Displaying similar documents to “Collision patterns on mollusc shells.”

Evolving morphogenetic fields in the zebra skin pattern based on Turing's morphogen hypothesis

Carlos Graván, Rafael Lahoz-Beltra (2004)

International Journal of Applied Mathematics and Computer Science

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One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm to the Young cellular...

The continuum reaction-diffusion limit of a stochastic cellular growth model

Stephan Luckhaus, Livio Triolo (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A competition-diffusion system, where populations of healthy and malignant cells compete and move on a neutral matrix, is analyzed. A coupled system of degenerate nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The healthy cells move much slower than the malignant ones, such that no diffusion for their density survives in the limit. The malignant cells may locally accumulate, while for the healthy ones an exclusion rule is...