Cellular-Automata-Rule30-Implementation
Published:
Rules of cellular automata:
It is defined that the element value A[i][j] based on three elements: A[i-1][j-1], A[i][j-1], A[i+1][j-1], details are shown in Table 1.
Table 1
| set | value |
|---|---|
| (1,1,1) | 0 |
| (1,1,0) | 0 |
| (1,0,1) | 0 |
| (1,0,0) | 1 |
| (0,1,1) | 1 |
| (0,1,0) | 1 |
| (0,0,1) | 1 |
| (0,0,0) | 0 |
Rule30Class is a implementation of Cellular Automata Rule30. The initial status of a Rule30Class instance will generate first_row, rowLength, columnLength, and a matrix(containing the first_row); new_row function is used for generating new_row by inputing a previous row, also return pattern_map, in order to generate the pattern_map (suppose an initial pattern_map is an empty dictionary), I transferred the 6-element submatrix into decimal for representing, use this as key, and its location as value. for example: 100010 is a submatrix, suppose the coordinates of the 5th element is (1,1) so this submatrix = 1*25 + 1*21 = 34, pattern_map = {34: [(1,1)]}
show_matrix function: display the matrix with only 0, 1 (no ‘[’, ‘]’, or others) get_pattern_occurrencies function: suppose pattern_k is a string, like this: ‘1-1-0/1-0-0’ first change it to decimal, then doing comparison in pattern_ma
class Rule30Class(object):
def __init__(self, first_row, rowLength):
''' initiate the matrix with firstRow, rowLength is 100, including the 1st row'''
self.first_row = first_row
self.rowLength = rowLength
self.colLength = len(first_row)
self.matrix = first_row
def new_row(self, object, prev_row, pattern_map):
state = {"111": 0, "110": 0, "101": 0, "000": 0,
"100": 1, "011": 1, "010": 1, "001": 1}
row = [0]
list1 = []
'''
from the second to second last element in the new_row,
tracking its pattern (A[i-1][j-1], A[i][j-1], A[i+1][j-1]) to determine this one,
num1 & num2 is used for calculating the decimal
'''
for j in range(1,len(prev_row)-1):
pattern = str(prev_row[j-1]) +str(prev_row[j]) +str(prev_row[j+1])
row.append(state[pattern])
num1 = int(pattern[0])*2**5 + int(pattern[1])*2**4 + int(pattern[2])*2**3 + state[pattern]*2**1
list1.append(num1)
'''generating the boundaries for each row'''
row[0] = row[len(prev_row)-2]
row.append(row[1])
for z in range(len(list1)):
if z+2 < len(row):
num2 = list1[z] + row[z]*2**2 + row[z+2]*2**0
if num2 in pattern_map.keys():
pattern_map[num2].append((z+1, self.matrix.size/self.colLength))
else:
pattern_map[num2] = [(z+1, self.matrix.size/self.colLength)]
'''append new row to existing matrix'''
self.matrix = np.vstack((self.matrix,row))
return row, pattern_map
def show_matrix(self):
print "The result is:"
result = ''
for i in range(self.matrix.shape[0]):
for j in range(self.matrix.shape[1]):
result = result + str(self.matrix[i][j])
print result
def get_pattern_occurrencies(self,pattern_k, pattern_map):
'''
suppose pattern_k is a string, format like this '1-1-0/1-0-0'
'''
coordinates = []
part1 = pattern_k.split('/')[0]
part2 = pattern_k.split('/')[1]
num_k = int(part1.split('-')[0])*2**5+int(part1.split('-')[1])*2**4+\
int(part1.split('-')[2])*2**3+int(part2.split('-')[0])*2**2+int(part2.split('-')[1])*2**1+\
int(part2.split('-')[2])*2**0
if num_k in pattern_map.keys():
coordinates.append(pattern_map[num_k])
print coordinates
Leave a Comment