As the usual stochastic case, the so called
deterministic walks describe the movement of a walker
in a certain medium, which can or cannot have a random
However, the rule of locomotion is always taken from some
purely deterministic model, instead from a probability
Deterministic walks usually present the technical difficulties
common to nonlinear dynamical systems.
Moreover, they can give rise to superdiffusive processes.
But in contrast to purely random walks, it seems that for
determinism walks there are no general guidelines indicating
when the evolution would originate power-law distributions
for the dynamical variables.
In the present contribution we study how superdiffusive
behavior can emerge in a deterministic walk.
We extend a recently proposed model, in which the
walker searches for randomly distributed targets in a
large, but finite, 2D region, following a
``go to the closest target site'' rule.
For certain very particular parameter conditions, this type of
dynamics surprisingly exhibits power law distribution of step
Here we reveal the mechanisms leading to such behavior,
showing that the crossover is due to a trapping effect associated
to specific spatial configurations of the search environment.
The onset of this phenomenon resembles a critical point in
thermodynamics, even thought there is no real phase transition
in the system.