""" Deep Patterns — The Scream Gray-Scott reaction-diffusion system (Turing morphogenesis) Equations: ∂u/∂t = Du·∇²u − u·v² + F·(1 − u) ∂v/∂t = Dv·∇²v + u·v² − (F + k)·v Species u (activator) and v (inhibitor) diffuse and react to produce spontaneous spatial patterning — spots, stripes, or labyrinths depending on feed rate F and kill rate k. Complexity: O(n) per step, where n = grid cells = W × H. Dependencies: numpy, matplotlib Install: pip install numpy matplotlib Run: python the_scream.py Parameter presets at the bottom of this file let you switch between pattern modes (spots, stripes, worms, Turing rings, coral). """ import numpy as np import matplotlib.pyplot as plt import matplotlib.animation as animation from matplotlib.colors import LinearSegmentedColormap # ── Pattern presets — uncomment one ────────────────────────────────────────── # Each preset is (F, k, Du) — these produce qualitatively different patterns. PRESET = "mitosis" # name for display PRESETS = { "mitosis": (0.0367, 0.0649, 0.19), # self-replicating spots "coral": (0.0545, 0.062, 0.18), # coral / dendritic growth "stripes": (0.022, 0.051, 0.14), # parallel stripe Turing patterns "worms": (0.078, 0.061, 0.16), # worm-like labyrinthine trails "fingerprint": (0.037, 0.060, 0.20), # fingerprint ridges } F0, K0, DU0 = PRESETS[PRESET] # ── Parameters (edit these) ────────────────────────────────────────────────── W, H = 200, 200 # grid dimensions F = F0 # feed rate K = K0 # kill rate DU = DU0 # diffusion coefficient for u DV = DU / 2 # diffusion coefficient for v (always DU/2) STEPS_PER_FRAME = 12 # steps per animation frame FPS = 30 # target frame rate SEED_RADIUS = 8 # radius of initial perturbation seeds N_SEEDS = 6 # number of initial seeds # ───────────────────────────────────────────────────────────────────────────── rng = np.random.default_rng(7) class GrayScott: def __init__(self): self.u = np.ones((H, W), dtype=np.float32) self.v = np.zeros((H, W), dtype=np.float32) self.t = 0 self._seed() def _seed(self): """Place small square perturbations of v to seed pattern formation.""" for _ in range(N_SEEDS): cx = rng.integers(SEED_RADIUS, W - SEED_RADIUS) cy = rng.integers(SEED_RADIUS, H - SEED_RADIUS) r = SEED_RADIUS self.v[cy-r:cy+r, cx-r:cx+r] = 0.25 + rng.uniform(-0.01, 0.01, (2*r, 2*r)) self.u[cy-r:cy+r, cx-r:cx+r] = 0.50 + rng.uniform(-0.01, 0.01, (2*r, 2*r)) def laplacian(self, grid: np.ndarray) -> np.ndarray: """5-point Laplacian with periodic (wrap-around) boundary conditions.""" return ( np.roll(grid, 1, axis=1) + np.roll(grid, -1, axis=1) + np.roll(grid, 1, axis=0) + np.roll(grid, -1, axis=0) - 4 * grid ) def step(self): """One Gray-Scott update step (Euler integration, dt = 1).""" uvv = self.u * self.v * self.v lu = self.laplacian(self.u) lv = self.laplacian(self.v) self.u += DU * lu - uvv + F * (1 - self.u) self.v += DV * lv + uvv - (F + K) * self.v np.clip(self.u, 0, 1, out=self.u) np.clip(self.v, 0, 1, out=self.v) self.t += 1 def add_seed(self, gx: int, gy: int): """Inject a small perturbation at (gx, gy) in grid coordinates.""" r = SEED_RADIUS gy = int(np.clip(gy, r, H - r - 1)) gx = int(np.clip(gx, r, W - r - 1)) self.v[gy-r:gy+r, gx-r:gx+r] = 0.25 self.u[gy-r:gy+r, gx-r:gx+r] = 0.50 def build_colormap(): """Munch blood-orange and tormented sky palette.""" colors = [ (0.05, 0.02, 0.03), # near-black (0.30, 0.08, 0.04), # dark blood (0.72, 0.20, 0.07), # blood orange (0.91, 0.38, 0.12), # Munch orange (0.97, 0.72, 0.30), # amber (0.99, 0.96, 0.80), # pale cream ] return LinearSegmentedColormap.from_list("the_scream", colors, N=256) def main(): sim = GrayScott() cmap = build_colormap() fig, ax = plt.subplots(figsize=(8, 8), dpi=100) fig.patch.set_facecolor("#0d0d14") ax.set_facecolor("#0d0407") ax.axis("off") fig.tight_layout(pad=0) img = ax.imshow( sim.v, cmap=cmap, vmin=0, vmax=0.35, origin="lower", interpolation="nearest", aspect="equal", extent=[0, W, 0, H], ) title = ax.set_title( "Gray-Scott · preset: {} · F={:.4f} k={:.4f} · {}×{}".format( PRESET, F, K, W, H), color="#aaaaaa", fontsize=9, pad=6, ) info = ax.text( 0.02, 0.97, "Click to seed new pattern · showing species v", transform=ax.transAxes, color="#554433", fontsize=8, va="top", fontfamily="monospace", ) def update(frame): for _ in range(STEPS_PER_FRAME): sim.step() img.set_data(sim.v) title.set_text( "Gray-Scott · preset: {} · t = {:,} · O(n)".format(PRESET, sim.t) ) return img, title def on_click(event): if event.inaxes is not ax: return gx = int(np.clip(event.xdata, 0, W - 1)) gy = int(np.clip(event.ydata, 0, H - 1)) sim.add_seed(gx, gy) fig.canvas.mpl_connect("button_press_event", on_click) ani = animation.FuncAnimation( fig, update, interval=1000 // FPS, blit=True, cache_frame_data=False ) print("Gray-Scott reaction-diffusion — Deep Patterns") print(" Preset: {} (F={}, k={}, Du={})".format(PRESET, F, K, DU)) print() print(" Other presets (edit PRESET at the top of the file):") for name, (f, k, du) in PRESETS.items(): marker = " ←" if name == PRESET else "" print(" {:12s} F={:.4f} k={:.4f} Du={}{}".format(name, f, k, du, marker)) print() print(" Click in the window to seed new patterns.") plt.show() if __name__ == "__main__": main()