Abstract
Three cellular automaton “toy”-models of fragmentation in two-dimensional lattices are explored. Of the three models, two can be considered in the class of simple bond percolation, and one as correlated bond percolation. Fractal fragment-size distribution in all models is found away from criticality, providing a certain fraction of the bonds is designated with considerably larger strengths than the rest in the system. As the fraction of these bonds is raised from zero, the fragment-size distribution transforms smoothly from exponential forms into a power law. Though each model takes a different path to the fractal distribution, they all show the same fractal exponent of 1.85(5). As might be expected in one dimension, the same models of their variants, failed to produce fractal distributions.
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Hatamian, S.T. Modeling fragmentation in two dimensions. PAGEOPH 146, 115–129 (1996). https://doi.org/10.1007/BF00876672
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DOI: https://doi.org/10.1007/BF00876672