Perfect Orthogonal Speeds in Life-like CA

[muzik]

Updated c/13 and c/44 on the OP page, but not in the rule yet.

[muzik]

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).

[wwei23]

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]

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

[wwei23]

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]

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

[wwei23]

Just use All_Speeds.

[muzik]

Just use All_Speeds.

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

[wwei23]

Just use All_Speeds.

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

As a last resort.

[wwei23]

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]

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.

[wwei23]

Does that mean it doesn't count?

[muzik]

obviously.

[wwei23]

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

Code: Select all

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

[wildmyron]

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.

[wwei23]

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]

c/11947 on a torus:

Code: Select all

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

[muzik]

c/11947 on a torus:

Code: Select all

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

How did you find this?

[wwei23]

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

[muzik]

Any such patterns in regular life?

[wwei23]

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]

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]

Any such patterns in regular life?

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

[muzik]

Any such patterns in regular life?

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

Guess it's worth sharing anyway.

[wwei23]

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

(49.7 KiB) Downloaded 169 times

c/19542:

Code: Select all

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

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