Gray-Scott Reaction-Diffusion

Math essence

Laplacian via numpy.roll with weights (axial: 0.2, diagonal: 0.05). Explicit Euler integration, U and V clipped to [0, 1] each sub-step. Boundary is periodic (roll handles wrap-around). Output is the V field mapped through one of five palettes (viridis, magma, ocean, pearl, gray).

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/toxi_openframeworks/ReactionDiffusionGS/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


_GS_PRESETS = {
    "spots": (0.0367, 0.0649),
    "stripes": (0.0545, 0.062),
    "solitons": (0.018, 0.051),
    "mitosis": (0.0367, 0.06),
    "coral": (0.0625, 0.0609),
}


class ReactionDiffusionGS:
    """Gray-Scott reaction-diffusion on a 2-D float grid.

    Two scalar species U, V diffuse on a periodic square grid and react
    via:

        dU/dt = Du * lap(U) - U*V*V + F * (1 - U)
        dV/dt = Dv * lap(V) + U*V*V - (F + k) * V

    The system is the canonical Gray-Scott model (Pearson 1993) and is
    a staple of the oF community — `ofxReactionDiffusion` by Atsushi
    Tadokoro, Robert Hodgin's early R-D patches, and Schmidt's
    toxiclibs R-D toy ports all use this same pair of PDEs.

    The Laplacian uses a 9-point stencil (4 axial + 4 diagonal
    weighted 0.05) on a periodic grid via `numpy.roll`, integrated
    with explicit Euler. Different (F, k) pairs produce spots,
    stripes, mitosis, solitons, and coral.
    """

    family: ClassVar[str] = "toxi_openframeworks"
    sketch: ClassVar[str] = "reactiondiffusiongs"

    def __init__(
        self,
        dim: int = 192,
        Du: float = 1.0,
        Dv: float = 0.5,
        F: float = 0.0367,
        k: float = 0.0649,
        dt: float = 1.0,
        steps_per_render: int = 24,
        seed_count: int = 9,
        seed_radius: float = 3.0,
        palette_mode: str = "viridis",
        preset: str | None = None,
        seed: int | None = None,
    ) -> None:
        self.dim = dim
        self.Du = Du
        self.Dv = Dv
        self.F = F
        self.k = k
        self.dt = dt