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bgneal@40
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1 """Chapter 6, exercise 1 in Allen Downey's Think Complexity book.
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2
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3 "Create a new class called CircularCA that extends CA so that the cells are
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4 arranged in a ring. Hint: you might find it useful to add a column of 'ghost
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5 cells' to the array."
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6
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7 """
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8
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9 import numpy
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10
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11 from CA import CA
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12
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13
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14 class CircularCA(CA):
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15 """A circular cellular automaton; the cells are arranged in a ring."""
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16
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bgneal@42
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17 def __init__(self, rule, n=100, m=50):
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bgneal@40
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18 """Parameters:
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19
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20 * rule: an integer in the range 0-255 that represents the CA rule
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21 using Wolfram's encoding
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22 * n: the number of rows (time steps) in the result
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23 * m: the number of columns
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24
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25 """
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26 self.table = self.make_table(rule)
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27 self.n = n
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28 # a ghost column is added to either end
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29 self.m = m + 2 # add 2 ghost columns
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30 self.array = numpy.zeros((n, self.m), dtype=numpy.int8)
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31 self.next = 0
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32
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33 def start_single(self):
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34 self.array[0, 1] = 1
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35 self.next = 1
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36
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37 def step(self):
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bgneal@40
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38 """Executes one time step by computing the next row of the array."""
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39 i = self.next
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40 self.next += 1
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41 assert i > 0, 'call start_single() or start_random() first'
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42
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43 a = self.array
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44 t = self.table
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45
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46 # update the ghost cells to enable wrapping
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47 a[i - 1, 0] = a[i - 1, self.m - 2]
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48 a[i - 1, self.m - 1] = a[i - 1, 1]
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49
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50 for j in xrange(1, self.m - 1):
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51 a[i, j] = t[tuple(a[i - 1, j-1:j+2])]
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52
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53 def loop(self, steps=1):
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bgneal@42
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54 """Executes the given number of time steps."""
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55 for i in xrange(steps):
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56 self.step()
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57
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58 def get_array(self, start=0, end=None):
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bgneal@40
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59 """Gets a slice of columns from the CA, with slice indices
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60 (start, end).
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61
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62 """
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63 # do not return the ghost columns
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64 if end==None:
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65 return self.array[:, start+1:self.m-1]
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66 else:
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67 return self.array[:, start+1:end+1]
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68
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69 def wrap(self):
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70 """Copies the last row to row 0, then resets the CA to start back at the
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71 top.
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72
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73 """
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74 a = self.array
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75 a[0, :] = a[self.next - 1, :]
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76 self.next = 1
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77
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78
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79 if __name__ == '__main__':
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80
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81 import sys
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82 from CADrawer import PyplotDrawer
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83
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84 def main(script, rule, n, m):
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85 rule = int(rule)
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86 n = int(n)
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87 m = int(m)
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88 ca = CircularCA(rule, n, m)
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89 ca.start_single()
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90 ca.loop(n - 1)
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91
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92 drawer = PyplotDrawer()
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93 drawer.draw(ca)
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94 drawer.show()
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95
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96
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97 main(*sys.argv)
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