Peter de Jong attractor

attractor_example.ipynb

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   "source": [
    "import numpy as np\n",
    "from numba import njit\n",
    "%config InlineBackend.print_figure_kwargs = {'bbox_inches': None}\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl"
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
   "id": "671b4fc6-2042-4526-ad36-71768580a2ae",
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   "source": [
    "@njit\n",
    "def next_step(y, x, a, b, c, d):\n",
    "    \"\"\"Peter De Jong attractor\n",
    "    \n",
    "    source:\n",
    "    https://paulbourke.net/fractals/peterdejong/\n",
    "    \"\"\"\n",
    "    return (\n",
    "        np.sin(c*x) - np.cos(d*y), # y+1\n",
    "        np.sin(a*y) - np.cos(b*x), # x+1\n",
    "    )\n",
    "\n",
    "@njit(boundscheck=True)\n",
    "def update_grid_bilinear(grid, y, x, ys, xs):\n",
    "    \"\"\"Increment the grid using bilinear interpolation\"\"\"\n",
    "    \n",
    "    dx = x - int(x)\n",
    "    dy = y - int(y)\n",
    "\n",
    "    x_px = int(x)\n",
    "    y_px = int(y)\n",
    "    \n",
    "    if (y_px >= 0) & (x_px >= 0) & (y_px < ys) & (x_px < xs):\n",
    "        grid[y_px, x_px] += (1 - dy) * (1 - dx)\n",
    "        \n",
    "    if (y_px >= 0) & (x_px >= -1) & (y_px < ys) & (x_px < xs-1):\n",
    "        grid[y_px, x_px+1] += (1 - dy) * dx\n",
    "        \n",
    "    if (y_px >= -1) & (x_px >= 0) & (y_px < ys-1) & (x_px < xs):\n",
    "        grid[y_px+1, x_px] += dy * (1 - dx)\n",
    "        \n",
    "    if (y_px >= -1) & (x_px >= -1) & (y_px < ys-1) & (x_px < xs-1):\n",
    "        grid[y_px+1, x_px+1] += dy * dx\n",
    "    \n",
    "@njit\n",
    "def run_attractor(grid, a, b, c, d, n_steps=2000, scale=100):\n",
    "    \"\"\"Iterate over an attractor\"\"\"\n",
    "    \n",
    "    ys, xs = grid.shape\n",
    "    yhw = ys / 2\n",
    "    xhw = xs / 2\n",
    "\n",
    "    # init\n",
    "    x = 0.0\n",
    "    y = 0.0\n",
    "    \n",
    "    for _ in range(n_steps):\n",
    "        \n",
    "        y, x = next_step(y, x, a, b, c, d)\n",
    "        \n",
    "        # scale \"attractor coordinates\" to grid\n",
    "        x_px = x * scale + xhw\n",
    "        y_px = y * scale + yhw\n",
    "        \n",
    "        update_grid_bilinear(grid, y_px, x_px, ys, xs)\n",
    "\n",
    "    return grid"
   ]
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  {
   "cell_type": "markdown",
   "id": "0b884624-43a4-4ca4-9561-df4a21185480",
   "metadata": {},
   "source": [
    "## Process attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e06ff61a-71b3-48f6-84e2-d6bf1d0a50dd",
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   "outputs": [],
   "source": [
    "# attractor parameters\n",
    "# from https://paulbourke.net/fractals/peterdejong/\n",
    "a = 1.4\n",
    "b = -2.3\n",
    "c = 2.4\n",
    "d = -2.1\n",
    "\n",
    "# size of the output image\n",
    "ys = 1024\n",
    "xs = 1024\n",
    "grid = np.zeros((ys, xs), dtype=np.float64)\n",
    "\n",
    "# running takes a minute, reduce n_steps to 10_000 when fiddling\n",
    "img = run_attractor(grid, a, b, c, d, n_steps=1_000_000_000, scale=ys/4.2)\n",
    "\n",
    "# convert to log for visualization\n",
    "tiny = 0.0000001\n",
    "img = np.log(img + tiny)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98929adc-657c-40c8-8054-dcbef3ff6271",
   "metadata": {},
   "source": [
    "## Visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6a3ecb9d-bb2b-4274-840f-17420d0d9f31",
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   "outputs": [
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