Reaction Diffusion (Gray-Scott)

Math essence

Gray-Scott PDE on a periodic grid: U_{t+1} = U + dt·(Du·∇²U − UV² + F·(1−U)), V_{t+1} = V + dt·(Dv·∇²V + UV² − (F+k)·V). The 4-neighbor Laplacian is ∇²U = U_N + U_S + U_E + U_W − 4U. The bistable (F, k) parameter space yields Turing patterns: spots that propagate, stripes that wind, mazes that fill, and mitosis-like cell division.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/complexification_net/reactionDiffusion/reference.py

from __future__ import annotations

from typing import ClassVar

import imageio.v2 as imageio
import numpy as np


_PALETTES: dict[str, np.ndarray] = {
    "ink": np.array(
        [
            [10, 10, 20],
            [30, 30, 50],
            [60, 60, 90],
            [95, 95, 130],
            [130, 130, 170],
            [170, 165, 200],
            [210, 200, 220],
            [240, 230, 235],
            [255, 255, 255],
            [240, 220, 195],
            [220, 180, 150],
            [200, 140, 110],
            [180, 100, 75],
            [150, 70, 50],
            [110, 50, 35],
            [70, 35, 25],
        ],
        dtype=np.uint8,
    ),
    "rust": np.array(
        [
            [25, 12, 8],
            [60, 22, 8],
            [110, 38, 12],
            [165, 60, 18],
            [210, 90, 30],
            [240, 130, 50],
            [255, 175, 80],
            [255, 220, 130],
            [255, 248, 200],
            [220, 240, 220],
            [180, 220, 220],
            [140, 195, 210],
            [100, 160, 195],
            [60, 120, 170],
            [30, 80, 130],
            [10, 40, 80],
        ],
        dtype=np.uint8,
    ),
    "coral": np.array(
        [
            [10, 30, 50],
            [20, 60, 80],
            [40, 100, 110],
            [80, 140, 130],
            [130, 180, 140],
            [180, 210, 150],
            [230, 235, 165],