Fractal pattern formation in the Ziff-Gulari-Barshad model

The dynamics of the Ziff-Gulari-Barshad (ZGB) model is studied on three different two-dimensional (2D) lattices: square (sq) lattice, hexagonal-honeycomb (hex-hon) lattice and purely hexagonal (hex) lattice. The effects of the support geometry on the steady state and the dynamics are assessed. In all 2D lattice geometries the ZGB model is shown to exhibit non-equilibrium phase transitions of the first and second order, but the critical values of the kinetic parameters depend crucially on the substrate geometry. Clustering and island formation are observed in all ranges of parameters, but the clusters are fractal only outside the active catalytic region. The fractal dimensions depend on the kinetic parameters