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Self-similar Turing patterns: An anomalous diffusion consequence

D. Hernández1, E. C. Herrera-Hernández2,*, M. Núñez-López3, and H. Hernández-Coronado4

  • 1Posgrado en Ciencias de la Complejidad, Universidad Autónoma de la Ciudad de México, Ciudad de México, Laboratorio Nacional de Ciencias de la Complejidad, Ciudad de México, Mexico
  • 2CONACYT-Centro de Ingeniería y Desarrollo Industrial, Av. Playa pie de la Cuesta 702, Desarrollo Sn. Pablo, 76125, Querétaro, Qro., Mexico
  • 3Departamento de Matemáticas Aplicadas y Sistemas, DMAS Universidad Autónoma Metropolitana, Cuajimalpa, Av. Vasco de Quiroga, 4871, Sta. Fe Cuajimalpa, Cuajimalpa de Morelos, 05300, Mexico
  • 4Departamento de Física, Facultad de Ciencias, UNAM, A. P. 50-542, Mexico DF, 04510, Mexico

  • *erik.herrera@cidesi.edu.mx
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Phys. Rev. E 95, 022210 – Published 16 February, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.022210

Abstract

In this work, we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries. The type of anomalous diffusion discussed in this work, either subdiffusion or superdiffusion, is a consequence of the medium heterogeneity, and it is modeled through a space-dependent diffusion coefficient with a power-law functional form.

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Phys. Rev. E 95, 022210– Published 16 February, 2017
  • Received 14 August 2016

©2017 American Physical Society

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