## All directions and infinite speeds

For discussion of other cellular automata.
AforAmpere
Posts: 1080
Joined: July 1st, 2016, 3:58 pm

### All directions and infinite speeds

Iv'e created a rule where every spaceship direction and almost every spaceship speed, under a limit, is possible. It is based off of Pteriforever's rule that had all orthogonal speeds, but now, it can go diagonal, and every other slope.

Code: Select all

@RULE All_Speeds

@TABLE

n_states: 12
neighborhood:Moore
symmetries:none

var a={0,1,2,3,4,5,6,7,8,9,10,11}
var b={a}
var c={a}
var d={a}
var e={a}
var f={a}
var g={a}
var h={a}

0,0,0,0,1,5,0,0,0,5
0,0,0,0,2,5,0,0,0,5
0,0,0,0,0,1,5,0,0,2
0,0,0,0,0,5,0,2,0,5
0,0,0,0,0,5,2,0,0,5
0,0,0,0,5,2,0,0,0,1
0,0,0,0,5,0,0,2,0,6
0,0,0,0,6,0,0,0,0,1
0,0,0,0,0,0,6,0,0,5
0,0,0,0,3,0,5,0,0,5
0,0,0,0,0,0,3,5,0,4
0,0,0,0,0,4,5,0,0,5
0,0,0,0,0,0,5,7,0,5
0,0,0,0,5,7,0,0,0,2
0,0,0,0,0,5,7,0,0,7
0,0,0,0,0,0,5,7,0,5
0,0,0,0,3,0,2,0,0,8
0,0,0,8,0,0,0,0,0,3
0,0,0,0,0,0,0,8,0,2
0,0,0,0,1,0,4,0,0,9
0,0,0,9,0,0,0,0,0,1
0,0,0,0,0,0,0,9,0,4
0,0,0,3,0,0,0,2,0,0
0,0,0,0,1,4,0,0,0,1
0,0,0,0,0,1,4,0,0,4
0,0,0,1,0,0,0,4,0,0
0,0,0,0,1,0,2,0,0,10
0,0,0,10,0,0,0,0,0,1
0,0,0,0,0,0,0,10,0,2
0,0,0,1,0,0,0,2,0,0

0,0,0,0,3,2,0,0,0,3
0,0,0,0,0,3,2,0,0,2
0,0,0,0,7,0,0,0,0,3
0,0,0,0,0,5,0,4,0,7
0,0,0,0,5,7,0,3,0,2
0,0,0,0,5,0,0,4,0,7
0,0,0,0,0,5,0,7,0,7
0,0,0,9,0,0,0,5,0,1
0,0,0,0,5,7,7,0,0,2

0,0,0,0,1,0,5,0,0,5
0,0,0,0,0,0,1,5,0,2
0,0,0,5,1,5,0,0,0,5
0,0,0,0,5,5,0,0,0,5

0,0,0,0,1,2,0,0,0,1
0,0,0,0,0,1,2,0,0,2
0,0,0,0,3,2,5,0,0,3
0,0,0,0,1,2,5,0,0,1
0,0,0,0,10,0,5,0,0,5
0,0,0,10,0,0,0,5,0,1
0,0,0,0,9,0,5,0,0,5
0,0,0,9,0,0,0,5,0,1
0,0,0,0,4,0,1,5,0,2
0,0,0,0,2,0,1,5,0,2
0,0,0,0,4,1,2,0,0,2
0,0,0,0,7,0,0,2,0,8
0,0,0,0,7,0,0,5,0,3
0,0,0,0,3,4,0,0,0,3
0,0,0,0,0,3,4,0,0,4
0,0,0,0,4,3,2,0,0,2
0,0,0,0,9,0,2,0,0,10
0,0,0,9,0,0,0,2,0,0
0,0,0,0,4,0,0,10,0,2
0,0,0,0,3,0,4,0,0,11
0,0,0,3,0,0,0,4,0,0
0,0,0,11,0,0,0,0,0,3
0,0,0,0,0,0,0,11,0,4
0,0,0,0,11,0,2,0,0,8
0,0,0,0,4,0,0,8,0,2
0,0,0,11,0,0,0,2,0,0
0,0,0,0,5,0,0,9,0,7
0,0,0,0,7,0,0,8,0,2
0,0,0,5,0,5,0,2,0,6
0,0,0,0,5,0,2,0,0,6
0,0,0,6,6,2,0,0,0,1
0,0,0,8,0,0,0,5,0,3
0,0,0,0,8,0,5,0,0,5
0,0,0,0,2,0,3,5,0,4
0,0,0,0,2,3,4,0,0,4
0,0,0,0,8,0,4,0,0,11
0,0,0,8,0,0,0,4,0,0
0,0,0,0,2,0,0,11,0,4
0,0,0,0,2,1,4,0,0,4
0,0,0,5,5,0,0,0,0,1
0,0,0,0,0,0,5,5,0,4
0,0,0,0,2,1,2,0,0,2

0,a,b,1,c,d,e,f,g,1
0,a,b,c,d,e,f,2,g,2
0,a,b,3,c,d,e,f,g,3
0,a,b,c,d,e,f,4,g,4

1,a,b,c,d,e,f,g,h,0
2,0,0,0,5,0,0,0,0,2
2,0,0,7,5,0,0,2,0,2
2,a,b,c,d,e,f,g,h,0
3,a,b,c,d,e,f,g,h,0
7,0,0,0,0,5,0,0,0,7
4,a,b,c,d,e,f,g,h,0
5,0,0,1,0,0,0,0,0,0
5,0,0,2,0,0,0,0,0,0
5,0,0,0,0,0,0,0,2,0
5,0,0,0,0,0,0,2,0,0
5,0,0,0,0,0,0,0,6,0
5,0,5,3,0,0,0,0,0,0
5,0,0,4,0,0,0,0,0,0
5,7,0,0,0,0,0,0,0,0
5,0,5,0,0,0,0,0,0,0
5,0,5,1,0,0,0,0,0,0
5,0,0,5,0,0,0,0,0,0
5,0,0,2,0,0,0,5,0,0
5,5,1,5,0,0,0,0,0,0
5,1,0,0,0,0,5,5,5,0
5,5,1,5,0,5,0,0,0,0
5,5,0,5,0,5,0,0,0,0
5,5,0,5,0,5,0,1,0,0
5,0,1,0,0,0,5,0,5,0
5,0,5,1,0,0,2,0,0,0
5,0,5,3,0,0,5,0,0,0
5,7,5,0,5,0,0,0,7,0
5,7,0,0,0,0,5,0,2,0

6,a,b,c,d,e,f,g,h,0
7,0,0,0,5,0,0,0,0,7
7,0,0,0,0,5,0,7,0,7
7,0,0,7,5,0,0,0,3,7
7,a,b,c,d,e,f,g,h,0
8,a,b,c,d,e,f,g,h,0
9,a,b,c,d,e,f,g,h,0
10,a,b,c,d,e,f,g,h,0
11,a,b,c,d,e,f,g,h,0

@COLORS
1 255 0 0
2 255 255 0
3 0 0 255
4 0 255 255
5 255 255 255
6 0 0 0
This is done by shifting the stationary cells by diagonal and orthogonal-pushing cells, which are the red and yellow colored and the blue and cyan colored states, respectively. There are a bunch of auxiliary states, but you only need to use states 1-5. To make a speed at slope (m,n), where m is the larger number, put a state 5 cell, then put n state 4 cells, each right 3 and down 1 from the last (If you need an example, see below), then put (m-n) state 2 cells in the same pattern, and then another state 5.

A preliminary example is a 3c/10 (6c/20) ship:

Code: Select all

x = 13, y = 5, rule = All_Speeds
E$3.B$6.B$9.B$12.E!

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!  Diagonal works as well: 2c/11 diagonal: Code: Select all x = 12, y = 4, rule = All_Speeds E$3.D$6.D$11.E!

C/4 diagonal:

Code: Select all

x = 6, y = 3, rule = All_Speeds
E$3.D$5.E!

2c/5 diagonal:

Code: Select all

x = 7, y = 4, rule = All_Speeds
E.CD2$4.2GE$5.E!


Another example is a (4,2)c/16 knightship:

Code: Select all

x = 10, y = 4, rule = All_Speeds
E$3.D$6.B$9.E!  The yellow cells push it N two spaces, and the diagonal ships push it two spaces diagonally NE. Another example is this (10,2)c/34: Code: Select all x = 19, y = 7, rule = All_Speeds E$3.B$6.B$9.B$12.B$15.D$18.E!  You can also compress ships by experimenting around a bit, here is a (4,2)c/8 knightship, the fastest possible in this rule: Code: Select all x = 6, y = 2, rule = All_Speeds E.AD$5.E!

There are limits to how fast a ship can go by compressing the spaces for the pushers (the things that push the stable cells)
The limit speed for a given slope (m,n) , with largest number first, as (2m,2n)/(3m+2n), giving (4,2)c/8 for a knightship.

I have found some guns in this rule, but only for orthogonal and diagonal, I don't know if one exists for knightships:

Code: Select all

x = 42, y = 11, rule = All_Speeds
3.E$2.E$E.E$.E$5.E$4.E22.E13.E$3.E.E4.E15.E.E$E3.E6.E15.E3.E$.E24.E3.
E4.E2.E$E3.2E3.E17.E2.E4.E$.E2.E5.E!

If you have any questions about how to make ships, I can show examples. It was easy to prove that the bounds on speed, and I am certain they are correct, but if you find a problem, please let me know. I worked on this for weeks, and I tried to make it work as well as possible.

P.S. Just for fun, here's a Waterbear speed (23,5)c/79:

Code: Select all

x = 77, y = 25, rule = All_Speeds
E$3.D$6.D$9.D$12.D$15.D$18.B$21.B$24.B$27.B$30.B$33.B$36.B$39.B$42.B$45.B$48.B$51.B$54.B$57.B$60.B$63.B$66.B$69.B$76.E!

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)

Ethanagor
Posts: 80
Joined: March 15th, 2017, 7:34 pm
Location: the Milky Way galaxy

### Re: All directions and infinite speeds

This rule is really interesting to mess around with!

a simple triplet emits a stream of red cells, and can be turned into different guns. Two most basic examples:

Code: Select all

x = 21, y = 5, rule = All_Speeds
3.E11.E$2.E.D9.E3.D$E.E4.E4.E.E5.E$.EA2.AE6.E2.A2.E$.E4.E6.E5.E!

Additionally, here is a simple (puffer? wickstretcher? rake/puffer combo?):

Code: Select all

x = 6, y = 3, rule = All_Speeds
.E$EA2.F$.E3.E!

The red stream can be converted into additional wicks:

Code: Select all

x = 18, y = 4, rule = All_Speeds
.E$E6.E5.E$.E4.E5.EA2.F$7.E5.E3.E!  Another one, this time oblique: Code: Select all x = 8, y = 4, rule = All_Speeds$.ED$E4.B$.E5.E!

A gun that looks like a transverse wave:

Code: Select all

x = 12, y = 4, rule = All_Speeds
E$E$11.E$11.E!  I love how such simple patterns can do a lot. Fantastic work! "It's not easy having a good time. Even smiling makes my face ache." - Frank N. Furter AforAmpere Posts: 1080 Joined: July 1st, 2016, 3:58 pm ### Re: All directions and infinite speeds Thanks Ethanagor, I'm glad that you like it. Challenge: Knightship gun! I haven't been able to find one yet, but I am not as experienced at finding guns as some people here. Also, have you figured out how to compress the ships? Nice find with the diagonal gun, here it is cleaned up: Code: Select all x = 11, y = 4, rule = All_Speeds E.E$2.E7.E$7.E.E$9.E!


Code: Select all

x = 41, y = 58, rule = All_Speeds
17.E$16.E3.DA2.E$15.E$7.A8.E$15.E$14.E$13.E$14.E$13.E$12.E$11.E$12.E$
11.E$10.E$9.E$10.E$9.E$8.E$7.E25.E$8.E23.E3.DA2.E$7.E23.E$6.E18.A6.E$
5.E25.E$6.E23.E$5.E23.E$4.E8.A16.E$3.E25.E$4.E23.E$.A2E23.E$2.E25.E$.
E25.E$2.E23.E$2E23.E$E25.E$25.E$E23.E$23.E$24.E$23.E$22.E$21.E$22.E$
21.E$20.E$19.E$20.E$19.E$18.E$17.E$18.E$17.E$16.E$15.E$16.E$15.E$14.E$13.E$14.E!  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) drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: All directions and infinite speeds Fun: Code: Select all x = 104, y = 4, rule = All_Speeds .E$2E101.E$102.E$101.2E!

\100\97\110\105

A for awesome
Posts: 1951
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: All directions and infinite speeds

P19 gun of some sort:

Code: Select all

x = 18, y = 19, rule = All_Speeds
6.E$5.E9.E.E$3.E.E5.E4.E$E.E3.E9.E$2.E13.E10$2.E10.E$E.E$2.E$3.E.E4.E
2.E$5.E4.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 Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: All directions and infinite speeds Orthogonal Transverse wave gun Code: Select all x = 13, y = 6, rule = All_Speeds E$2.E$.E5.E$2.E8.E$.E5.2E3.E$2.E4.E!

Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
18.E.E$8.E18.E20.E!  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) Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: All directions and infinite speeds Rake of sorts! Code: Select all x = 10, y = 5, rule = All_Speeds 3.E$5.D$9.E$ED$3.C3.E!  And um Code: Select all x = 41, y = 9, rule = All_Speeds 40.E2$37.E2$16.E17.E$18.D$E21.E8.E$13.ED$3.E12.C3.E7.E!  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)

AforAmpere
Posts: 1080
Joined: July 1st, 2016, 3:58 pm

### Re: All directions and infinite speeds

Yeah, I found that too, while I was testing the rule, it can be used to make a dot puffer:

Code: Select all

x = 20, y = 10, rule = All_Speeds
8.E$11.D$6.E6.E$7.D$E6.C3.E$.D2$7.D5.E$16.D$13.D4.E!

And a rake:

Code: Select all

x = 34, y = 34, rule = All_Speeds
22.E.C$26.2GE$20.E6.E$24.G$14.E3.C6.E$18.D2$24.D2.E.C$31.2GE$30.D.E2$30.E2$28.E2$26.E2$24.E2$22.E2$20.E2$18.E2$16.E2$14.E2$5.E6.E$7.D$E4.C
4.E$3.D!  EDIT, what the heck is this? Code: Select all x = 497, y = 161, rule = All_Speeds 479.E$197.E280.E$479.E$.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.
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6.A4.A6.A4.A6.A3.2E$158.E286.E$301.A11.A11.A11.A11.A11.A11.A11.A11.A
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6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A2.2E$149.E287.E$229.A11.A11.A11.A
11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A2.E$149.2E4.B 3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B 4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B 2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B 5.E$147.E.EA2.A3.A4.A2.A3.A4.A2.A3.A4.A2.A3.A4.A2.A3.A4.A2.A3.A4.A2.A
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4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.2E$148.E286.E$211.A11.A11.A11.A11.
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4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A3.2E$146.E286.E$193.A11.A11.A11.A
11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A10.E$145.2EB3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4. B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2. B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3. B2.B4.B3.B2.B2.E$143.E.E4.A2.A3.A4.A2.A3.A4.A2.A3.A4.A2.A5.A4.A6.A4.A
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6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.2E$142.E286.E$157.A11.A
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11.A11.A11.A11.A11.A11.A11.A10.E$139.2E4.B2.B4.B3.B2.B4.B3.B2.B4.B3.B 2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B 3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B 4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B2.E$137.E.E.A4.A6.A4.A6.
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6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A3.2E$128.E 286.E$31.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.
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$127.2E5.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B5.B2.B4.B3.B2. B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3. B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B2.E$125.E.E
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4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A3.2E$122.E286.E$.A11.A11.A11.A11.
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4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.2E$118.E286.E$.A
11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A
11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A6.E$117.2E.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B 4.B6.B4.B6.B4.B6.B4.B6.B4.B5.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B 4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B3.2B.E$115.E.E5.A4.A6.A4.A6.A4.A
6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A
4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A3.2E$116.E286.E$7.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A
11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A10.E$115.2E5.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B 4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B5.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B 3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B2.E$113.E.E.A4.A6.A4.A6.A4.A6.A4.A6.
A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.
A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A2.2E$114.E286.E$.A
11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A
11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A11.A2.E$4.A2.A2.A5.A2.A2.A5.A2.A2.A5.A2.A2.A5.A2.A2.A5.A2.A2.A5.A2.A2.A5.A2.A 2.A5.A2.A2.A5.A2E2.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B 6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B6.B4.B5.B2.B4.B3.B2.B 4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B3.B2.B4.B5.E$113.E2.A6.A4.A6.A4.A6.A4.A
6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A
4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.A4.A6.2E$112.E286.E!  I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule - Finish a rule with ships with period >= f_e_0(n) (in progress) Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: All directions and infinite speeds I like how this looks like an actual "factory" Code: Select all x = 40, y = 7, rule = All_Speeds .E2$E26.E$.E3.E21.E10.E$6.E19.B12.E$3.E.E21.2E9.E$5.E21.E!

This is also interesting to, it regenerates the dot with reds and yellows

Code: Select all

x = 14, y = 7, rule = All_Speeds
2.E2.E.C$E3.E$2.E.E$2.E$4.2E2.B4.E$2.E.E2.A4.E$3.E8.E!

Transverse display

Code: Select all

x = 20, y = 168, rule = All_Speeds
2.E8.E70$18.E$E18.E$2.E$.E5.E$2.E8.E$.E5.2E3.E$2.E4.E16$2.E8.E69$18.E$E18.E$2.E$.E5.E$2.E8.E$.E5.2E3.E$2.E4.E!  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)

Posts: 1942
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: All directions and infinite speeds

Alternate version of this rule with (EDIT: now two fewer states) and cleaner use of auxiliary states:

Code: Select all

@RULE Speedy
0 void
1 left vertical
2 right vertical
3 left diagonal
4 right diagonal
5 fencepost

@TABLE
n_states:10
neighborhood:Moore
symmetries:none
var a = {0,1,2,3,4,5,6,7,8,9}
var b = a
var c = b
var d = c
var e = d
var f = e
var g = f
var h = g
var l = {1,3}
var r = {2,4}

#left particle goes left
0,0,0,1,0,0,0,0,0,1
1,a,b,c,d,e,f,g,h,0
#right particle goes right
0,0,0,0,0,0,0,2,0,2
2,a,b,c,d,e,f,g,h,0
#left-d particle goes left
0,0,0,3,0,0,0,0,0,3
3,a,b,c,d,e,f,g,h,0
#right-d particle goes right
0,0,0,0,0,0,0,4,0,4
0,0,0,0,0,0,0,4,5,4
4,a,b,c,d,e,f,g,h,0
0,0,0,0,1,0,5,0,0,6
5,0,6,0,0,0,0,0,0,0
0,0,0,0,6,0,0,0,0,5
0,0,0,0,0,0,0,6,0,2
6,a,b,c,d,e,f,g,h,0
0,0,0,0,5,0,0,2,0,7
5,0,0,0,0,0,0,0,7,0
0,0,0,0,0,0,7,0,0,5
0,0,0,0,7,0,0,0,0,1
7,a,b,c,d,e,f,g,h,0
0,0,0,0,3,0,5,0,0,8
5,0,8,0,0,0,0,0,0,0
0,0,0,0,0,0,8,0,0,5
0,0,0,0,0,0,0,8,0,4
8,a,b,c,d,e,f,g,h,0
0,0,0,0,5,0,0,4,0,9
5,0,8,5,0,0,0,0,0,0
5,8,0,0,0,0,0,5,0,0
0,0,0,0,9,0,0,0,0,3
0,0,0,0,0,5,0,9,0,9
0,0,0,0,0,0,5,9,0,8
0,0,0,0,0,0,0,5,9,5
9,a,b,c,d,e,f,g,h,0
#slipstream
0,0,0,l,0,0,0,r,0,r
0,0,0,0,l,0,r,0,0,l
0,0,0,l,r,0,0,0,0,l
0,0,0,0,0,0,r,l,0,r
0,0,0,0,0,l,r,0,0,r
0,0,0,0,l,r,0,0,0,l

@COLORS
1 255 0 0
2 255 255 0
3 0 0 255
4 0 255 255
5 255 255 255
6 255 127 127
7 255 255 127
8 127 127 255
9 127 255 255

Ships can be directly pasted in without modification unless they are in phases with auxiliary states.
No funky signal-gun patterns here, though.

P.S. I liked in the original all-orthogonal-speeds rule how you could get strange things to happen when ships collided.
Looks like you can have fun with that here too:

Code: Select all

x = 31, y = 19, rule = All_Speeds
E$5.D$8.F$9.E9$12.E$16.B$19.B$22.B$25.B$28.D$30.E!

Last edited by BlinkerSpawn on June 28th, 2017, 2:52 pm, edited 1 time in total.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: All directions and infinite speeds

A gun. Guns are fun and look cool in this rule.

Code: Select all

x = 69, y = 8, rule = All_Speeds
3.E42.E$E.E40.E.E$2.E42.E$2.E5.E36.E5.E$9.E3.E11.E26.E3.E4.E$14.E16.E 25.E9.E$11.E.E11.2E5.E21.E.E4.2E5.E$13.E11.E30.E4.E!  CHALLENGE: Make a gun you can flip left-right and it will still work. 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)

AforAmpere
Posts: 1080
Joined: July 1st, 2016, 3:58 pm

### Re: All directions and infinite speeds

Do you mean that it still shoots the same color "pushers" ? Because I don't think that is possible, because each color goes in one direction. Red and blur go left, cyan and yellow go right.
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)

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: All directions and infinite speeds

AforAmpere wrote:Do you mean that it still shoots the same color "pushers" ? Because I don't think that is possible, because each color goes in one direction. Red and blur go left, cyan and yellow go right.
No. Just that it works when flipped.
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$4bob2o2bobobo!  (Check gen 2) Ethanagor Posts: 80 Joined: March 15th, 2017, 7:34 pm Location: the Milky Way galaxy ### Re: All directions and infinite speeds Saka wrote: AforAmpere wrote:Do you mean that it still shoots the same color "pushers" ? Because I don't think that is possible, because each color goes in one direction. Red and blur go left, cyan and yellow go right. No. Just that it works when flipped. Easy: Code: Select all x = 11, y = 4, rule = All_Speeds E9.E$.E7.E$.E.E3.E.E$2.E5.E!

"It's not easy having a good time. Even smiling makes my face ache." - Frank N. Furter

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: All directions and infinite speeds

Ethanagor wrote: Easy:

Code: Select all

x = 11, y = 4, rule = All_Speeds
E9.E$.E7.E$.E.E3.E.E$2.E5.E!  It doesnt work at all..? 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)

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: All directions and infinite speeds

Do you think the gun on the left will eventually break?

Code: Select all

x = 44, y = 7, rule = All_Speeds
.E21.E$2.E21.E$E21.E$.E21.E$.E8.E12.E19.E$7.E.E30.E.E$9.E32.E!

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$4bob2o2bobobo!  (Check gen 2) Ethanagor Posts: 80 Joined: March 15th, 2017, 7:34 pm Location: the Milky Way galaxy ### Re: All directions and infinite speeds Saka wrote: Ethanagor wrote: Easy: Code: Select all x = 11, y = 4, rule = All_Speeds E9.E$.E7.E$.E.E3.E.E$2.E5.E!

It doesnt work at all..?
oh crap, I didn't copy the whole things correctly. Let me try again:

Code: Select all

x = 14, y = 11, rule = All_Speeds
7.E6$.E10.E$2.E8.E$E.E8.E.E$.E10.E$.E10.E!  "It's not easy having a good time. Even smiling makes my face ache." - Frank N. Furter Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: All directions and infinite speeds I accidentally made one heck of a gun. Cleanup? Code: Select all x = 24, y = 9, rule = All_Speeds 6.E$5.E16.E$6.E16.E$E.E2.E16.E$2.E3.E8.E$5.E8.E$6.E7.2E$6.E6.E$14.E!  EDIT: And this fun one that features a "staircase" Code: Select all x = 30, y = 18, rule = All_Speeds E.E$2.2E$.E$2.E$.E2.C21.E$2.E17.E2.E.E.E.E$.E17.E5.E.E$2.E13.G.E.E$.E 15.E$2.E13.E.E$.E6.C6.E$2.E11.E.E$.E5.C5.E$2.E7.G.E.E$.E5.C3.E$2.ED2.
D.G.E.E$2.E6.E$10.E!

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) A for awesome Posts: 1951 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: All directions and infinite speeds Weird: Code: Select all x = 108, y = 26, rule = All_Speeds 31.E$10.E.E17.3E$8.E.E20.E$5.E.E.E13.D$4.E2.E2.EA2.A16.E$3.E19.E6.3E$E.E.E.B7.C3.C3.E$.EA2.A2.A2.A3.D2.D4.E$.E2.E4.D2.D7.E57.E.E$2.3E15.2E
58.2E$3.E75.E$80.E$79.E2.C21.E$80.E17.E2.E.E.E.E$79.E17.E5.E.E$80.E
13.G.E.E$79.E15.E$80.E13.E.E$79.E6.C6.E$80.E11.E.E$79.E5.C5.E$80.E7.G
.E.E$79.E5.C3.E$80.ED2.D.G.E.E$80.E6.E$88.E!

EDIT: State-4-to-ship converter:

Code: Select all

x = 11, y = 7, rule = All_Speeds
4.E$5.E$3.E$D$8.E$9.E$9.2E!

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

toroidalet
Posts: 1055
Joined: August 7th, 2016, 1:48 pm
Location: My computer
Contact:

### Re: All directions and infinite speeds

Saka wrote:Do you think the gun on the left will eventually break?

Code: Select all

x = 44, y = 7, rule = All_Speeds
.E21.E$2.E21.E$E21.E$.E21.E$.E8.E12.E19.E$7.E.E30.E.E$9.E32.E!

The one on the right does. The one on the left becomes period 52 by generation 1000.
This almost works as a knightship gun:

Code: Select all

x = 32, y = 5, rule = All_Speeds
2.E$12.E$E.E$.E9.AE$12.E18.E!

This better one almost works, but a single dot that goes missing ruins it:

Code: Select all

x = 26, y = 7, rule = All_Speeds
2.E.E$5.E4.E$E.E$.E2.AE$5.E18.E$23.E.E$24.E!

A for awesome wrote: EDIT: State-4-to-ship converter:

Code: Select all

x = 11, y = 7, rule = All_Speeds
4.E$5.E$3.E$D$8.E$9.E$9.2E!

smaller:

Code: Select all

x = 10, y = 7, rule = All_Speeds
4.E$5.E$3.E$D$8.E$9.E$7.E!

state 4 to 2 state 3s:

Code: Select all

x = 10, y = 3, rule = All_Speeds
D8.E$7.E$8.E!

state 4 to state 3:

Code: Select all

x = 9, y = 4, rule = All_Speeds
7.E$D7.E$6.E$7.E!  state 1 to state 2 and related heisenburp Code: Select all x = 7, y = 13, rule = All_Speeds 2.E2$E.E$.E4.A6$2.E2$2.E$6.A!

state 2 to state 1

Code: Select all

x = 10, y = 4, rule = All_Speeds
9.E$B$8.E$9.E!  state 2 to a parabola of state 1s Code: Select all x = 17, y = 25, rule = All_Speeds 12.E3.E2$11.E2$10.E2$9.E2$8.E2$7.E2$6.E2$5.E2$4.E2$3.E2$E.E$.E13.E$6. B9.E$14.E$15.E!  "Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life." -Terry Pratchett Ethanagor Posts: 80 Joined: March 15th, 2017, 7:34 pm Location: the Milky Way galaxy ### Re: All directions and infinite speeds Ethanagor wrote: Saka wrote: Ethanagor wrote: Easy: Code: Select all x = 11, y = 4, rule = All_Speeds E9.E$.E7.E$.E.E3.E.E$2.E5.E!

It doesnt work at all..?
oh crap, I didn't copy the whole things correctly. Let me try again:

Code: Select all

x = 14, y = 11, rule = All_Speeds
7.E6$.E10.E$2.E8.E$E.E8.E.E$.E10.E$.E10.E!  Wow, still left one cell out. This one works for real, I hope: Code: Select all x = 14, y = 13, rule = All_Speeds 8.E$7.E7$.E10.E$2.E8.E$E.E8.E.E$.E10.E$.E10.E!  sorry for all of that. I need to test things I copy to make sure I have the whole thing. I hate myself. "It's not easy having a good time. Even smiling makes my face ache." - Frank N. Furter BlinkerSpawn Posts: 1942 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: All directions and infinite speeds Ethanagor wrote:Wow, still left one cell out. This one works for real, I hope: Code: Select all x = 14, y = 13, rule = All_Speeds 8.E$7.E7$.E10.E$2.E8.E$E.E8.E.E$.E10.E$.E10.E!  sorry for all of that. It works fine, but can be shrunk down a bit: Code: Select all x = 12, y = 11, rule = All_Speeds 7.E$6.E7$E10.E$.E8.E$.E8.E!  EDIT #dunno: Much smaller and symmetrical: Code: Select all x = 10, y = 6, rule = All_Speeds E8.E$.E6.E$2.E4.E$.E6.E$2.E4.E$2.E4.E!

This one's tiny but I didn't want to throw out the other one because that one's orthogonal(EDIT #toomany: ok how is it even smaller now):

Code: Select all

x = 6, y = 2, rule = All_Speeds
E4.E\$E4.E!

Why do fenceposts create signals in this rule anyway?
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]