ON A CLASS OF FRACTAL MATRICES (I) EXCESS-MATRICES AND THEIR SELF-SIMILAR PROPERTIES
André M. Barbé · International Journal of Bifurcation and Chaos · 1992
An infinite class of integer valued matrices of unbounded size and of arbitrary dimensions is presented here as a generalization of the so-called excess-matrix associated with a particular cellular automaton. These matrices are constructed through a recursive arithmetical procedure, and show an intricate fractal-like distribution of integers. The elements in these matrices have a number theoretical interpretation which is directly related to a proper number-base representation of the coordinates of the element. These excess-matrices exhibit numerical and symbolical self-similarities under agglomerating and decimating coarse-graining operations, and under so-called disguising transformations.