## Perfect Orthogonal Speeds in Life-like CA

For discussion of other cellular automata.

### 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.

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

drc wrote:Throwing a curveball. (c/15d. Yes, I read the title. #rebel):
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.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3465
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

drc wrote:#rebel

gcc wrote:foo.c:1:2: error: invalid preprocessing directive #rebel
#rebel
^~~~~
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

A for awesome

Posts: 1876
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

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

toroidalet wrote:c:
x = 2, y = 3, rule = B2ace/S
2o2$o! This can be improved upon to make its period 1. I don't quite understand rule syntax, but the rule in which the same ship is period 1: a rule with no survival conditions, a two neighbor on birth condition, and a two cells on opposite sides of the cell birth condition. There is life on Mars. We put it there with not-completely-sterilized rovers. And, for that matter, the Moon, Jupiter, Titan, and 67P/Churyumov–Gerasimenko. Mr. Missed Her Posts: 90 Joined: December 7th, 2016, 12:27 pm Location: Somewhere within [time in years since this was entered] light-years of you. ### Re: Perfect Orthogonal Speeds in Life-like CA Mr. Missed Her wrote: toroidalet wrote:c: x = 2, y = 3, rule = B2ace/S 2o2$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.

x = 2, y = 3, rule = B2a3r/S
2o2$o! This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) Current rule interest: B2ce3-ir4a5y/S2-c3-y drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Perfect Orthogonal Speeds in Life-like CA improvements: c: x = 2, y = 3, rule = B2a3r/S 2o2$o!

c/2:
x = 3, y = 2, rule = B2a3e/S1c2c3e
bo$obo! or: x = 3, y = 2, rule = B2e3i/S1c2ce bo$obo!

c/3:
x = 4, y = 1, rule = B2cin3aiy6c/S02ac3i
ob2o!

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

c/5:
x = 4, y = 1, rule = B2cin3aijy4i6c/S02ace3i
ob2o!

c/6:
x = 4, y = 1, rule = B2cin3aijy6c/S02acek3i
ob2o!

c/12:
x = 2, y = 3, rule = B2-a3-ai5a6ai/S1e23-ai
bo$o$bo!

c/17:
x = 10, y = 5, rule = B34n7/S23
8b2o$b2o4b2o$o2bo2bo2bo$b2o4b2o$8b2o!

c/18:
x = 6, y = 7, rule = B0234/S0124
5bo4$5bo2$o4bo!

c/26:
x = 8, y = 10, rule = B02345/S0124
7bo$6b2o$5b3o$6o$6o$6o$6o$5b3o$6b2o$7bo! c/60: x = 17, y = 8, rule = B36/S035678 12bo$4b9obo$b14o$17o$17o$b14o$4b9obo$12bo!
"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

toroidalet

Posts: 1002
Joined: August 7th, 2016, 1:48 pm
Location: my computer

### 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.
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] BlinkerSpawn Posts: 1889 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: Minimum size for a speed BlinkerSpawn wrote: 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. 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.
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$D3.3D.D.D2.D2.D.D.2D2.3D2.2D. D.D2.D2.D.D.3D2.D2.D.D6.D3.D! It should be true that we need only to count half of a symmetrical ship, because if the ship's symmetrical, both halves are doing the exact same thing. (Count the cells on the axis of symmetry, because they don't have a matching row of cells.) Same general thing for glide-symmetric. Now, I was going for "what would the minimum size for a certain speed spaceship be" and not "what would the minimum speed for a certain spaceship be," but your post does point out that the smallest spaceships for a certain speed should be asymmetrical. There is life on Mars. We put it there with not-completely-sterilized rovers. And, for that matter, the Moon, Jupiter, Titan, and 67P/Churyumov–Gerasimenko. Mr. Missed Her Posts: 90 Joined: December 7th, 2016, 12:27 pm Location: Somewhere within [time in years since this was entered] light-years of you. ### Re: Perfect Orthogonal Speeds in Life-like CA Back on topic, a small c/10 from 83bismuth38: x = 3, y = 4, rule = B34aenrw5c/S12-n3e4c obo$o$o$bo!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1889
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

BlinkerSpawn wrote:Back on topic, a small c/10 from 83bismuth38:
x = 3, y = 4, rule = B34aenrw5c/S12-n3e4c
obo$o$o$bo! Works in B34/S12. This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) Current rule interest: B2ce3-ir4a5y/S2-c3-y drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Perfect Orthogonal Speeds in Life-like CA Finally got around to updating the op. This leaves these speeds currently not covered: 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: 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: 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. Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3465 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: @RULE RainbowASOv0.0 @TABLE n_states:8 neighborhood:Moore symmetries:rotate4reflect var aa=1 var ab=2 var ac=3 var ad=4 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 0,ad,0,0,ad,0,0,0,0,ad 0,ad,0,0,0,ad,0,0,0,ad 0,ad,ad,ad,0,0,0,0,0,ad 0,ad,ad,0,ad,0,0,0,0,ad 0,ad,ad,0,0,ad,0,0,0,ad 0,ad,ad,0,0,0,ad,0,0,ad 0,ad,ad,0,0,0,0,ad,0,ad 0,ad,ad,0,0,0,0,0,ad,ad 0,ad,0,ad,0,ad,0,0,0,ad 0,ad,0,ad,0,0,ad,0,0,ad 0,ad,0,0,ad,0,ad,0,0,ad 0,0,ad,0,ad,0,ad,0,0,ad 0,ad,ad,0,ad,ad,0,0,0,ad ad,ad,0,0,0,0,0,0,0,ad ad,0,ad,0,0,0,0,0,0,ad ad,ad,ad,ad,0,0,0,0,0,ad ad,ad,ad,0,ad,0,0,0,0,ad ad,ad,ad,0,0,ad,0,0,0,ad ad,ad,ad,0,0,0,ad,0,0,ad ad,ad,ad,0,0,0,0,ad,0,ad ad,ad,ad,0,0,0,0,0,ad,ad ad,ad,0,ad,0,0,ad,0,0,ad ad,ad,0,0,ad,0,ad,0,0,ad ad,0,ad,0,ad,0,ad,0,0,ad #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 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! Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3465 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds in Life-like CA Asked for a c/21? Here you go. x = 5, y = 8, rule = B36/S0135 bobo$2bo$2bo$bobo$bobo$o3bo2$2bo! I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule - Finish a rule with ships with period >= f_e_0(n) (in progress) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### Re: Perfect Orthogonal Speeds in Life-like CA that's fantastic, one more checked off the list. Of course, there's infinitely more of them. Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3465 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds in Life-like CA c/22: x = 8, y = 6, rule = B3567/S1367 b2o2b2o$obo2bobo$2bo2bo3$3b2o!

c/29:
x = 7, y = 4, rule = B345/S0478
2b3o$ob3obo$b5o$o5bo! c/30: x = 9, y = 5, rule = B346/S3578 bo5bo$b2obob2o$3o3b3o$4bo$bo5bo! 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) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### 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? Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3465 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds in Life-like CA I have a huge list of spaceships, most from the glider database. 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) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### 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? Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3465 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### 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. 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) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### Re: Perfect Orthogonal Speeds in Life-like CA Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3465 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds in Life-like CA c/20 orthogonal: x = 3, y = 5, rule = B35678/S1247 b2o$2o$3o$2o$b2o! c/23 orthogonal: x = 4, y = 7, rule = B3/S0145678 bo$bo2$2obo2$bo$bo! c/26 orthogonal: x = 7, y = 6, rule = B3457/S04578 2bobo$4ob2o$o5bo$o5bo$4ob2o$2bobo!
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)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

### 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:

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

Posts: 3465
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

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

c/27 orthogonal:
x = 5, y = 5, rule = B34568/S3678
bo$ob3o$o$ob3o$bo!

c/28 orthogonal:
x = 5, y = 5, rule = B35678/S2467
obobo$3b2o$bo2bo$3b2o$obobo!

c/31 orthogonal:
x = 6, y = 7, rule = B34678/S026
3bo$bo$4b2o$o3bo$4b2o$bo$3bo!

c/32 orthogonal:
x = 7, y = 6, rule = B3678/S2378
o3b2o$o3b3o$o$o$o3b3o$o3b2o! c/33 orthogonal: x = 7, y = 4, rule = B37/S024578 o2b2obo$ob2o2bo$ob2o2bo$o2b2obo!

c/35 orthogonal:
x = 4, y = 13, rule = B36/S237
2o$2o4$bobo$o2bo$bobo4$2o$2o!

c/36 orthogonal:
x = 5, y = 6, rule = B35/S3467
3b2o$o2b2o$2obo$2obo$o2b2o$3b2o! c/37 orthogonal: x = 6, y = 6, rule = B346/S356 3b2o$2o2b2o$2obobo$2obobo$2o2b2o$3b2o!

c/38 orthogonal:
x = 10, y = 5, rule = B3467/S01567
2bo2bo2$3o6bo2$2bo2bo!

c/39 orthogonal:
x = 5, y = 17, rule = B378/S24568
o$2o$2o$obo2$bo$2b3o4$2b3o$bo2$obo$2o$2o$o! 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) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### 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. Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3465 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### 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: 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.
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)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

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