Abstract
Cellular automata in two dimensions that generalize the bootstrap percolation dynamics are considered, focusing on the thresholdp c of the initial density for convergence to total occupancy to occur; these models are classified according top c being 0, 1, or strictly between these extreme values. Explicit upper and lower bounds are provided in the third case.
Article PDF
Avoid common mistakes on your manuscript.
References
J. Adler and A. Aharony Diffusion percolation: I. Infinite time limit and bootstrap percolation,J. Phys. A: Math. Gen. 21:1387–1404 (1988).
J. A. M. S. Duarte, Simulation of a cellular automat with an oriented bootstrap rule,Physica A 157:1075–1079 (1989).
A. C. D. van Enter, Proof of Straley's argument for bootstrap percolation,J. Stat. Phys. 48:943–945 (1987).
R. H. Schonmann, On the behavior of some cellular automata related to bootstrap percolation, Preprint (1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schonmann, R.H. Critical points of two-dimensional bootstrap percolation-like cellular automata. J Stat Phys 58, 1239–1244 (1990). https://doi.org/10.1007/BF01026574
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01026574