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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 one-dimensional 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 Quiz 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