  A simple model of macroevolution is proposed exhibiting both the property of
punctuated equilibrium and the dynamics of potentialities for different species
to evolve towards increasingly higher complexity. It is based on the phenomenon
of "fractal evolution" which has been shown to constitute a fundamental
property of nonlinear discretized systems with one memory- or random-based
feedback loop. The latter involves a basic "cognitive" function of each species
given by the power of distinction of states within some predefined resolution.
The introduction of a realistic background noise limiting the range of the
feedback operation yields a pattern signature in fitness space with a
distribution of temporal boost/mutation distances according to a randomized
devil's staircase function. Introducing a further level in the hierarchy of the
system's rules, the possibility of an adaptive evolutionary change of the
resolution itself is implemented, thereby providing a time-dependent measure of
the species' cognitive abilities: an additional feedback loop makes use of the
inevitable intrinsic fluctuations within the fitness landscape to direct the
temporal change of the resolution. Feeding back the small adaptive changes of
resolution into the essentially directionless variations of the patterns'
lifetimes in fitness space effectively leads to a clear tendency towards
increasing evolution potentials for each species ("hierarchically emergent
fractal evolution").
