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========================================
Most of us have probably heard of Conway’s Game of Life, but there are
other
cellular automata that are equally interesting. In fact, there is a
group of
256 onedimensional cellular automata that are quite easy to simulate
but still
fun to observe.
To simulate these elementary cellular automata, you first need to
construct a
rule table. This table is a description of the changes that happen in
each
discreet step of time. Here’s the table for the “rule 30” automaton:
±+
 Neighborhood  111  110  101  100  011  010  001  000 
±+
 New Center Cell  0  0  0  1  1  1  1  0 
±+
The first row is the same for this whole family of automata. It
represents the
“neighborhood” of the cell currently being examined, which includes the
cell
itself and one cell to either side of it. The current values of those
cells,
ones being on and zeros being off, can be used to determine the new
value for
this cell in the next discreet step of time.
That new value comes from the bottom row. This row is generated by
taking the
rule number, 30 in this case, in binary form. 1110 is 30 in binary, so
we just
pad the right side with zeros and we have our table.
Once you have the rules, you just apply them to a string of cells. For
example,
given the cells:
11001
The rule 30 table creates:
1101111
Note that cells outside of what I had were off (zeros) for the purposes
of
calculating neighborhoods.
This week’s Ruby Q. is to write a program that accepts up to three
parameters:
the rule as an integer in decimal, the number of steps to simulate, and
the
starting state of the cells as a String of ones and zeros. Here’s a
sample run
of my solution using all three options:
$ ruby cellular_automaton.rb r 110 s 20 c 1
X
XX
XXX
XX X
XXXXX
XX X
XXX XX
XX X XXX
XXXXXXX X
XX XXX
XXX XX X
XX X XXXXX
XXXXX XX X
XX X XXX XX
XXX XXXX X XXX
XX X XX XXXXX X
XXXXXXXX XX XXX
XX XXXX XX X
XXX XX X XXXXX
XX X XXX XXXX X
XXXXX XX XXX X XX
To impress your friends, try adding in support for graphic output in
addition to
printing to the terminal.