1.H. Driven IFS and Data Analysis

A natural question, as far as we know first posed by Ian Stewart, is
What picture does the Random Algorithm generate if the driving sequence is not random?
After studying examples of the pictures produced by different sorts of nonrandom sequences, we use this rough visual vocabulary to detect patterns in real data.
Because we use a data sequence to select the order in which the transformations are applied, we call this approach driven IFS. The data drive the order in which the IFS rules are applied.
Stewart's examples are the first instances of driven IFS.
Square functions The rules we shall use for driven IFS
DNA sequences The rules need not be labeled 1, 2, 3, and 4. Any four labels will do. "Homer," "Marge," "Bart," and "Lisa," for example. Or perhaps C, A, T, and G. What experiments does this suggest?
Cyclic driven IFS What happens if we drive an IFS in a repeating pattern?
Driven IFS with forbidden combinations Gaps in the driven IFS picture indicate combinations of transformations that do not occur.
IFS driven by data What can driven IFS tell us about patterns in measured data?