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Randomized model shows a first-order percolation transition in cluster dynamics, indicating new insights into percolation theory.
We show that considering only the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation, our models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that the cluster perimeters are fractal at the transition point, yielding a fractal dimension of 1.23 ± 0.03, close to that of watersheds.
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Araújo et al. (2010) studied this question.
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