Generating isotropic discrete waves on cellular automata

Cellular automata are a massively parallel computation model with discrete time and local rules. They are well adapted to biological or physical simul ations. However, they are intrinsically anisotropic. The possibility of com puting isotropic figures on cellular automata such as circles has already b een proved.(4) Moreover, the previous construction enables to compute all t he major discretizations known in the literature. We present in this articl e an extension of this work to the construction of spheres in three dimensi ons. A local characterization of a sphere is presented based upon the relat ionship between spheres and circles. This leads to the possibility of const ructing a family of concentric discrete spheres in real time. Moreover, the approach can use many discretization schemes leading to the construction o f various discrete spheres as done for circles.