  We establish a correspondence between Pavlovian conditioning processes and
fractals. The association strength at a training trial corresponds to a point
in a disconnected set at a given iteration level. In this way, one can
represent a training process as a hopping on a fractal set, instead of the
traditional learning curve as a function of the trial. The main advantage of
this novel perspective is to provide an elegant classification of associative
theories in terms of the geometric features of fractal sets. In particular, the
dimension of fractals can measure the efficiency of conditioning models. We
illustrate the correspondence with the examples of the Hull, Rescorla-Wagner,
and Mackintosh models and show that they are equivalent to a Cantor set. More
generally, conditioning programs are described by the geometry of their
associated fractal, which gives much more information than just its dimension.
We show this in several examples of random fractals and also comment on a
possible relation between our formalism and other "fractal" findings in the
cognitive literature.
