The height version of self-organized critically subject to lattice cyclicity is simulated on the triangular net. Both the static exponent describing the distribution of sizes for avalanches and the dynamic exponents describing their time duration, are found to be close to the standard model on...

Higher connectivity percolation (site valence ⩾ 2) is considered for selected 2, 3, 4-dimensional lattices, by the method of exact series expansions. The set of critical exponents obtained from the perimeter-to-size ratio and the moments of the cluster size distribution favours the same...

Simulations for bootstrap cellular automata on an oriented square lattice are shown to be consistent with exact results on the critical threshold (p∞c = 1) and a finite size scaling bound. Regimes above, below and close to pc (for finite samples) are detailed and characterized by a wide choice...

The evolution of a cellular automat with a culling or bootstrap condition on the minimum number of neighbours for survival has been simulated. The introduction of an orientational constraint converts the lattice from isotropic to semidirected. Simulations of systems of up to 230 million sites...

Some new critical properties related to the spread along the anisotropy axis of directed percolation as a model for wind-biased forest or wild land fire, are introduced and discussed. We show that it is possible to extract the burned mass along the axis, its appropriate exponent, and the gap...