with James B. Golden

Submitted to Physica D

Traditional iterated function system fractals, in which contraction
maps are called in an iterated random or data-driven sequence, are *
forgetful*. Random numbers or data items more than a few steps in the
past have little influence on the position of the moving point used to
generate the fractal. This is because the contraction associated with
each of the iterated functions rapidly shrink the influence of past
inputs below the pixel size of any displayed version of the fractal. To
permit iterated function system fractals whose appearance can depend on
relatively remote data items, e.g. changes of distribution in a data
source, we introduce the *chaos automata*. A chaos automata is a
finite state machine with a contraction map associated with each state.
The random numbers or data previously used to drive the selection of
contraction maps now drive the finite state machine with the contraction
map on each state being applied as it would in a standard iterated
function system. Chaos automata are used to create iterated function
systems that yield fractals with different appearances when driven by
different types of data. The parameter selection, including finite
state transition diagram and selection of contraction maps, for the
chaos automata is performed with an evolutionary algorithm in a data
driven manner. Random sources over the DNA alphabet with distinct
distributions and intron and exon sequences derived from Zea mays are
used to test the chaos automata/evolutionary algorithm system.