## All directions and infinite speeds

For discussion of other cellular automata.

### Re: All directions and infinite speeds

Interesting tagalong:
x = 15, y = 4, rule = All_Speeds.ED$14.E2$E2.C8.E!
I have the best signature ever.

toroidalet

Posts: 676
Joined: August 7th, 2016, 1:48 pm
Location: Somewhere on a planet called "Earth"

Weird:
x = 27, y = 12, rule = All_Speeds19.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 A for awesome Posts: 1354 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### 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. @ICONSXPM/* 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 Ethanagor Posts: 78 Joined: March 15th, 2017, 7:34 pm Location: the Milky Way galaxy ### Re: All directions and infinite speeds Breeder: x = 23, y = 4, rule = All_Speeds2E$6.B6.2E$9.E9.B$22.E!
Replicator!
x = 3, y = 3, rule = B3/S234y2bo$3o$bo!

wwei23

Posts: 642
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: All directions and infinite speeds

Smallest still lives:
x = 13, y = 44, rule = All_SpeedsE10$E$.E9$E.E$.E9$E.E7.E.E$.E9.E$2.E8.E8$2.E7.E.E$.E9.E$2E9.E$.E10.E! Replicator! x = 3, y = 3, rule = B3/S234y2bo$3o$bo! wwei23 Posts: 642 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe ### Re: All directions and infinite speeds You could almost make a caterpillar out of this: x = 27, y = 12, rule = All_Speeds12.E$26.E8$E$3.D$7.E! 2c/n spaceships project Current priorities: see here muzik Posts: 2462 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: All directions and infinite speeds AforAmpere wrote:Or a 2c/3 orthogonal ship, the fastest orthogonal speed in this rule: x = 6, y = 2, rule = All_SpeedsE.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.
Replicator!
x = 3, y = 3, rule = B3/S234y2bo$3o$bo!

wwei23

Posts: 642
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: All directions and infinite speeds

lol, this is why i like to click randomly:
x = 25, y = 33, rule = All_Speeds11.E$10.E$9.2E7.E.E$19.E3.E$19.E5$11.E4.A2.E2$4.E$E2.E$.E.E19.DE$.E10.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.E10.E$6.E.E$8.E3.E2.G.E$9.E.E4.E2.E$11.E4.E! x = 8, y = 10, rule = B3/S233b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!

No football of any dui mauris said that.

83bismuth38

Posts: 291
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...

### Re: All directions and infinite speeds

easy obique gun:
x = 9, y = 5, rule = All_Speeds3.E$E.E.D$2.E5.E$5.E.E$7.E!
x = 8, y = 10, rule = B3/S233b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo! No football of any dui mauris said that. 83bismuth38 Posts: 291 Joined: March 2nd, 2017, 4:23 pm Location: Still sitting around in Sagittarius A... ### Re: All directions and infinite speeds 83bismuth38 wrote:easy obique gun: x = 9, y = 5, rule = All_Speeds3.E$E.E.D$2.E5.E$5.E.E$7.E! It shoots diagonals. Everyone, please stop posting B/S about CA The Bugs Range 1 to 100 Project Saka Posts: 1921 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: All directions and infinite speeds oops... it's hard for me to tell for some reason. x = 8, y = 10, rule = B3/S233b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!

No football of any dui mauris said that.

83bismuth38

Posts: 291
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...

### 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.
Things to work on:
- An Isotropic version of All_Speeds
- Find more ships in B2ek3-ajny4ajqr5a/S02ack3ackny4aq5y
- Find a p4 knightship in a Non-totalistic rule (someone please search the rules)
AforAmpere

Posts: 210
Joined: July 1st, 2016, 3:58 pm

### 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]

Posts: 1426
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### 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.
Things to work on:
- An Isotropic version of All_Speeds
- Find more ships in B2ek3-ajny4ajqr5a/S02ack3ackny4aq5y
- Find a p4 knightship in a Non-totalistic rule (someone please search the rules)
AforAmpere

Posts: 210
Joined: July 1st, 2016, 3:58 pm

### Re: All directions and infinite speeds

Gun produces cool wavy effect:

x = 67, y = 13, rule = All_Speeds27.E2.C35.E2$25.E7.C30.E2$23.E12.C25.E2$21.E17.C20.E$2.E$E18.E18.C3.C15.E$.2E5.A2.A2.A2.AE$E17.E37.E$.2E3.ED2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.E$6.E49.E! Gun for a smaller ship: x = 26, y = 7, rule = All_Speeds3.E14.E.C3.BG$2.E22.E$E.E13.E2.C4.E$.E11.A.E5.2G$.E2.E.E8.E6.E$5.E7.A2.A2.A.E\$5.E15.E!
2c/n spaceships project

Current priorities: see here
muzik

Posts: 2462
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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