## Perfect Orthogonal Speeds in Life-like CA

For discussion of other cellular automata.
Mr. Missed Her
Posts: 90
Joined: December 7th, 2016, 12:27 pm
Location: Somewhere within [time in years since this was entered] light-years of you.

### Minimum size for a speed

I've had this idea for a while that the smallest possible spaceship for speed c/x has a maximum bounding box area of log2(x). More specifically, (less sure of this) running the pattern in b12345678/s012345678 for one generation will give you a minimum of log2(x) cells. The idea is this: the cells involved in the spaceship can be regarded as information, and the densest way to store information with a bunch of things with two states is in binary. So for an oscillator or spaceship, the maximum number of phases is 2^[number of cells on in at least one phase]. And a spaceship has to move by at least one cell over the course of those phases, giving it a minimum speed of c/[number of phases]. Anyways, a more refined and accurate conjecture would be:

In a semi-totalistic rule with two states, the minimum size of a spaceship of speed c/x is log2(x), size being defined by the number of cells that are on at some point through the spaceship's cycle.

PS: the absolute minimum cell count of a spaceship* is 3. That's when the spaceship's asymmetrical enough to travel in just one direction.
*In a semi-totalistic rule with two states.
There is life on Mars. We put it there with not-completely-sterilized rovers.
And, for that matter, the Moon, Jupiter, Titan, and 67P/Churyumov–Gerasimenko.

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

drc wrote:Throwing a curveball. (c/15d. Yes, I read the title. #rebel):

Code: Select all

``````x = 3, y = 6, rule = B2ce3a/S12
obo\$obo\$bo2\$2bo\$2bo!
``````
I mean, you could start a diagonal type thread if you wanted? I was planning on doing that but I'm disgustingly lazy.

A for awesome
Posts: 2357
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:

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

drc wrote:#rebel
gcc wrote:foo.c:1:2: error: invalid preprocessing directive #rebel
#rebel
^~~~~
praosylen#5847 (Discord)

of flowers, to jump universes to one of springtime in
a land of former winter, where no invisible walls stood,
or could stand for more than a few hours at most...

Mr. Missed Her
Posts: 90
Joined: December 7th, 2016, 12:27 pm
Location: Somewhere within [time in years since this was entered] light-years of you.

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

toroidalet wrote:c:

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``````x = 2, y = 3, rule = B2ace/S
2o2\$o!``````
This can be improved upon to make its period 1. I don't quite understand rule syntax, but the rule in which the same ship is period 1: a rule with no survival conditions, a two neighbor on birth condition, and a two cells on opposite sides of the cell birth condition.
There is life on Mars. We put it there with not-completely-sterilized rovers.
And, for that matter, the Moon, Jupiter, Titan, and 67P/Churyumov–Gerasimenko.

drc
Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

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

Mr. Missed Her wrote:
toroidalet wrote:c:

Code: Select all

``````x = 2, y = 3, rule = B2ace/S
2o2\$o!``````
This can be improved upon to make its period 1. I don't quite understand rule syntax, but the rule in which the same ship is period 1: a rule with no survival conditions, a two neighbor on birth condition, and a two cells on opposite sides of the cell birth condition.

Code: Select all

``````x = 2, y = 3, rule = B2a3r/S
2o2\$o!``````

toroidalet
Posts: 1270
Joined: August 7th, 2016, 1:48 pm
Location: My computer
Contact:

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

improvements:
c:

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``````x = 2, y = 3, rule = B2a3r/S
2o2\$o!``````
c/2:

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``````x = 3, y = 2, rule = B2a3e/S1c2c3e
bo\$obo!``````
or:

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``````x = 3, y = 2, rule = B2e3i/S1c2ce
bo\$obo!
``````
c/3:

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``````x = 4, y = 1, rule = B2cin3aiy6c/S02ac3i
ob2o!
``````
c/4:

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``````x = 4, y = 1, rule = B2cin3aiy/S02-ikn3i
ob2o!
``````
c/5:

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``````x = 4, y = 1, rule = B2cin3aijy4i6c/S02ace3i
ob2o!
``````
c/6:

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``````x = 4, y = 1, rule = B2cin3aijy6c/S02acek3i
ob2o!
``````
c/12:

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``````x = 2, y = 3, rule = B2-a3-ai5a6ai/S1e23-ai
bo\$o\$bo!``````
c/17:

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``````x = 10, y = 5, rule = B34n7/S23
8b2o\$b2o4b2o\$o2bo2bo2bo\$b2o4b2o\$8b2o!
``````
c/18:

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``````x = 6, y = 7, rule = B0234/S0124
5bo4\$5bo2\$o4bo!
``````
c/26:

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``````x = 8, y = 10, rule = B02345/S0124
7bo\$6b2o\$5b3o\$6o\$6o\$6o\$6o\$5b3o\$6b2o\$7bo!
``````
c/60:

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``````x = 17, y = 8, rule = B36/S035678
12bo\$4b9obo\$b14o\$17o\$17o\$b14o\$4b9obo\$12bo!
``````
"But if you close your eyes—does it almost feel like nothing's changed at all?
And if you close your eyes—does it almost feel like you've been here before..."

Posts: 1981
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: Minimum size for a speed

Mr. Missed Her wrote:The idea is this: the cells involved in the spaceship can be regarded as information, and the densest way to store information with a bunch of things with two states is in binary. So for an oscillator or spaceship, the maximum number of phases is 2^[number of cells on in at least one phase].
The problem with this is that information is stored both in ON and OFF cells, so the "size" isn't minimum population but bounding box area, specifically envelope area.
Take a look at the c/5648 in B3457/S4568.

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``````x = 12, y = 14, rule = B3457/S4568
4bo2bo\$4b4o\$2b8o\$2b2ob2ob2o\$obobo2bobobo\$2ob6ob2o\$ob3o2b3obo\$3ob4ob3o\$
2ob6ob2o\$b3o4b3o\$b3o4b3o\$3b2o2b2o\$3bo4bo\$5b2o!``````

The cells in the pattern change pseudorandomly and changes gradually shift the shape forward. If we let A be the total number of cells that are ON at least once in a single period, then each of the A cells can be either on or off, giving 2^A, which is greater than 2^P, considering that some cells are OFF at any given time. In this case, the minimum speed would be c/2^162 (~1.7e-49 cells/gen).
BUT WAIT! The total number of unknown cells can't be 182 in this case, because the ship is even-bilateral symmetric, so the actual minimum speed is 2^-81 (~4.1e-25 cells/gen).
This is still slower than your bound of at least 2^-78.
Similar modification is required for odd symmetric (with variation to prevent half-counting middle cells) and glide symmetry (A = total number of cells ON at any point in a half-period).
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Mr. Missed Her
Posts: 90
Joined: December 7th, 2016, 12:27 pm
Location: Somewhere within [time in years since this was entered] light-years of you.

### Re: Minimum size for a speed

Mr. Missed Her wrote:The idea is this: the cells involved in the spaceship can be regarded as information, and the densest way to store information with a bunch of things with two states is in binary. So for an oscillator or spaceship, the maximum number of phases is 2^[number of cells on in at least one phase].
The problem with this is that information is stored both in ON and OFF cells, so the "size" isn't minimum population but bounding box area, specifically envelope area.
Take a look at the c/5648 in B3457/S4568.

Code: Select all

``````x = 12, y = 14, rule = B3457/S4568
4bo2bo\$4b4o\$2b8o\$2b2ob2ob2o\$obobo2bobobo\$2ob6ob2o\$ob3o2b3obo\$3ob4ob3o\$
2ob6ob2o\$b3o4b3o\$b3o4b3o\$3b2o2b2o\$3bo4bo\$5b2o!``````

The cells in the pattern change pseudorandomly and changes gradually shift the shape forward. If we let A be the total number of cells that are ON at least once in a single period, then each of the A cells can be either on or off, giving 2^A, which is greater than 2^P, considering that some cells are OFF at any given time. In this case, the minimum speed would be c/2^162 (~1.7e-49 cells/gen).
BUT WAIT! The total number of unknown cells can't be 182 in this case, because the ship is even-bilateral symmetric, so the actual minimum speed is 2^-81 (~4.1e-25 cells/gen).
This is still slower than your bound of at least 2^-78.
Similar modification is required for odd symmetric (with variation to prevent half-counting middle cells) and glide symmetry (A = total number of cells ON at any point in a half-period).
Your totally right. Only thing was, I meant the number of cells you'd get if you overlapped all the phases on top of each other and then counted.

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``````x = 67, y = 18, rule = LifeHistory
33.2B\$31.6B\$29.10B\$27.4BA4BA4B\$26.3B2AB4AB2A3B\$27.4BA4BA4B\$29.10B\$31.
6B\$33.2B5\$2D2.3D.D.D.3D2.D2.2D2.3D2.2D2.D2.3D.D.D.D4.D2.D.D6.D3.D\$D.D
.D3.3D2.D2.D.D.D.D.D3.D3.D.D2.D2.D.D.D3.D.D.3D.3D.D.D.D.D\$2D2.2D2.3D
2.D2.3D.D.D.2D2.D3.3D2.D2.3D.D3.D.D.3D6.D2.D.D\$D3.D3.D.D2.D2.D.D.D.D.
D3.D3.D.D2.D2.D.D.D3.D.D.D.D.3D.D.D.D.D\$D3.3D.D.D2.D2.D.D.2D2.3D2.2D.
D.D2.D2.D.D.3D2.D2.D.D6.D3.D!``````
It should be true that we need only to count half of a symmetrical ship, because if the ship's symmetrical, both halves are doing the exact same thing. (Count the cells on the axis of symmetry, because they don't have a matching row of cells.) Same general thing for glide-symmetric. Now, I was going for "what would the minimum size for a certain speed spaceship be" and not "what would the minimum speed for a certain spaceship be," but your post does point out that the smallest spaceships for a certain speed should be asymmetrical.
There is life on Mars. We put it there with not-completely-sterilized rovers.
And, for that matter, the Moon, Jupiter, Titan, and 67P/Churyumov–Gerasimenko.

Posts: 1981
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

Back on topic, a small c/10 from 83bismuth38:

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``````x = 3, y = 4, rule = B34aenrw5c/S12-n3e4c
obo\$o\$o\$bo!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

drc
Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

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

BlinkerSpawn wrote:Back on topic, a small c/10 from 83bismuth38:

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``````x = 3, y = 4, rule = B34aenrw5c/S12-n3e4c
obo\$o\$o\$bo!
``````
Works in B34/S12.

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

Finally got around to updating the op. This leaves these speeds currently not covered:

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``````c/15 (EDIT: found)
c/19 (EDIT: found)
c/20 (EDIT: kinda found) (EDIT: found)
c/21 (EDIT: found)
c/22
c/24 (EDIT: found)
c/28 (EDIT: kinda found)
c/29
c/30
c/31
c/32
c/33 (EDIT: kinda found)
c/36
c/37
c/38
c/39
c/41-c/59 (EDIT: realized I forgot a c/47) (EDIT: c/44 found)
c/61-c/72 (EDIT: c/64 found) (EDIT: c/70 kinda found)
c/74-c/97 (EDIT: c/76 kinda found)
c/99-c/131
c/133-c/140
c/142-c/153
c/155
c/156
c/157
c/159-c/2067
c/2069-c/5647
c/5649+``````
these speeds without true period ships:

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``````c/18 (EDIT: done)
c/20 (new) (EDIT: done)
c/23 (EDIT: done)
c/27
c/28 (new)
c/33 (new)
c/35
c/47
c/132
c/158``````
and these speeds without non-B0 ships:

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``````c/20 (EDIT: done)
c/26 (EDIT: done)
c/33
c/47
[b]c[/b]/70
[b]c[/b]/76
c/132
c/153
``````
Last edited by muzik on June 17th, 2017, 4:16 pm, edited 13 times in total.

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

A WIP rule mashup for these spaceships to aid in visualizing different speeds, currently up to c/13:

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``````@RULE RainbowASOv0.0
@TABLE
n_states:8
neighborhood:Moore
symmetries:rotate4reflect
var aa=1
var ab=2
var ac=3
var ae=5
var af=6
var ag=7
var a={0,1,2,3,4,5,6,7}
var b=a
var d=a
var e=a
var f=a
var g=a
var i=a
var j=a
var k=a
#life
0,aa,aa,aa,0,0,0,0,0,aa
0,aa,aa,0,aa,0,0,0,0,aa
0,aa,aa,0,0,aa,0,0,0,aa
0,aa,aa,0,0,0,aa,0,0,aa
0,aa,aa,0,0,0,0,aa,0,aa
0,aa,aa,0,0,0,0,0,aa,aa
0,aa,0,aa,0,aa,0,0,0,aa
0,aa,0,aa,0,0,aa,0,0,aa
0,aa,0,0,aa,0,aa,0,0,aa
0,0,aa,0,aa,0,aa,0,0,aa
aa,aa,aa,0,0,0,0,0,0,aa
aa,aa,0,aa,0,0,0,0,0,aa
aa,aa,0,0,aa,0,0,0,0,aa
aa,aa,0,0,0,aa,0,0,0,aa
aa,0,aa,0,aa,0,0,0,0,aa
aa,0,aa,0,0,aa,0,0,0,aa
aa,0,aa,0,0,0,aa,0,0,aa
aa,aa,aa,aa,0,0,0,0,0,aa
aa,aa,aa,0,aa,0,0,0,0,aa
aa,aa,aa,0,0,aa,0,0,0,aa
aa,aa,aa,0,0,0,aa,0,0,aa
aa,aa,aa,0,0,0,0,aa,0,aa
aa,aa,aa,0,0,0,0,0,aa,aa
aa,aa,0,aa,0,aa,0,0,0,aa
aa,aa,0,aa,0,0,aa,0,0,aa
aa,aa,0,0,aa,0,aa,0,0,aa
aa,0,aa,0,aa,0,aa,0,0,aa
#c1
0,ab,ab,0,0,0,0,0,0,ab
0,ab,ab,0,0,ab,0,0,0,ab
#c8
0,ac,0,ac,0,0,0,0,0,ac
0,ac,0,0,ac,0,0,0,0,ac
0,ac,0,0,0,ac,0,0,0,ac
0,0,ac,0,ac,0,0,0,0,ac
0,0,ac,0,0,0,ac,0,0,ac
0,ac,ac,ac,0,0,0,0,0,ac
0,ac,ac,0,ac,0,0,0,0,ac
0,ac,ac,0,0,ac,0,0,0,ac
0,ac,ac,0,0,0,ac,0,0,ac
0,ac,0,ac,0,ac,0,0,0,ac
0,ac,0,ac,0,0,ac,0,0,ac
0,ac,0,0,ac,0,ac,0,0,ac
0,0,ac,0,ac,0,ac,0,0,ac
ac,ac,0,0,0,0,0,0,0,ac
ac,0,ac,0,0,0,0,0,0,ac
ac,ac,ac,ac,0,0,0,0,0,ac
ac,ac,ac,0,ac,0,0,0,0,ac
ac,ac,ac,0,0,ac,0,0,0,ac
ac,ac,ac,0,0,0,ac,0,0,ac
ac,ac,ac,0,0,0,0,ac,0,ac
ac,ac,ac,0,0,0,0,0,ac,ac
ac,ac,0,ac,0,ac,0,0,0,ac
ac,ac,0,ac,0,0,ac,0,0,ac
ac,ac,0,0,ac,0,ac,0,0,ac
ac,0,ac,0,ac,0,ac,0,0,ac
#c9
#c11
0,ae,ae,0,0,0,0,0,0,ae
0,ae,0,ae,0,0,0,0,0,ae
0,ae,0,0,ae,0,0,0,0,ae
0,ae,0,0,0,ae,0,0,0,ae
0,0,ae,0,ae,0,0,0,0,ae
0,0,ae,0,0,0,ae,0,0,ae
0,ae,ae,ae,ae,0,0,0,0,ae
0,ae,ae,ae,0,ae,0,0,0,ae
0,ae,ae,ae,0,0,ae,0,0,ae
0,ae,ae,0,ae,ae,0,0,0,ae
0,ae,ae,0,ae,0,ae,0,0,ae
0,ae,ae,0,ae,0,0,ae,0,ae
0,ae,ae,0,ae,0,0,0,ae,ae
0,ae,ae,0,0,ae,ae,0,0,ae
0,ae,ae,0,0,ae,0,ae,0,ae
0,ae,ae,0,0,ae,0,0,ae,ae
0,ae,ae,0,0,0,ae,ae,0,ae
0,ae,0,ae,0,ae,0,ae,0,ae
0,0,ae,0,ae,0,ae,0,ae,ae
ae,0,0,0,0,0,0,0,0,ae
ae,ae,ae,0,0,0,0,0,0,ae
ae,ae,0,ae,0,0,0,0,0,ae
ae,ae,0,0,ae,0,0,0,0,ae
ae,ae,0,0,0,ae,0,0,0,ae
ae,0,ae,0,ae,0,0,0,0,ae
ae,0,ae,0,0,0,ae,0,0,ae
#c12
0,af,af,af,0,0,0,0,0,af
0,af,af,0,af,0,0,0,0,af
0,af,af,0,0,af,0,0,0,af
0,af,af,0,0,0,af,0,0,af
0,af,af,0,0,0,0,af,0,af
0,af,af,0,0,0,0,0,af,af
0,af,0,af,0,af,0,0,0,af
0,af,0,af,0,0,af,0,0,af
0,af,0,0,af,0,af,0,0,af
0,0,af,0,af,0,af,0,0,af
af,af,0,af,0,0,0,0,0,af
af,af,0,0,af,0,0,0,0,af
af,af,0,0,0,af,0,0,0,af
af,0,af,0,af,0,0,0,0,af
af,0,af,0,0,0,af,0,0,af
af,af,af,0,af,0,0,0,0,af
af,af,af,0,0,af,0,0,0,af
af,af,af,0,0,0,af,0,0,af
af,af,af,0,0,0,0,af,0,af
af,af,af,0,0,0,0,0,af,af
af,af,0,af,0,af,0,0,0,af
af,af,0,af,0,0,af,0,0,af
af,af,0,0,af,0,af,0,0,af
af,0,af,0,af,0,af,0,0,af
af,af,af,af,0,af,0,0,0,af
af,af,af,af,0,0,af,0,0,af
af,af,af,0,af,0,af,0,0,af
af,af,af,0,af,0,0,af,0,af
af,af,af,0,af,0,0,0,af,af
af,af,af,0,0,af,af,0,0,af
af,af,af,0,0,af,0,af,0,af
af,af,af,0,0,af,0,0,af,af
af,af,af,0,0,0,af,af,0,af
af,af,0,af,0,af,0,af,0,af
af,0,af,0,af,0,af,0,af,af
af,af,af,af,af,af,0,0,0,af
af,af,af,af,af,0,0,af,0,af
af,af,af,af,af,0,0,0,af,af
af,af,af,0,af,af,0,af,0,af
af,af,af,0,af,0,af,af,0,af
#c13
0,ag,ag,ag,0,0,0,0,0,ag
0,ag,ag,0,ag,0,0,0,0,ag
0,ag,ag,0,0,ag,0,0,0,ag
0,ag,ag,0,0,0,ag,0,0,ag
0,ag,ag,0,0,0,0,ag,0,ag
0,ag,ag,0,0,0,0,0,ag,ag
0,ag,0,ag,0,ag,0,0,0,ag
0,ag,0,ag,0,0,ag,0,0,ag
0,ag,0,0,ag,0,ag,0,0,ag
0,0,ag,0,ag,0,ag,0,0,ag
ag,ag,ag,0,0,0,0,0,0,ag
ag,ag,0,ag,0,0,0,0,0,ag
ag,ag,0,0,ag,0,0,0,0,ag
ag,ag,0,0,0,ag,0,0,0,ag
ag,0,ag,0,ag,0,0,0,0,ag
ag,0,ag,0,0,0,ag,0,0,ag
ag,ag,ag,ag,ag,0,0,0,0,ag
ag,ag,ag,ag,0,ag,0,0,0,ag
ag,ag,ag,ag,0,0,ag,0,0,ag
ag,ag,ag,0,ag,ag,0,0,0,ag
ag,ag,ag,0,ag,0,ag,0,0,ag
ag,ag,ag,0,ag,0,0,ag,0,ag
ag,ag,ag,0,ag,0,0,0,ag,ag
ag,ag,ag,0,0,ag,ag,0,0,ag
ag,ag,ag,0,0,ag,0,ag,0,ag
ag,ag,ag,0,0,ag,0,0,ag,ag
ag,ag,ag,0,0,0,ag,ag,0,ag
ag,ag,0,ag,0,ag,0,ag,0,ag
ag,0,ag,0,ag,0,ag,0,ag,ag
ag,ag,ag,ag,ag,ag,0,0,0,ag
ag,ag,ag,ag,ag,0,ag,0,0,ag
ag,ag,ag,ag,ag,0,0,ag,0,ag
ag,ag,ag,ag,ag,0,0,0,ag,ag
ag,ag,ag,ag,0,ag,ag,0,0,ag
ag,ag,ag,ag,0,ag,0,ag,0,ag
ag,ag,ag,0,ag,ag,ag,0,0,ag
ag,ag,ag,0,ag,ag,0,ag,0,ag
ag,ag,ag,0,ag,0,ag,ag,0,ag
ag,ag,ag,0,ag,0,ag,0,ag,ag
ag,ag,ag,ag,ag,ag,ag,0,0,ag
ag,ag,ag,ag,ag,ag,0,ag,0,ag
ag,ag,ag,ag,ag,0,ag,ag,0,ag
ag,ag,ag,ag,ag,0,ag,0,ag,ag
ag,ag,ag,ag,0,ag,ag,ag,0,ag
ag,ag,ag,0,ag,ag,ag,0,ag,ag

#death
a,b,d,e,f,g,i,j,k,0

@COLORS

0 0 0 0
1 255 255 255
2 255 0 0
3 0 255 0
4 0 0 255
5 0 255 255
6 255 0 255
7 255 255 0``````

Code: Select all

``````x = 117, y = 31, rule = RainbowASOv0.0
2.2G4.4F9.E8.A11.D3.C4.2A.A2.2A11.A8.2A12.A5.A5.A.A6.B.B\$.2G6.F.F5.E
2.E9.A9.D5.C.C3.2A2.A2.A10.A5.2A2.A9.A3.2A2.A.A4.A2.A7.B\$G2.G.G3.F.F
9.E9.A2.A8.D12.A.A11.A5.2A2.A8.2A2.A4.A.A7.2A\$.G.3G2.4F17.3A.2A.A3.D
16.A23.A7.2A9.A9.A\$.G.G21.2A6.2A.2A4.D3.C.C2.A16.3A5.A.4A8.A9.2A6.4A\$
.G.3G19.2A6.2A.2A8.C4.3A17.A3.2A.A11.2A7.A.A5.A4.A\$G2.G.G23.3A.2A.A
17.A16.A7.3A8.A18.A2.A\$.2G28.A2.A18.A7.A3.2A4.A8.A10.A8.3A6.A2.A\$2.2G
26.A20.2A7.A.A.A4.A10.2A9.3A6.A.A8.A\$30.A33.2A16.A7.A8.A.A3.A.4A\$63.
2A2.2A12.A6.2A4.A6.2A2.A3.A\$64.A.2A.A11.A26.A\$64.A5.A6.3A12.2A7.A4.A.
A\$64.A5.A16.A4.A6.A.A\$64.A.2A.A7.3A8.2A.A7.A.A5.3A\$63.2A2.2A12.A7.A.A
8.A7.2A\$64.2A15.A6.3A16.3A\$60.A.A.A4.A12.A.2A2.A\$61.A3.2A4.A8.2A4.A
19.A.A\$71.A8.A27.A\$71.A7.3A23.A3.A\$68.3A4.2A.A26.A.4A\$76.A.4A29.A\$70.
A10.A27.A2.A\$70.A5.2A2.A28.A2.A\$70.A5.2A2.A26.A4.A\$79.2A27.4A\$110.A\$
108.2A\$105.A2.A\$105.A.A!
``````

AforAmpere
Posts: 1230
Joined: July 1st, 2016, 3:58 pm

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

Asked for a c/21? Here you go.

Code: Select all

``````x = 5, y = 8, rule = B36/S0135
bobo\$2bo\$2bo\$bobo\$bobo\$o3bo2\$2bo!
``````
Wildmyron and I 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

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

that's fantastic, one more checked off the list.

Of course, there's infinitely more of them.

AforAmpere
Posts: 1230
Joined: July 1st, 2016, 3:58 pm

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

c/22:

Code: Select all

``````x = 8, y = 6, rule = B3567/S1367
b2o2b2o\$obo2bobo\$2bo2bo3\$3b2o!
``````
c/29:

Code: Select all

``````x = 7, y = 4, rule = B345/S0478
2b3o\$ob3obo\$b5o\$o5bo!
``````
c/30:

Code: Select all

``````x = 9, y = 5, rule = B346/S3578
bo5bo\$b2obob2o\$3o3b3o\$4bo\$bo5bo!
``````
Wildmyron and I 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

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

...how are you finding these so fast? Is there some secret database I don't know about?

AforAmpere
Posts: 1230
Joined: July 1st, 2016, 3:58 pm

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

I have a huge list of spaceships, most from the glider database.
Wildmyron and I 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

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

right then

Is there a script or search engine trick that can let you look up any period and speed on the glider database?

AforAmpere
Posts: 1230
Joined: July 1st, 2016, 3:58 pm

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

No, I just looked through thousands of rules, because I had a lot of time. It is kind of ridiculous, but I have like 200 speeds, with many at 5 cell ships. A script could be written for it, David Eppstein has a raw data file, that with a simple python program, it could probably read. I tried to write the script on an IPad, but it couldn't process that much (go figure).

EDIT: Actually, you can use the search on page stuff on the file to find certain speeds, you just have to know the notation.
Wildmyron and I 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

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

I definitely remembered it from somewhere:

viewtopic.php?f=11&t=2111&p=29221&hilit=database#p29220

AforAmpere
Posts: 1230
Joined: July 1st, 2016, 3:58 pm

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

c/20 orthogonal:

Code: Select all

``````x = 3, y = 5, rule = B35678/S1247
b2o\$2o\$3o\$2o\$b2o!
``````
c/23 orthogonal:

Code: Select all

``````x = 4, y = 7, rule = B3/S0145678
bo\$bo2\$2obo2\$bo\$bo!
``````
c/26 orthogonal:

Code: Select all

``````x = 7, y = 6, rule = B3457/S04578
2bobo\$4ob2o\$o5bo\$o5bo\$4ob2o\$2bobo!
``````
Wildmyron and I 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

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

Thanks for the help, I do appreciate it you know.

A list of every speed up to c/100 not yet covered correctly, I would not be surprised if some of these speeds have not yet been found:

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
--
<FOUND> c/27 - current example is p54
<FOUND> c/28 - current example is p56
<FOUND> c/31
<FOUND> c/32
<FOUND> c/33 - current example is p264 and in a B0 rule
<FOUND> c/35 - current example is p70
<FOUND> c/36
<FOUND> c/37
<FOUND> c/38
<FOUND> c/39
<FOUND> c/41
<FOUND> c/43
<FOUND> c/45
<FOUND> c/46
<FOUND> c/47 - current example is p94 and in a B0 rule
<FOUND> c/48
<FOUND> c/49
<FOUND> c/50
<FOUND> c/53
<FOUND> c/54
<FOUND> c/55 - current example is p110
<FOUND> c/56
<FOUND> c/59
<FOUND> c/63
<FOUND> c/66
<FOUND> c/67
<FOUND> c/70
<FOUND> c/81
<FOUND> c/83
<FOUND> c/86
<FOUND> c/87
<FOUND> c/89
<FOUND> c/92
<REPLACED BY ADJUSTABLE RULE> c/42 - current example is p84
<REPLACED BY ADJUSTABLE RULE> c/62 - current example is in a B0 rule
<REPLACED BY ADJUSTABLE RULE> c/68 - current example is in a B0 rule
<REPLACED BY ADJUSTABLE RULE> c/74 - current example is in a B0 rule
<REPLACED BY ADJUSTABLE RULE> c/76 - current example is in a B0 rule
<REPLACED BY ADJUSTABLE RULE> c/80 - current example is in a B0 rule
``````
Last edited by muzik on July 4th, 2017, 3:51 pm, edited 6 times in total.

AforAmpere
Posts: 1230
Joined: July 1st, 2016, 3:58 pm

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

Thanks for that Muzik. Here's speeds up to c/40.

c/27 orthogonal:

Code: Select all

``````x = 5, y = 5, rule = B34568/S3678
bo\$ob3o\$o\$ob3o\$bo!
``````
c/28 orthogonal:

Code: Select all

``````x = 5, y = 5, rule = B35678/S2467
obobo\$3b2o\$bo2bo\$3b2o\$obobo!
``````
c/31 orthogonal:

Code: Select all

``````x = 6, y = 7, rule = B34678/S026
3bo\$bo\$4b2o\$o3bo\$4b2o\$bo\$3bo!
``````
c/32 orthogonal:

Code: Select all

``````x = 7, y = 6, rule = B3678/S2378
o3b2o\$o3b3o\$o\$o\$o3b3o\$o3b2o!
``````
c/33 orthogonal:

Code: Select all

``````x = 7, y = 4, rule = B37/S024578
o2b2obo\$ob2o2bo\$ob2o2bo\$o2b2obo!
``````
c/35 orthogonal:

Code: Select all

``````x = 4, y = 13, rule = B36/S237
2o\$2o4\$bobo\$o2bo\$bobo4\$2o\$2o!
``````
c/36 orthogonal:

Code: Select all

``````x = 5, y = 6, rule = B35/S3467
3b2o\$o2b2o\$2obo\$2obo\$o2b2o\$3b2o!
``````
c/37 orthogonal:

Code: Select all

``````x = 6, y = 6, rule = B346/S356
3b2o\$2o2b2o\$2obobo\$2obobo\$2o2b2o\$3b2o!
``````
c/38 orthogonal:

Code: Select all

``````x = 10, y = 5, rule = B3467/S01567
2bo2bo2\$3o6bo2\$2bo2bo!
``````
c/39 orthogonal:

Code: Select all

``````x = 5, y = 17, rule = B378/S24568
o\$2o\$2o\$obo2\$bo\$2b3o4\$2b3o\$bo2\$obo\$2o\$2o\$o!
``````
Wildmyron and I 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

muzik
Posts: 4181
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

So you have all speeds up to c/40? That's a pretty insanely expansive glider collection. Not bad.

I also managed to find a c/55 while raking through the threads here in OCA since i took a massive break and want to see what went on. It's p110 though, so will need a reduced period version.

AforAmpere
Posts: 1230
Joined: July 1st, 2016, 3:58 pm

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

Actually, I was missing a c/39, but I did a search on the raw data and found one, it is fast, and I am planning to add more to my list.

EDIT, a c/55, only one on the database that is not higher period:

Code: Select all

``````x = 8, y = 9, rule = B3457/S158
3bo\$bo3bo\$2bobo\$2bo\$3o4bo\$2bo\$2bobo\$bo3bo\$3bo!
``````
Last edited by AforAmpere on June 17th, 2017, 5:26 pm, edited 1 time in total.
Wildmyron and I 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