Alan Turing-ek morfogenesiaren inguruan egindako ikerketaren analisi matematikoa

Abstract

In this article, we show and mathematically develop a part of the work that the mathematician Alan Turing did on Morphogenesis which he published in 1952 in his article The Chemical Basis of Morphogenesis. We will explain the mathematical concepts and resources needed to do so: differential equations, reaction-diffusion equations, Fourier series and function linearization. Specifically, we will show and explain all these mathematical tools that Alan Turing used but did not develop nor delve into a lot in his aforementioned article’s two sections: “Reactions and Diffusion in a Ring of Cells" (for the discrete ring region) and “Continuous Ring of Tissue" (for the continuous ring region). This article is based on the UPV/EHU former student Idoia Marauri’s Final Degree Project.