bgneal@46: """ Code example from Complexity and Computation, a book about
bgneal@46: exploring complexity science with Python.  Available free from
bgneal@46: 
bgneal@46: http://greenteapress.com/complexity
bgneal@46: 
bgneal@46: Copyright 2011 Allen B. Downey.
bgneal@46: Distributed under the GNU General Public License at gnu.org/licenses/gpl.html.
bgneal@46: """
bgneal@46: 
bgneal@46: import numpy
bgneal@46: 
bgneal@46: class CA(object):
bgneal@46:     """A CA is a cellular automaton; the parameters for __init__ are:
bgneal@46: 
bgneal@46:     rule:  an integer in the range 0-255 that represents the CA rule
bgneal@46:            using Wolfram's encoding.
bgneal@46:     n:     the number of rows (timesteps) in the result.
bgneal@46:     ratio: the ratio of columns to rows.
bgneal@46:     """
bgneal@46: 
bgneal@46:     def __init__(self, rule, n=100, ratio=2):
bgneal@46:         """Attributes:
bgneal@46:         table:  rule dictionary that maps from triple to next state.
bgneal@46:         n, m:   are the number of rows, columns.
bgneal@46:         array:  the numpy array that contains the data.
bgneal@46:         next:   the index of the next empty row.
bgneal@46:         """
bgneal@46:         self.table = self.make_table(rule)
bgneal@46:         self.n = n
bgneal@46:         self.m = ratio*n + 1
bgneal@46:         self.array = numpy.zeros((n, self.m), dtype=numpy.int8)
bgneal@46:         self.next = 0
bgneal@46: 
bgneal@46:     def make_table(self, rule):
bgneal@46:         """Returns a table for the given CA rule.  The table is a 
bgneal@46:         dictionary that maps 3-tuples to binary values.
bgneal@46:         """
bgneal@46:         table = {}
bgneal@46:         for i, bit in enumerate(binary(rule, 8)):
bgneal@46:             t = binary(7-i, 3)
bgneal@46:             table[t] = bit
bgneal@46:         return table
bgneal@46: 
bgneal@46:     def start_single(self):
bgneal@46:         """Starts with one cell in the middle of the top row."""
bgneal@46:         self.array[0, self.m/2] = 1
bgneal@46:         self.next += 1
bgneal@46: 
bgneal@46:     def start_random(self):
bgneal@46:         """Start with random values in the top row."""
bgneal@46:         self.array[0] = numpy.random.random([1,self.m]).round()
bgneal@46:         self.next += 1
bgneal@46: 
bgneal@46:     def loop(self, steps=1):
bgneal@46:         """Executes the given number of time steps."""
bgneal@46:         [self.step() for i in xrange(steps)]
bgneal@46: 
bgneal@46:     def step(self):
bgneal@46:         """Executes one time step by computing the next row of the array."""
bgneal@46:         i = self.next
bgneal@46:         self.next += 1
bgneal@46: 
bgneal@46:         a = self.array
bgneal@46:         t = self.table
bgneal@46:         for j in xrange(1,self.m-1):
bgneal@46:             a[i,j] = t[tuple(a[i-1, j-1:j+2])]
bgneal@46: 
bgneal@46:     def get_array(self, start=0, end=None):
bgneal@46:         """Gets a slice of columns from the CA, with slice indices
bgneal@46:         (start, end).  Avoid copying if possible.
bgneal@46:         """
bgneal@46:         if start==0 and end==None:
bgneal@46:             return self.array
bgneal@46:         else:
bgneal@46:             return self.array[:, start:end]
bgneal@46: 
bgneal@46: 
bgneal@46: def binary(n, digits):
bgneal@46:     """Returns a tuple of (digits) integers representing the
bgneal@46:     integer (n) in binary.  For example, binary(3,3) returns (0, 1, 1)"""
bgneal@46:     t = []
bgneal@46:     for i in range(digits):
bgneal@46:         n, r = divmod(n, 2)
bgneal@46:         t.append(r)
bgneal@46: 
bgneal@46:     return tuple(reversed(t))
bgneal@46: 
bgneal@46: 
bgneal@46: def print_table(table):
bgneal@46:     """Prints the rule table in LaTeX format."""
bgneal@46:     t = table.items()
bgneal@46:     t.sort(reverse=True)
bgneal@46: 
bgneal@46:     print '\\beforefig'
bgneal@46:     print '\\centerline{'
bgneal@46:     print '\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}'
bgneal@46:     print '\\hline'
bgneal@46: 
bgneal@46:     res = ['prev']
bgneal@46:     for k, v in t:
bgneal@46:         s = ''.join([str(x) for x in k])
bgneal@46:         res.append(s)
bgneal@46:     print ' & '.join(res) + ' \\\\ \n\\hline'
bgneal@46: 
bgneal@46:     res = ['next']
bgneal@46:     for k, v in t:
bgneal@46:         res.append(str(v))
bgneal@46:     print ' &   '.join(res) + ' \\\\ \n\\hline'
bgneal@46: 
bgneal@46:     print '\\end{tabular}}'
bgneal@46: 
bgneal@46: