Driven IFS and Financial Cartoons

Procedure

Select a data set {x1, x2, ... , xn}
and possibly preprocess it: derive the related data sets, for example
{x2 - x1, x3 - x2, ... } (difference delay = 1, offset = 1),
one-step differences
{x3 - x1, x4 - x2, ... } (difference delay = 2, offset = 1),
two-step differences with overlap
{x3 - x1, x5 - x3, ... } (difference delay = 2, offset = 2)
two-step differences without overlap
Run these data sets through a driven IFS program, taking care to select appropriate bin boundaries.
Interpret the results, looking for forbidden combinations and more commonly occurring combinations.
Translate your observations back into the context of the original data set.

Do this for a stock index and for several self-affine cartoons.
Experiment with the bin boundaries and compare the driven IFS pictures.
Can you find a cartoon IFS that resembles the data IFS?
What does this suggest about the data?

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