CONCEPTION DES AUTOMATES MIMANT LA STRUCTURE STRIPPÉE DES PEAUX D'ANIMAUX

For many years, creators or designers of patterns used, for the reproduction of drawings observed in nature, the usual drawing tools such as pencil, eraser, ruler, colors... In order to mimic the patterns or drawings observed in nature, the Turing model used, in particular, the simple BVAM model which is defined as a system of two coupled partial differential equations named reaction-diffusion equations. After determining the mathematical model, a study of the dynamic behavior of this system led to the determination of the condition to obtain Turing patterns. The numerical simulations of this system with Fortran 90, gave the results which, plotted on Matlab, permitted to reproduce of many complex Turing patterns for instance patterns drawn with lines, which describe the skin of zebra; and those with points which describe a skin of a leopard. The method used to obtain these patterns constitutes the first automaton called numerical-mathematical automaton. With the aim of controlling the system and its results, it is proposed a second automaton, conceived with analogical calculators which reproduced in (1+1) dimensions these figures. The temporal behavior of morphogens u and v obtained from this analogical automaton agree with those obtained by the numerical-mathematical automaton.


Master Thesis