## Perfect Orthogonal Speeds in Life-like CA

For discussion of other cellular automata.
muzik
Posts: 3910
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### 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
Posts: 3910
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### 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!

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

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

AbhpzTa wrote:c/2n p2n spaceships for any integer n>1:

Code: Select all

``````x = 10, y = 38, rule = B2c3ae4ai56c/S2-kn3-enq4
bo2bo\$ob3o\$bo2bo5\$bo3bo\$ob4o\$bo3bo5\$bo4bo\$ob5o\$bo4bo5\$bo5bo\$ob6o\$bo5bo
5\$bo6bo\$ob7o\$bo6bo5\$bo7bo\$ob8o\$bo7bo!``````
Look at this rule AbphzTa found(B2c3ae4ai56c/S2-kn3-enq4):

Code: Select all

``````░▓░░░░░░░░░▓
▓░[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
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

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

For all other speeds, I fetch you this, that AforAmpere made:

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``````
Last edited by wwei23 on July 4th, 2017, 3:42 pm, edited 1 time in total.

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### 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.

muzik
Posts: 3910
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

These speeds below c/100 currently remain:

Code: Select all

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

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

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

Just use All_Speeds.

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

### 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!

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### 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
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### 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.

muzik
Posts: 3910
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### 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!

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

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

Does that mean it doesn't count?

muzik
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Location: Scotland

### 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!

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

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

c/56(Who does this belong to?):

Code: Select all

``````x = 4, y = 3, rule = B2-ai3aek4ijtz5e7e/S01c2aik3-akry4aknwy5jn6ikn7
o\$3bo\$o!``````

wildmyron
Posts: 1447
Joined: August 9th, 2013, 12:45 am

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

wwei23 wrote:c/56(Who does this belong to?):

Code: Select all

``````x = 4, y = 3, rule = B2-ai3aek4ijtz5e7e/S01c2aik3-akry4aknwy5jn6ikn7
o\$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 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

wwei23
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Joined: May 22nd, 2017, 6:14 pm
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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
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

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

c/11947 on a torus:

Code: Select all

``````x = 100, y = 1, rule = B36/S23:T100,1
bo3bob3o3bo2bo3b3ob3ob3ob3ob3obo3bo6bo3bo3b3ob3ob3ob6ob3ob3obo3bo6bo!
``````

muzik
Posts: 3910
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

wwei23 wrote:c/11947 on a torus:

Code: Select all

``````x = 100, y = 1, rule = B36/S23:T100,1
bo3bob3o3bo2bo3b3ob3ob3ob3ob3obo3bo6bo3bo3b3ob3ob3ob6ob3ob3obo3bo6bo!
``````
How did you find this?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### 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.

muzik
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Location: Scotland

### 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!

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### 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:

Code: Select all

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

Code: Select all

``````x = 50 , y = 1 , rule = B36/S23:T50,1
ooobooobbboboooboooboooooobobbbobbboooboooboooooob``````
EDIT:
c/2583 on a torus:

Code: Select all

``````x = 60 , y = 1 , rule = B36/S23:T60,1
boooboooboooboooboooooobooobooobooobooobbbobbbobooobbobbbobb``````

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

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

muzik wrote:c/106: (B0)

Code: Select all

``````x = 15, y = 6, rule = B0148/S02
ob2ob5ob2obo\$15o\$15o\$15o\$15o\$bob2o5b2obo!
``````
c/132: (p264) (B0)

Code: Select all

``````x = 4, y = 5, rule = B0135/S014
2b2o\$bo\$2bo\$b2o\$obo!
``````
c/154: (B0)

Code: Select all

``````x = 10, y = 8, rule = B0235/S1234
2bo4bo\$2b6o\$2b6o\$2ob4ob2o\$10o\$ob6obo\$10o\$10o!
``````
c/158: (p316)

Code: Select all

``````x = 8, y = 10, rule = B34567/S0456
b4obo\$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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Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### 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.

muzik
Posts: 3910
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### 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!

wwei23
Posts: 1201
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### 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
``````x = 32 , y = 1 , rule = B3/S23:T32,1