1D rules in a finite universe
Posted: November 27th, 2010, 3:45 pm
I decided to have a look at a few aspects of these rules. For convenience, I made a rule table that only stores the current generation. This saves processing power, allows us to use features like pop-plot.py and oscar.py, and, allows us to compare two different patterns one on top of the other. Here is the table for W110 (I saved it as R110.table).
For W22, simply use B3/S23:T0,1. Of course, this does not allow you to compare multiple patterns side-by-side, so a rule table would still be helpful.
Actually, how hard would it be to write a script to generate a rule tree for 1d elementary CA?
One question is: if you start with a single cell in a circular world, what will the eventual period be?
For R110, in a circular universe of width n, we have period:
1,1,1,2,1,9,14,7,7,25,110,18,351...
For W22 we have:
1,1,1,1,1,1,1,1,4,4,4,4,4,1,1,1,12,12,12,12
Then, there's the question of how long it takes to stabilize. In W22, the time taken for a single cell to stabilize in an n cell circular universe is:
1,0,2,2,5,4,4,4,2,2,2,2,2,8...
Code: Select all
n_states:2
neighborhood:vonNeumann
symmetries:none
var a={0,1}
var b={0,1}
# C,N,E,S,W,C'
0,a,0,b,0,0
0,a,0,b,1,0
0,a,1,b,0,1
0,a,1,b,1,1
1,a,0,b,0,1
1,a,0,b,1,1
1,a,1,b,0,1
1,a,1,b,1,0
Actually, how hard would it be to write a script to generate a rule tree for 1d elementary CA?
One question is: if you start with a single cell in a circular world, what will the eventual period be?
For R110, in a circular universe of width n, we have period:
1,1,1,2,1,9,14,7,7,25,110,18,351...
For W22 we have:
1,1,1,1,1,1,1,1,4,4,4,4,4,1,1,1,12,12,12,12
Then, there's the question of how long it takes to stabilize. In W22, the time taken for a single cell to stabilize in an n cell circular universe is:
1,0,2,2,5,4,4,4,2,2,2,2,2,8...