Super Multi-Armed and Segmented Spiral Pattern in a Reaction-Diffusion Model

Abstract

The super multi-armed and segmented (SMAS) spiral pattern has been observed in nature, such as sunflower inflorescence, spiral aloe, pine cone, ball cactus and Roman broccoli, which is characterized by several segmented spiral arms sharing the same spiral tip. The mechanism for the emergency of the SMAS spiral pattern has not been found. In this article, we observed the emergence of the SMAS spiral pattern by the simulations of a reaction-diffusion model. Additionally, our theoretical analysis found that the instability of concentrations in spiral arms leads to the emergence of this pattern. This study provides an alternative explanation for the formation of this type of pattern in nature and sheds light on the dynamics of pattern formation.

Keywords

• Spiral pattern
• reaction-diffusion model
• target-like pattern
• superstructure