ISSN:
0192-8651
Keywords:
Computational Chemistry and Molecular Modeling
;
Biochemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Computer Science
Notes:
Space-time lattice (cellular automaton) models of pattern formation and growth are described. Suitable local rules for automation evolution represent the spreading of wave fronts of activity in an excitable medium. A random distribution of seeds produces expanding rings that fuse and are annihilated. The seeding density, pA, is used as a scaling parameter to give unique, reduced dynamics in an arbitrary dimension d. For d = 2, in this (continuum) picture, the rings fuse globally (percolate) at a critical instant, t̂c = 0.45. For the unscaled time evolution, dynamical percolation is examined in the pA × t plane. A swath of these percolating states is found. On the “explosion” boundary of this swath the percolation cluster just forms; on the “implosion” boundary it breaks up. Using a small-sample method the fractal dimension of the critical (boundary) cluster is estimated to be 1.9 (±0.01). Also percolation for continuously emitting seeds, which produce “discs” of activity, is related to ring evolution.
Additional Material:
3 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/jcc.540080420
