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Dimitri Lozeve 2020-12-07 19:26:38 +01:00
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* Reaction-Diffusion Model
Reaction-Diffusion system simulation using the Gray-Scott model, in [[https://www.dyalog.com/][Dyalog APL]].
#+begin_src
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺ ⌺⌺⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺ ⌺⌺⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺
⌺⌺ ⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺
⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺
⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺ ⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺⌺ ⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺
⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺ ⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺ ⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺⌺
#+end_src

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⎕IO←0
⍝ Discrete Laplacian
lapl←(⊃(+/1 ¯1(⌽+⊖)¨⊂)-(⊂4∘×))
⍝ Gray-Scott update
diffa←{dt×(da×lapl ⍺)+(-⍺×⍵*2)+f×1-⍺}
diffb←{dt×(db×lapl ⍵)+(⍺×⍵*2)-⍵×k+f}
update←{⍵+(⊃⍵[0])((⊂diffa),(⊂diffb))⊃⍵[1]}
⍝ Parameters
dt da db f k←1.0 0.16 0.08 0.060 0.062
⍝ Initialization
N←200
A←0.8+0.2×?N N⍴0
A[((N÷2)-10)+⍳20;((N÷2)-10)+⍳20]←0.5
B←0.2×?N N⍴0
B[((N÷2)-10)+⍳20;((N÷2)-10)+⍳20]←0.25
⍝ Run
steps←10000
Ap Bp←(update⍣steps)A B
⍝ ' ⌺'[Ap>0.5]
⍝ Export to image file
mat2pbm←{'P1'(⍕⌽⍴⍵),⍕¨↓⍵>0.5} ⍝ black and white
mat2pgm←{'P2'(⍕⌽⍴⍵),(⊂'255'),⍕¨↓⌊255×⍵} ⍝ grayscale
(⊂mat2pbm Ap)⎕NPUT'img.pnm'1

BIN
img.png Normal file
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After

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502
img.pnm Normal file
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@ -0,0 +1,502 @@
P1
500 500
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