## Perfect Orthogonal Speeds in Life-like CA

For discussion of other cellular automata.

### Re: Perfect Orthogonal Speeds in Life-like CA

Updated c/13 and c/44 on the OP page, but not in the rule yet.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Perfect Orthogonal Speeds in Life-like CA

Finally got a method to implement all even speeds, which should reduce the size of the mashup by lots even if the cell counts aren't all optimal. Keeping everything here the same except for the flawed rules (wrong period and/or B0).
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Perfect Orthogonal Speeds in Life-like CA

AbhpzTa wrote:c/2n p2n spaceships for any integer n>1:
`x = 10, y = 38, rule = B2c3ae4ai56c/S2-kn3-enq4bo2bo\$ob3o\$bo2bo5\$bo3bo\$ob4o\$bo3bo5\$bo4bo\$ob5o\$bo4bo5\$bo5bo\$ob6o\$bo5bo5\$bo6bo\$ob7o\$bo6bo5\$bo7bo\$ob8o\$bo7bo!`

Look at this rule AbphzTa found(B2c3ae4ai56c/S2-kn3-enq4):
`░▓░░░░░░░░░▓▓░[n cells]▓░▓░░░░░░░░░▓n>1, the whole thing travels at c/2n with a period of 2n.`

EDIT:
Then I found that you had beat me to it.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

For all other speeds, I fetch you this, that AforAmpere made:
`@RULE All_Speeds@TABLEn_states: 12neighborhood:Mooresymmetries:nonevar 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}0,0,0,0,1,5,0,0,0,50,0,0,0,2,5,0,0,0,50,0,0,0,0,1,5,0,0,20,0,0,0,0,5,0,2,0,50,0,0,0,0,5,2,0,0,50,0,0,0,5,2,0,0,0,10,0,0,0,5,0,0,2,0,60,0,0,0,6,0,0,0,0,10,0,0,0,0,0,6,0,0,50,0,0,0,3,0,5,0,0,50,0,0,0,0,0,3,5,0,40,0,0,0,0,4,5,0,0,50,0,0,0,0,0,5,7,0,50,0,0,0,5,7,0,0,0,20,0,0,0,0,5,7,0,0,70,0,0,0,0,0,5,7,0,50,0,0,0,3,0,2,0,0,80,0,0,8,0,0,0,0,0,30,0,0,0,0,0,0,8,0,20,0,0,0,1,0,4,0,0,90,0,0,9,0,0,0,0,0,10,0,0,0,0,0,0,9,0,40,0,0,3,0,0,0,2,0,00,0,0,0,1,4,0,0,0,10,0,0,0,0,1,4,0,0,40,0,0,1,0,0,0,4,0,00,0,0,0,1,0,2,0,0,100,0,0,10,0,0,0,0,0,10,0,0,0,0,0,0,10,0,20,0,0,1,0,0,0,2,0,00,0,0,0,3,2,0,0,0,30,0,0,0,0,3,2,0,0,20,0,0,0,7,0,0,0,0,30,0,0,0,0,5,0,4,0,70,0,0,0,5,7,0,3,0,20,0,0,0,5,0,0,4,0,70,0,0,0,0,5,0,7,0,70,0,0,9,0,0,0,5,0,10,0,0,0,5,7,7,0,0,20,0,0,0,1,0,5,0,0,50,0,0,0,0,0,1,5,0,20,0,0,5,1,5,0,0,0,50,0,0,0,5,5,0,0,0,50,0,0,0,1,2,0,0,0,10,0,0,0,0,1,2,0,0,20,0,0,0,3,2,5,0,0,30,0,0,0,1,2,5,0,0,10,0,0,0,10,0,5,0,0,50,0,0,10,0,0,0,5,0,10,0,0,0,9,0,5,0,0,50,0,0,9,0,0,0,5,0,10,0,0,0,4,0,1,5,0,20,0,0,0,2,0,1,5,0,20,0,0,0,4,1,2,0,0,20,0,0,0,7,0,0,2,0,80,0,0,0,7,0,0,5,0,30,0,0,0,3,4,0,0,0,30,0,0,0,0,3,4,0,0,40,0,0,0,4,3,2,0,0,20,0,0,0,9,0,2,0,0,100,0,0,9,0,0,0,2,0,00,0,0,0,4,0,0,10,0,20,0,0,0,3,0,4,0,0,110,0,0,3,0,0,0,4,0,00,0,0,11,0,0,0,0,0,30,0,0,0,0,0,0,11,0,40,0,0,0,11,0,2,0,0,80,0,0,0,4,0,0,8,0,20,0,0,11,0,0,0,2,0,00,0,0,0,5,0,0,9,0,70,0,0,0,7,0,0,8,0,20,0,0,5,0,5,0,2,0,60,0,0,0,5,0,2,0,0,60,0,0,6,6,2,0,0,0,10,0,0,8,0,0,0,5,0,30,0,0,0,8,0,5,0,0,50,0,0,0,2,0,3,5,0,40,0,0,0,2,3,4,0,0,40,0,0,0,8,0,4,0,0,110,0,0,8,0,0,0,4,0,00,0,0,0,2,0,0,11,0,40,0,0,0,2,1,4,0,0,40,0,0,5,5,0,0,0,0,10,0,0,0,0,0,5,5,0,40,0,0,0,2,1,2,0,0,20,a,b,1,c,d,e,f,g,10,a,b,c,d,e,f,2,g,20,a,b,3,c,d,e,f,g,30,a,b,c,d,e,f,4,g,41,a,b,c,d,e,f,g,h,02,0,0,0,5,0,0,0,0,22,0,0,7,5,0,0,2,0,22,a,b,c,d,e,f,g,h,03,a,b,c,d,e,f,g,h,07,0,0,0,0,5,0,0,0,74,a,b,c,d,e,f,g,h,05,0,0,1,0,0,0,0,0,05,0,0,2,0,0,0,0,0,05,0,0,0,0,0,0,0,2,05,0,0,0,0,0,0,2,0,05,0,0,0,0,0,0,0,6,05,0,5,3,0,0,0,0,0,05,0,0,4,0,0,0,0,0,05,7,0,0,0,0,0,0,0,05,0,5,0,0,0,0,0,0,05,0,5,1,0,0,0,0,0,05,0,0,5,0,0,0,0,0,05,0,0,2,0,0,0,5,0,05,5,1,5,0,0,0,0,0,05,1,0,0,0,0,5,5,5,05,5,1,5,0,5,0,0,0,05,5,0,5,0,5,0,0,0,05,5,0,5,0,5,0,1,0,05,0,1,0,0,0,5,0,5,05,0,5,1,0,0,2,0,0,05,0,5,3,0,0,5,0,0,05,7,5,0,5,0,0,0,7,05,7,0,0,0,0,5,0,2,06,a,b,c,d,e,f,g,h,07,0,0,0,5,0,0,0,0,77,0,0,0,0,5,0,7,0,77,0,0,7,5,0,0,0,3,77,a,b,c,d,e,f,g,h,08,a,b,c,d,e,f,g,h,09,a,b,c,d,e,f,g,h,010,a,b,c,d,e,f,g,h,011,a,b,c,d,e,f,g,h,0@COLORS1 255 0 02 255 255 03 0 0 2554 0 255 2555 255 255 2556 0 0 0`
Last edited by wwei23 on July 4th, 2017, 3:42 pm, edited 1 time in total.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

muzik wrote:Finally got a method to implement all even speeds, which should reduce the size of the mashup by lots even if the cell counts aren't all optimal. Keeping everything here the same except for the flawed rules (wrong period and/or B0).

Good choice. The spaceships get gigantic quickly. Only to be used as a last resort.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

These speeds below c/100 currently remain:

`c/51c/57c/61c/65c/69c/71c/75c/77c/79c/85c/91c/93c/95c/97c/99`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Perfect Orthogonal Speeds in Life-like CA

Just use All_Speeds.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

wwei23 wrote:Just use All_Speeds.

...which defeats the entire purpose of this whole thread.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Perfect Orthogonal Speeds in Life-like CA

muzik wrote:
wwei23 wrote:Just use All_Speeds.

...which defeats the entire purpose of this whole thread.

As a last resort.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

wwei23 wrote:
muzik wrote:
wwei23 wrote:Just use All_Speeds.

...which defeats the entire purpose of this whole thread.

As a last resort.

Like the way that B2c3ae4ai56c/S2-kn3-enq4 is for c/2x.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

wwei23 wrote:
muzik wrote:
wwei23 wrote:Just use All_Speeds.

...which defeats the entire purpose of this whole thread.

As a last resort.

It's not an isotropic single-state rule.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Perfect Orthogonal Speeds in Life-like CA

Does that mean it doesn't count?

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

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

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### Re: Perfect Orthogonal Speeds in Life-like CA

c/56(Who does this belong to?):
`x = 4, y = 3, rule = B2-ai3aek4ijtz5e7e/S01c2aik3-akry4aknwy5jn6ikn7o\$3bo\$o!`

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

wwei23 wrote:c/56(Who does this belong to?):
`x = 4, y = 3, rule = B2-ai3aek4ijtz5e7e/S01c2aik3-akry4aknwy5jn6ikn7o\$3bo\$o!`

I posted that here yesterday, but I make no claim to it being novel.
The latest version of the 5S Project contains over 221,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
wildmyron

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### Re: Perfect Orthogonal Speeds in Life-like CA

Daily I search Catagolue for spaceships in new rules. Nothing yet.
EDIT:
Two c/63 diagonals:
https://catagolue.appspot.com/census/b2 ... 3r/C1/xq63
EDIT:
Never mind, you already got it.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

c/11947 on a torus:
`x = 100, y = 1, rule = B36/S23:T100,1bo3bob3o3bo2bo3b3ob3ob3ob3ob3obo3bo6bo3bo3b3ob3ob3ob6ob3ob3obo3bo6bo!`

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

wwei23 wrote:c/11947 on a torus:
`x = 100, y = 1, rule = B36/S23:T100,1bo3bob3o3bo2bo3b3ob3ob3ob3ob3obo3bo6bo3bo3b3ob3ob3ob6ob3ob3obo3bo6bo!`

How did you find this?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Perfect Orthogonal Speeds in Life-like CA

I was using Oscar and filling a section randomly. B36/S23:TX,1 Corresponds to Rule 54 in TX.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

Any such patterns in regular life?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Perfect Orthogonal Speeds in Life-like CA

muzik wrote:Any such patterns in regular life?

Not that I have seen. But Life is Rule 22, known to have extreme chaos. Usually, I get oscillators instead of spaceships.
EDIT:
c/416 on a torus:
`x = 50 , y = 1 , rule = B36/S23:T50,1ooobooobboooooboooboooboooboooboooobbbooobooobooob`

c/468 on a torus:
`x = 50 , y = 1 , rule = B36/S23:T50,1ooobooobbboboooboooboooooobobbbobbboooboooboooooob`

EDIT:
c/2583 on a torus:
`x = 60 , y = 1 , rule = B36/S23:T60,1boooboooboooboooboooooobooobooobooobooobbbobbbobooobbobbbobb`

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

muzik wrote:c/106: (B0)
`x = 15, y = 6, rule = B0148/S02ob2ob5ob2obo\$15o\$15o\$15o\$15o\$bob2o5b2obo!`

c/132: (p264) (B0)
`x = 4, y = 5, rule = B0135/S0142b2o\$bo\$2bo\$b2o\$obo!`

c/154: (B0)
`x = 10, y = 8, rule = B0235/S12342bo4bo\$2b6o\$2b6o\$2ob4ob2o\$10o\$ob6obo\$10o\$10o!`

c/158: (p316)
`x = 8, y = 10, rule = B34567/S0456b4obo\$b7o\$o2b4o\$bob5o\$o2b4o\$bo5bo\$o4b2o\$bo2b4o\$b4o\$3bobo!`

Why aren't we using adjustable rules here? Also, this probably qualifies for the post with the most edits in it.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

muzik wrote:Any such patterns in regular life?

Actually, I just found one, but it isn't true-period.

wwei23

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### Re: Perfect Orthogonal Speeds in Life-like CA

wwei23 wrote:
muzik wrote:Any such patterns in regular life?

Actually, I just found one, but it isn't true-period.

Guess it's worth sharing anyway.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Perfect Orthogonal Speeds in Life-like CA

muzik wrote:
wwei23 wrote:
muzik wrote:Any such patterns in regular life?

Actually, I just found one, but it isn't true-period.

Guess it's worth sharing anyway.

Actually, width 24 has LOADS of true-periods:
T24.txt

c/19542:
`x = 32 , y = 1 , rule = B3/S23:T32,1bobbobobbbbbbbbbobbbbboobbbboooo`

Never mind, Oscar can be inaccurate. Still, there may be some good spaceships.

wwei23

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