Andrew wrote:wildmyron wrote:The two gliders in this rule presented by Carter Bays in his
1987 paper ...
The correct paper and link for the above rule is:
"Patterns for Simple Cellular Automata in a Universe of Dense-Packed Spheres"
http://www.complex-systems.com/pdf/01-5-1.pdf
That is a much more comprehensive discussion of the rule, though in my defense the rule and its gliders are mentioned in the earlier paper.
Andrew wrote:I used [3D.lua's] Random Pattern command for a few minutes and discovered this previously unknown diagonal glider (the Bays paper mentions only 2 known gliders, both orthogonal):
Code: Select all
3D version=1 size=40 pos=19,19,19
# diagonal c/2 spaceship
x=3 y=3 z=2 rule=3D3/3H
bbo$bbo$oo/boo$o!
This has to be the same as the other glider, just traveling in the direction of one of the "diagonal" neighbours when considered from the PoV of the cubic lattice used to simulate the FCC lattice.
I'm sure it's the same effect as why these two orientations of a c/5 glider in B2/S3H appear to be different orthogonal and diagonal gliders when viewed on a square grid:
Code: Select all
#C [[ SQUARECELLS ]]
x = 7, y = 17, rule = B2/S3H
bobo$o$bo2bo$3bobo$2bo2bo$2bo$4bobo4$2bo$2bobo$2o$3bo2bo$bo3bo$4b2o$3b
o!
Andrew wrote:
Could well be so! Here's a table of the resulting patterns for each tree with L layers:
Andrew: Ha, you beat me this time. Continuing the Christmas Tree sequence:
Code: Select all
L result
21 p124
22 p4094
23 p16
24 p2046
25 p252
26 p1022
27 p56
28 p32766
29 p60
30 p62
31 dies
32 p62
33 p60
34 p8190
35 p56
36 unknown
37 p2044
38 p8190
39 p48
40 p2046
This continues to match A160657 for even L, though I didn't verify L=36 due to the time required.
It's worth noting that some of the trees (in particular with odd L) evolve into oscillators with the given period - they don't all have the triangular layer pattern as a phase of the resulting oscillator. This may or may not help with understanding where this behaviour comes from.
For anyone else interested, here's a script to generate these tree patterns
Code: Select all
-- Christmas tree for 3D.lua
local size = 12
local offset = size//2
ClearCells()
for len = size, 1, -1 do
local dy = size - 2*len
for x = 0, len-1 do
for z = 0, x do
SetCell(x-offset, dy, len-z-offset)
end
end
end
For larger trees the grid size will need to be increased above the default.
The
5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on
GitHub and contains well over 1,000,000 spaceships.
Semi-active here - recovering from a severe case of
LWTDS.