Many of the existing fire spread simulation applications make use of square-cell grid based maps, a solution that is not free of problems due to the discrete interpretation of reality and the segmentation of space into geometric shapes. These particularities entail systematic errors when programming cellular automata for forest fire simulation, particularly in the computation of distances, hence delivering erroneous simulations of fire front size and position. Inspired in the concept of taxicab geometry, coined by Minkowsky in the 19th century, a new one, that has been labelled here as ‘Extended Taxicab Geometry’and which underlies in most of the grid-based fire spread automata, is described in this paper. Algorithmic improvements for the computer code to avoid unwanted effects in the simulations are also presented. A second common problem, appearing when the elliptical shape associated to spread propagation is too narrow, is described, and an algorithmic solution is proposed for its implementation in a computer program.