## All directions and infinite speeds

For discussion of other cellular automata.
toroidalet
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### Re: All directions and infinite speeds

Interesting tagalong:

Code: Select all

x = 15, y = 4, rule = All_Speeds
.ED$14.E2$E2.C8.E!

"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

A for awesome
Posts: 1997
Joined: September 13th, 2014, 5:36 pm
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### Re: All directions and infinite speeds

Weird:

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x = 27, y = 12, rule = All_Speeds
19.E$5.E12.3E$2.E3.E14.E$3.E.E14.B$3.2E$2.E.A20.E$3.2E4.B3.D3.E6.E.E$3.E12.E.E6.E$.E2.ED5.A3.E$E3.E10.E$.E2.D2.D2.D3.E$.E12.E!  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 Ethanagor Posts: 80 Joined: March 15th, 2017, 7:34 pm Location: the Milky Way galaxy ### Re: All directions and infinite speeds I threw together some simple icons for the first four states. The written direction is that in which the cell travels, while the arrow is the direction in which it pushes a cell of state 5. To use these, just paste the whole mess at the bottom of the rule. Code: Select all @ICONS XPM /* width height num_colors chars_per_pixel */ "31 155 2 1" /* colors */ "A c #FFFFFF" ". c #0000FF" /* icon for state 1 */ "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAA.AAAA...AA...AA.....AAAAAA" "AAAAA.AAAA.AAAA.AAAAAA.AAAAAAAA" "AAAAA.AAAA..AAA..AAAAA.AAAAAAAA" "AAAAA.AAAA.AAAA.AAAAAA.AAAAAAAA" "AAAAA...AA...AA.AAAAAA.AAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAA.AAAAAAAAAAAAAAAA" "AAAAAAAAAAAAA...AAAAAAAAAAAAAAA" "AAAAAAAAAAAA.....AAAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAA.........AAAAAAAAAAAA" "AAAAAAAAA...........AAAAAAAAAAA" "AAAAAAAA.............AAAAAAAAAA" "AAAAAAA...............AAAAAAAAA" "AAAAAA.................AAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAA.......AAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" /* icon for state 2 */ "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AA....AAA.AAA...AAA.AA.AA.....A" "AA.AAA.AA.AA.AAAAAA.AA.AAAA.AAA" "AA....AAA.AA.AA..AA....AAAA.AAA" "AA.AAA.AA.AA.AAA.AA.AA.AAAA.AAA" "AA.AAA.AA.AAA...AAA.AA.AAAA.AAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA.AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAA...AAAAAAAAAAAAAA" "AAAAAAAAAAAAA.....AAAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAA.........AAAAAAAAAAA" "AAAAAAAAAA...........AAAAAAAAAA" "AAAAAAAAA.............AAAAAAAAA" "AAAAAAAA...............AAAAAAAA" "AAAAAAA.................AAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAA.......AAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" /* icon for state 3 */ "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAA.AAAA...AA...AA.....AAAAAA" "AAAAA.AAAA.AAAA.AAAAAA.AAAAAAAA" "AAAAA.AAAA..AAA..AAAAA.AAAAAAAA" "AAAAA.AAAA.AAAA.AAAAAA.AAAAAAAA" "AAAAA...AA...AA.AAAAAA.AAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAA..............AAAAAAAAA" "AAAAAAAAA.............AAAAAAAAA" "AAAAAAAAAA............AAAAAAAAA" "AAAAAAAAAAA...........AAAAAAAAA" "AAAAAAAAAAAA..........AAAAAAAAA" "AAAAAAAAAAA...........AAAAAAAAA" "AAAAAAAAAA............AAAAAAAAA" "AAAAAAAAA.............AAAAAAAAA" "AAAAAAAA..............AAAAAAAAA" "AAAAAAA...............AAAAAAAAA" "AAAAAA..........AA....AAAAAAAAA" "AAAAAAA........AAAA...AAAAAAAAA" "AAAAAAAA......AAAAAA..AAAAAAAAA" "AAAAAAAAA....AAAAAAAA.AAAAAAAAA" "AAAAAAAAAA..AAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" /* icon for state 4 */ "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AA....AAA.AAA...AAA.AA.AA.....A" "AA.AAA.AA.AA.AAAAAA.AA.AAAA.AAA" "AA....AAA.AA.AA..AA....AAAA.AAA" "AA.AAA.AA.AA.AAA.AA.AA.AAAA.AAA" "AA.AAA.AA.AAA...AAA.AA.AAAA.AAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAA..............AAAAAAAAA" "AAAAAAAAA.............AAAAAAAAA" "AAAAAAAAAA............AAAAAAAAA" "AAAAAAAAAAA...........AAAAAAAAA" "AAAAAAAAAAAA..........AAAAAAAAA" "AAAAAAAAAAA...........AAAAAAAAA" "AAAAAAAAAA............AAAAAAAAA" "AAAAAAAAA.............AAAAAAAAA" "AAAAAAAA..............AAAAAAAAA" "AAAAAAA...............AAAAAAAAA" "AAAAAA..........AA....AAAAAAAAA" "AAAAAAA........AAAA...AAAAAAAAA" "AAAAAAAA......AAAAAA..AAAAAAAAA" "AAAAAAAAA....AAAAAAAA.AAAAAAAAA" "AAAAAAAAAA..AAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" /* icon for state 5 */ "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA" XPM /* width height num_colors chars_per_pixel */ "15 75 2 1" /* colors */ "A c #FFFFFF" ". c #000000" /* icon for state 1 */ "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAA.AAAAAAA" "AAAAAA...AAAAAA" "AAAAA.....AAAAA" "AAAA.......AAAA" "AAA.........AAA" "AA...........AA" "AAAAA.....AAAAA" "AAAAA.....AAAAA" "AAAAA.....AAAAA" "AAAAA.....AAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" /* icon for state 2 */ "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAA.AAAAAAA" "AAAAAA...AAAAAA" "AAAAA.....AAAAA" "AAAA.......AAAA" "AAA.........AAA" "AA...........AA" "AAAAA.....AAAAA" "AAAAA.....AAAAA" "AAAAA.....AAAAA" "AAAAA.....AAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" /* icon for state 3 */ "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAA.......AAA" "AAAAAA......AAA" "AAAAAA......AAA" "AAAAA.......AAA" "AAAA........AAA" "AAA......A..AAA" "AAAA....AAA.AAA" "AAAAA..AAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" /* icon for state 4 */ "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAA.......AAA" "AAAAAA......AAA" "AAAAAA......AAA" "AAAAA.......AAA" "AAAA........AAA" "AAA......A..AAA" "AAAA....AAA.AAA" "AAAAA..AAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" /* icon for state 5 */ "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" "AAAAAAAAAAAAAAA" XPM /* width height num_colors chars_per_pixel */ "7 35 2 1" /* colors */ "A c #FFFFFF" ". c #000000" /* icon for state 1 */ "AAAAAAA" "AAA.AAA" "AA...AA" "A.....A" "AAA.AAA" "AAA.AAA" "AAAAAAA" /* icon for state 2 */ "AAAAAAA" "AAA.AAA" "AA...AA" "A.....A" "AAA.AAA" "AAA.AAA" "AAAAAAA" /* icon for state 3 */ "AAAAAAA" "AA....A" "AAA...A" "AA....A" "A...A.A" "AA.AAAA" "AAAAAAA" /* icon for state 4 */ "AAAAAAA" "AA....A" "AAA...A" "AA....A" "A...A.A" "AA.AAAA" "AAAAAAA" /* icon for state 5 */ "AAAAAAA" "AAAAAAA" "AAAAAAA" "AAAAAAA" "AAAAAAA" "AAAAAAA" "AAAAAAA" "It's not easy having a good time. Even smiling makes my face ache." - Frank N. Furter wwei23 Posts: 950 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe ### Re: All directions and infinite speeds Breeder: Code: Select all x = 23, y = 4, rule = All_Speeds 2E$6.B6.2E$9.E9.B$22.E!


wwei23
Posts: 950
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: All directions and infinite speeds

Smallest still lives:

Code: Select all

x = 13, y = 44, rule = All_Speeds
E10$E$.E9$E.E$.E9$E.E7.E.E$.E9.E$2.E8.E8$2.E7.E.E$.E9.E$2E9.E$.E10.E!  muzik Posts: 3775 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: All directions and infinite speeds You could almost make a caterpillar out of this: Code: Select all x = 27, y = 12, rule = All_Speeds 12.E$26.E8$E$3.D$7.E!  Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! wwei23 Posts: 950 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe ### Re: All directions and infinite speeds AforAmpere wrote: Or a 2c/3 orthogonal ship, the fastest orthogonal speed in this rule: Code: Select all x = 6, y = 2, rule = All_Speeds E.AB$5.E!

EDIT:
Accidentally put my comment in the quotes.
The "pusher cells" move at lightspeed, making c the fastest possible. Also, elusive left-travelers possible by this mech.

83bismuth38
Posts: 461
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...
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### Re: All directions and infinite speeds

lol, this is why i like to click randomly:

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x = 25, y = 33, rule = All_Speeds
11.E$10.E$9.2E7.E.E$19.E3.E$19.E5$11.E4.A2.E2$4.E$E2.E$.E.E19.DE$.E 10.E.C$3.E7.E7.E$9.E.E6.E$6.E.E3.E.B2.2E$8.E.A7$11.E.AB$17.E$9.E$8.E 10.E$6.E.E$8.E3.E2.G.E$9.E.E4.E2.E$11.E4.E!  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.

83bismuth38
Posts: 461
Joined: March 2nd, 2017, 4:23 pm
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### Re: All directions and infinite speeds

easy obique gun:

Code: Select all

x = 9, y = 5, rule = All_Speeds
3.E$E.E.D$2.E5.E$5.E.E$7.E!

Code: Select all

x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!  No football of any dui mauris said that. Saka Posts: 3207 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X Contact: ### Re: All directions and infinite speeds 83bismuth38 wrote:easy obique gun: Code: Select all x = 9, y = 5, rule = All_Speeds 3.E$E.E.D$2.E5.E$5.E.E$7.E! It shoots diagonals. Code: Select all x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

83bismuth38
Posts: 461
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...
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### Re: All directions and infinite speeds

oops... it's hard for me to tell for some reason.

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. AforAmpere Posts: 1092 Joined: July 1st, 2016, 3:58 pm ### Re: All directions and infinite speeds Next thing to do here, find an isotropic rule with the same concept. I was working on it, and got infinite orthogonal and diagonal speeds, but only works for (1,n) slopes. I don't know how hard it will end up being, symmetry really makes it tougher. 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) BlinkerSpawn Posts: 1954 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: All directions and infinite speeds AforAmpere wrote:Next thing to do here, find an isotropic rule with the same concept. I was working on it, and got infinite orthogonal and diagonal speeds, but only works for (1,n) slopes. I don't know how hard it will end up being, symmetry really makes it tougher. Just to clarify for people who want to try, "isotropic" means the same as "rotate4reflect", correct? LifeWiki: Like Wikipedia but with more spaceships. [citation needed] AforAmpere Posts: 1092 Joined: July 1st, 2016, 3:58 pm ### Re: All directions and infinite speeds Yes, it does. I have a feeling there is some easy solution to this that I am just not seeing. 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: 3775 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: All directions and infinite speeds Gun produces cool wavy effect: Code: Select all x = 67, y = 13, rule = All_Speeds 27.E2.C35.E2$25.E7.C30.E2$23.E12.C25.E2$21.E17.C20.E$2.E$E18.E18.C3.C
15.E$.2E5.A2.A2.A2.AE$E17.E37.E$.2E3.ED2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D 2.D2.D2.D2.D2.D2.D2.E$6.E49.E!

Gun for a smaller ship:

Code: Select all

x = 26, y = 7, rule = All_Speeds
3.E14.E.C3.BG$2.E22.E$E.E13.E2.C4.E$.E11.A.E5.2G$.E2.E.E8.E6.E$5.E7.A 2.A2.A.E$5.E15.E!

Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!