Driven IFS with Forbidden Combinations

Software Representation

In our software allowed transitions are represented by a 4 x 4 x 4 array of squares.
Think of the rows, columns, and faces as labeled 1 through 4.

The face gives the most recent transformation,

the column gives the preceding transformation,

the row gives the transformation before that.
For example, this array allows all combinations except row = 1, column = 2, and face = 3.
Consequently, the combination 1 -> 2 -> 3 is forbidden.
In the driven IFS, the square with address 321 is empty. Below are the first and fifth generations of the attractor of the IFS driven with this exclusion.
Here is an example to illustrate the relation between the software representation and addresses.

Return to Higher-Order Exclusions.