Self-similar Turing Patterns: An Anomalous diffusion consequence

In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries not reported before. The type of anomalous diffusion discussed in this work, either subdiffusion or superdiffusion, is a consequence of the medium heterogeneity, and is modelled through a space-dependent diffusion coefficient with a power-law functional form.