Unstructured triangular cellular automata for modeling geographic spread

In this work we propose the use of a cellular automata defined on unstructured triangular grids to simulate geographic spread. A grid structure of a finite element implementation is adopted to cellular automata computations. This approach allow us to model and simulate with cellular automata on computational domains with complex geometries (polygonal boundaries), it still retains the easy implementation of cellular automata and does not present the anisotropy induced by regular grids. We show a comparison (storage and number of evaluations required) of our approach with the classical cellular automata implementations on regular grids: rectangular, equilateral triangulation and hexagonal. The geographical spread on unstructured triangular grids is presented by defining two simple cellular automata models a binary spread (two states) and a deforestation spread (three states). Using unstructured triangular grids no anisotropy effects induced by grid and neighborhood are presented; circular fronts spread as circular fronts. Moreover, the use of unstructured triangular grids for cellular automata can simplifies the coupling of cellular automata with other numerical techniques such as finite element or finite volume.