# gst: surface geometry for pattern dynamics, how a static model on a flat surface can propagate over a curved one

<< Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces have been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. >>

AA << report for the first time that a static Turing pattern on a flat surface can propagate on a curved surface, as opposed to previous studies, where the pattern is presupposed to be static irrespective of the surface geometry. To understand such significant changes on curved surfaces, (AA) investigate reaction-diffusion systems on axisymmetric curved surfaces. (..) both the symmetries of the surface and pattern participate in the initiation of pattern propagation. >>️

Ryosuke Nishide, Shuji Ishihara. Pattern Propagation Driven by Surface Curvature. arXiv:2205.08064v1 [nlin.PS]. May 17, 2022. 

https://arxiv.org/abs/2205.08064

Keywords: gst, pattern formation, curved surface, transition, geometry