5 research outputs found
The Strange Man in Random Networks of Automata
We have performed computer simulations of Kauffman's automata on several
graphs such as the regular square lattice and invasion percolation clusters in
order to investigate phase transitions, radial distributions of the mean total
damage (dynamical exponent ) and propagation speeds of the damage when one
adds a damaging agent, nicknamed "strange man". Despite the increase in the
damaging efficiency, we have not observed any appreciable change at the
transition threshold to chaos neither for the short-range nor for the
small-world case on the square lattices when the strange man is added in
comparison to when small initial damages are inserted in the system. The
propagation speed of the damage cloud until touching the border of the system
in both cases obeys a power law with a critical exponent that strongly
depends on the lattice. Particularly, we have ckecked the damage spreading when
some connections are removed on the square lattice and when one considers
special invasion percolation clusters (high boundary-saturation clusters). It
is seen that the propagation speed in these systems is quite sensible to the
degree of dilution.Comment: AMS-LaTeX v1.2, 7 pages with 14 figures Encapsulated Postscript, to
be publishe
The Kauffman model on Small-World Topology
We apply Kauffman's automata on small-world networks to study the crossover
between the short-range and the infinite-range case. We perform accurate
calculations on square lattices to obtain both critical exponents and fractal
dimensions. Particularly, we find an increase of the damage propagation and a
decrease in the fractal dimensions when adding long-range connections.Comment: AMS-LaTeX v1.2, 8 pages with 8 figures Encapsulated Postscript, to be
published in Physica