# 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

# life: apropos of transitions (in visual perceptions), 'when the reasoning mind melts away, only shapes remain'.

<< Those who drink the hallucinogenic ayahuasca report seeing two-dimensional patterns or throbbing, three-dimensional hexahedral cells. When the reasoning mind melts away, only shapes remain. >>

<< Geometry gives us a world unclad. "Euclid alone has looked on Beauty bare," wrote Edna St. Vincent Millay. That feeling of mystical revelation — of a shimmering, underlying order that we can apprehend if we purify our perception — might explain the mutual affinity between poets and geometers.  (..) Many of the mathematicians cited in Ellenberg’s book (Jordan Ellenberg,  'Shape' ) wrote verse. >>

<< “I prove a theorem,” the poet Rita Dove wrote, “and the house expands.” >>️

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Parul Sehgal. ‘Shape’ Makes Geometry Entertaining. Really, It Does. NYT. May 20, 2021.

https://www.nytimes.com/2021/05/18/books/review-shape-geometry-jordan-ellenberg.html

Jordan Ellenberg. Shape. The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else. 463 pages. Penguin Press.

https://www.nytimes.com/column/books-of-the-times

Also

keyword 'ayahuasca'  | 'magic string' in FonT

https://flashontrack.blogspot.com/search?q=ayahuasca

https://flashontrack.blogspot.com/search?q=magic+string

keyword 'transition' in FonT

https://flashontrack.blogspot.com/search?q=transition

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=transition

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transizioni