Diffusion Limited Aggregation

Math essence

Witten-Sander diffusion-limited aggregation on a discrete lattice: at each step up to N walkers spawn at radius r_spawn and execute angle-uniform random-walk steps of length 1; a walker that enters an 8-neighborhood of any occupied cell is immediately absorbed (added to the cluster), while a walker that drifts beyond radius r_kill is recycled.

Parameters

Reference

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

from __future__ import annotations

from typing import ClassVar

import imageio.v2 as imageio
import numpy as np


class DiffusionLimitedAggregation:
    family: ClassVar[str] = "complexification_net"
    sketch: ClassVar[str] = "diffusionLimitedAggregation"

    def __init__(
        self,
        dim: int = 400,
        spawn_margin: float = 6.0,
        kill_margin: float = 12.0,
        max_walkers: int = 64,
        walk_steps_per_step: int = 64,
        bg_color: tuple[int, int, int] = (0, 0, 0),
        fg_color: tuple[int, int, int] = (255, 240, 220),
        seed: int | None = None,
    ) -> None:
        self.dim = dim
        self.spawn_margin = float(spawn_margin)
        self.kill_margin = float(kill_margin)
        self.max_walkers = max_walkers
        self.walk_steps_per_step = walk_steps_per_step
        self.bg_color = np.array(bg_color, dtype=np.uint8)
        self.fg_color = np.array(fg_color, dtype=np.uint8)
        self._seed = seed
        self.cx = 0.0
        self.cy = 0.0
        self.cluster_radius = 1.0
        self.rng = np.random.default_rng(seed)
        self.canvas = np.full((dim, dim, 3), self.bg_color, dtype=np.uint8)
        self.occupied = np.zeros((dim, dim), dtype=bool)
        self.walkers_x = np.empty(0, dtype=np.float32)
        self.walkers_y = np.empty(0, dtype=np.float32)
        self.num_stuck = 0
        self.time = 0
        self.reset()

    def reset(self, seed: int | None = None) -> None:
        if seed is not None:
            self._seed = seed
        self.rng = np.random.default_rng(self._seed)
        self.canvas = np.full((self.dim, self.dim, 3), self.bg_color, dtype=np.uint8)
        self.occupied = np.zeros((self.dim, self.dim), dtype=bool)
        self.cx = self.dim / 2.0
        self.cy = self.dim / 2.0
        ix, iy = int(self.cx), int(self.cy)
        if 0 <= ix < self.dim and 0 <= iy < self.dim:
            self.occupied[iy, ix] = True
            self.canvas[iy, ix] = self.fg_color
        self.cluster_radius = 1.0
        self.walkers_x = np.empty(0, dtype=np.float32)
        self.walkers_y = np.empty(0, dtype=np.float32)
        self.num_stuck = 1
        self.time = 0