IFS with Memory

Software Representation

In our software allowed transitions are represented by a 4 × 4 array of squares.

Think of the rows as labeled 1 through 4, and the columns as labeled 1 through 4. If the square in the ith row and jth column is filled, then Tj can follow Ti. If the square is empty, Tj cannot follow Ti.

For example, this array allows all combinations except that T3 cannot follow T1.

Here is the corresponding IFS. Recaling the notion of addresses of portions of a fractal, we see that the square 31 is empty. In addition, subsquares 131, 231, 331, and 431 are empty. Continuing, every subsquare with address containing 31 is empty.

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