboooobooo$
bbboooobbboooobo$oobooboooooboooo$
booboobbboobooob$ooobobobobbbobob$
oboooooooboboboo$ooooooboobbobbbo$
bobboobbobbobbob$obboboooobbobooo$
boboobbooboobboo$obbbooobobobbooo$
obooboobbboboboo$bbbooobooobobobo$
oboobobobboooobb$boboooobbbbooooo$
boboobboooobbobo!

Code: Select all

x = 16, y = 16, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
ooooooooooobbooo$oboboboobobobooo$
boobobobobbboobo$bbbboobobboboooo$
obbobobboobooobo$oooobboobobbbboo$
obbboooobbobobbo$oooboobobbbobooo$
oobooboobbbboboo$boobbobbooboboob$
bboboobbbbooobob$bbbobobooboobooo$
boooobooooboboob$obbbobbbbobbobbb$
bobbboobbobbobbo$bobooboobobbobbb! And a yl8: Code: Select all x = 16, y = 16, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67 bboboobooboobbbb$
bbbbbobbbboooboo$boboobbooooobbbb$
ooooooboboobbboo$bbobbbooooobobob$
obbboboooooboooo$bbooobbboobbbboo$
bbobbboobboooooo$obbooobbobbbbbbo$
bboboboobobboobo$bbbobbbbobbboboo$
bbobboooooboobbb$obobbbboobobobbo$
boooobbbbboooboo$bbbbbobbobbbbobo$
oobbbbobobobboob!
one of those sqrt growers things:

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bbbobboobooboobb$ooooobbbooboobbo$
obooobooooobbbbo$ooobbbboobooboob$
bbobbbobbobobbbo$bbbbobbboobbbbbo$
oooobbbbooobobob$bbbbbbbboboooobb$
booobooobbbobobb$boooooobbbobbbob$
obooooobobobobob$bobooobbbobobbob$
bbooboooooobbboo$bboboboobboooboo$
obbooboobboboobb$bobbbooboobbooob$
obbooboobboboobb$bboboboobboooboo$
bbooboooooobbboo$bobooobbbobobbob$
obooooobobobobob$boooooobbbobbbob$
booobooobbbobobb$bbbbbbbboboooobb$
oooobbbbooobobob$bbbbobbboobbbbbo$
bbobbbobbobobbbo$ooobbbboobooboob$
obooobooooobbbbo$ooooobbbooboobbo$
bbbobboobooboobb!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

wwei23
Posts: 939
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: Miscellaneous Discoveries in Other Cellular Automata

muzik wrote: one of those sqrt growers things:

Code: Select all

big soup
I thought that apgsearch made small soup not big soup.
Run this:

Code: Select all

x = 8, y = 8, rule = B34w/S23
3b3o$2bo3bo$bo5bo$o6bo$o6bo$o5bo$bo3bo$2b3o!  wwei23 Posts: 939 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe ### Re: Miscellaneous Discoveries in Other Cellular Automata Symbiosis P39: Code: Select all x = 12, y = 5, rule = Symbiosis 4.AB$2.B.B3.2A$B3A.A.AB.AB$3.A.A.3AB$5.A.A!  Symbiosis P54 predecessor based on the P39: Code: Select all x = 12, y = 12, rule = Symbiosis 4.AB$2.B.B3.2A$B3A.A.AB.AB$3.A.A.3AB$5.A.A6$7.A$7.B!  Last edited by wwei23 on July 29th, 2017, 8:19 pm, edited 1 time in total. toroidalet Posts: 1022 Joined: August 7th, 2016, 1:48 pm Location: my computer Contact: ### Re: Miscellaneous Discoveries in Other Cellular Automata wwei23 wrote: I thought that apgsearch made small soup not big soup. Run this: Code: Select all pattern  Observations do not necessitate a post like that. Apgsearch has several symmetries. Some feature the soup (containing 256 on/off cells) reflected or rotated superimposed on itself. That is where these bigger soups come from. The 3c/6 ship in B34w/S23 is well-known. Also, please post your symbiosis patterns in the symbiosis thread. I would also argue that a new thread be made for B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67 so it doesn't clog up this thread like its predecessor. The oscillators can be made smaller: Code: Select all x = 11, y = 5, rule = Symbiosis 7.B$2.B.B3.A$B3A.A.AB$3.A.A.3AB$5.A.A!  Code: Select all x = 11, y = 12, rule = Symbiosis 7.B$2.B.B3.A$B3A.A.AB$3.A.A.3AB$5.A.A6$7.A$7.B!  "Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life." -Terry Pratchett AforAmpere Posts: 1050 Joined: July 1st, 2016, 3:58 pm ### Re: Miscellaneous Discoveries in Other Cellular Automata First knightship in a B2a rule? (2,1)c/7 Code: Select all x = 2, y = 5, rule = B2ain3aceny4-aeirz5jknry6aek8/S02n3c4kry5inr6i o2$bo2$bo!  I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule - Finish a rule with ships with period >= f_e_0(n) (in progress) wwei23 Posts: 939 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe ### Re: Miscellaneous Discoveries in Other Cellular Automata I wonder what this will do: Code: Select all x = 1, y = 1, rule = 23/03/3 A!  AforAmpere Posts: 1050 Joined: July 1st, 2016, 3:58 pm ### Re: Miscellaneous Discoveries in Other Cellular Automata 4c/7! Finally, I think this is the second velocity between c and c/2 that is not a 2c/3. Can someone confirm this? Code: Select all x = 4, y = 1, rule = B2-ek3ack4acrtw5eijk6-in7/S03ei4aj5eijq6k 2obo!  I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule - Finish a rule with ships with period >= f_e_0(n) (in progress) wwei23 Posts: 939 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe ### Re: Miscellaneous Discoveries in Other Cellular Automata drc wrote:Potential p652 in a rule that borders on explosive, but doesn't explode Code: Select all x = 3, y = 4, rule = B3_S235e 2o$b2o$2o$o!

What's with all the small lakes? Also, why do the honey farms have tubs in the middle?

Gamedziner
Posts: 796
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Miscellaneous Discoveries in Other Cellular Automata

wwei23 wrote:What's with all the small lakes? Also, why do the honey farms have tubs in the middle?
For the honey farms, the interaction that destroys the tub cannot occur here due to s5e. Interestingly, this interaction only occurs once (between T = 11 and T = 12 in the code below) for both tub destruction and usage of s5e.

Code: Select all

x = 5, y = 5, rule = B3_S235e
2bo$b3o$o3bo$b3o$2bo!

Code: Select all

x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27. A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!  A for awesome Posts: 1904 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Miscellaneous Discoveries in Other Cellular Automata AforAmpere wrote:First knightship in a B2a rule? (2,1)c/7 Code: Select all x = 2, y = 5, rule = B2ain3aceny4-aeirz5jknry6aek8/S02n3c4kry5inr6i o2$bo2$bo!  This is really interesting! I don't know of any others, but I feel like a p5 knightship might be possible in Live Free or Die (based on preliminary JLS searches, although I may not be remembering correctly). AforAmpere wrote:4c/7! Finally, I think this is the second velocity between c and c/2 that is not a 2c/3. Can someone confirm this? Code: Select all x = 4, y = 1, rule = B2-ek3ack4acrtw5eijk6-in7/S03ei4aj5eijq6k 2obo!  I know of two others, both in B0 rules (5c/8 orthogonal and 3c/4 diagonal, although I don't remember where I saw the former). I feel like I've seen a 3c/4 or a 3c/5 somewhere before, too, but I don't remember for sure. Anyway, that's a pretty good discovery, and definitely the smallest possible example of such a velocity. A puffer: Code: Select all x = 4, y = 11, rule = B2-ek3ack4acrtw5eijk6-in7/S03ei4aj5eijq6k 3o$2b2o$3o8$2obo!

EDIT: Here's a 3c/4 puffer:

Code: Select all

x = 11, y = 7, rule = B2-ek3ak/S03j4in
3b2ob2o$2b2o3b2o$b2o5b2o$2b2o3b2o$b2obobob2o$4bobo$o9bo!

x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

Apple Bottom
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Contact:

### Re: Miscellaneous Discoveries in Other Cellular Automata

toroidalet wrote:I would also argue that a new thread be made for B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67 so it doesn't clog up this thread like its predecessor.
Good idea; here it is.
If you speak, your speech must be better than your silence would have been. — Arabian proverb

Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_

Proud member of the Pattern Raiders!

AforAmpere
Posts: 1050
Joined: July 1st, 2016, 3:58 pm

### Re: Miscellaneous Discoveries in Other Cellular Automata

This is the only 3c/5 that I know of, found by Wildmyron, but first identified by me (it was found using Wildmyron's script).

Code: Select all

x = 3, y = 3, rule = B2-ek3-ijn4-cjkn5-aqry6en7c8/S02ain3ceiqr4jqw5-ak6an
2bo$o$2bo!
Where did that 3c/4 puffer come from?
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

muzik
Posts: 3511
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Miscellaneous Discoveries in Other Cellular Automata

Apple Bottom wrote:
toroidalet wrote:I would also argue that a new thread be made for B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67 so it doesn't clog up this thread like its predecessor.
Good idea; here it is.
...and the other "it".
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!