Magical Maze : Seeing the World Through Mathematical Eyes (9780471674498) by Stewart Ian

Author:Stewart, Ian
Language: eng
Format: epub
Publisher: John Wiley & Sons Inc

Figure 45 Creating patterns with cellular automata: (a) uniform, (b) stripes, (c) check ‘spots’, (d) chaotic triangles.

The colour of any cell in the next row is the opposite to that of the cell immediately above it.

Then, of course, the next row will be all white. The row after that will be all black, and we’ll get alternate rows of black cells and white ones. That’s one way to get a striped pattern (Figure 45(b)).

For a third possibility, suppose that we apply the second rule above, but now start with cells that alternate black and white. Then the next row will also alternate black and white, but with white replaced by black and black by white. That yields a chequered pattern – in effect, spots (Figure 45(c)).

For a more exotic pattern, we start with a series of black cells, sandwiched between white ones. Now the rule is this:

If the two cells immediately above a given cell, to its left and right, are the same, paint the new cell white. If they are different, paint it black.

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