propagation.ipynb

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    "tags": []
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   "source": [
    "%matplotlib ipympl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d8f98c92-e55f-4af8-af1a-3dc7a36ada71",
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   "source": [
    "import itertools\n",
    "\n",
    "import IPython.display\n",
    "import matplotlib.animation\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c621798-579c-48a3-baf9-c1f77dc66bbe",
   "metadata": {
    "tags": []
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   "source": [
    "# Data objects\n",
    "\n",
    "- `state`: \n",
    "- `propagation`:\n",
    "\n",
    "We create two matrixes, `state`, which represent the current state as the propagation happens, and `rate`, which holds the propagation coefficients."
   ]
  },
  {
   "cell_type": "code",
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   "id": "f5aa0605-20a7-4e23-a812-2dbd89a8730f",
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100,   0, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],\n",
       "       [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]])"
      ]
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     "execution_count": 3,
     "metadata": {},
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   "source": [
    "state = np.full((11, 11), 100)\n",
    "state[5, 5] = 0\n",
    "state"
   ]
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  {
   "cell_type": "markdown",
   "id": "a2aca43c-c2e4-479b-93fe-b7be486924af",
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   "source": [
    "Here, we create a 11x11array with the `100` value on all cells, with the exception of the center, which is 0. The value in each cell tracks how close it is to be propagated to. `100` is an arbitrary value we choose as an initial value."
   ]
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    {
     "data": {
      "text/plain": [
       "array([[10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20],\n",
       "       [10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rate = np.full((11, 11), 10)\n",
    "rate[:, 6:] = 20\n",
    "rate[6:, 5:] = 20\n",
    "rate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc3bf716-e520-410e-bba9-5f5149d65273",
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   "source": [
    "Here, we create the propagation coefficients array, it has the same size as `state`. Each cell contains the propagation rate for the equivalent cell in the `state` array. In our example, we use `10` as the rate for the left side, and `20` for the right one, meaning the right side will propagate twice as fast as the left side."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10f07397-453c-4843-8efa-3810e9049e21",
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   "source": [
    "# Algorithm\n",
    "\n",
    "The algorithm is fairly simple, we go over every cell in the `state` matrix, if the cell is not `0` (already propagated to) and one of its neighbors is `0`, we subtract the corresponding propagation value specified in the `propagation` matrix.\n",
    "\n",
    "In our example, we will use `100`ms for each iteration, meaning that with a `100` starting value for all elements, cells on the left (`10` units/iteration) side will take `1`s to be propagated to, and cells on the right side (`20` units/iteration) will take `0.5`s."
   ]
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  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c6b2398e-1c54-48f5-9326-5d5608a26e0d",
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   "source": [
    "def neighbors(matrix, index):\n",
    "    for x, y in itertools.permutations((-1, 0, 1), 2):\n",
    "        if x == 0 and y == 0:\n",
    "            continue\n",
    "        n = (index[0] + x, index[1] + y)\n",
    "        if n[0] < 0 or n[1] < 0 or n[0] >= matrix.shape[0] or n[1] >= matrix.shape[1]:\n",
    "            continue\n",
    "        yield matrix[n]\n",
    "\n",
    "def algorithm(state, rate):\n",
    "    for x, y in np.ndindex(state.shape):\n",
    "        if state[x, y] == 0:\n",
    "            continue\n",
    "        if any(i == 0 for i in neighbors(state, (x, y))):\n",
    "            state[x, y] = max(0, state[x, y] - rate[x, y])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbdebafb-bcb0-48e0-a57e-1be2cacb73fe",
   "metadata": {},
   "source": [
    "## Plotting\n",
    "\n",
    "Now let's plot the data and have a look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7e0f0edd-41a6-4928-a1a5-122d10b66f9f",
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   "source": [
    "def frames(state, rate):\n",
    "    def iterate(state):\n",
    "        while np.any(state):\n",
    "            algorithm(state, rate)\n",
    "            yield state.copy()\n",
    "    return [state.copy(), *iterate(state.copy())]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bcfda793-bbe3-40df-b3e6-18d167e4bc3f",
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   "source": [
    "def plot(frames):\n",
    "    plt.close()\n",
    "    fig, ax = plt.subplots()\n",
    "\n",
    "    def animate(n):\n",
    "        return ax.imshow(frames[n])\n",
    "\n",
    "    ani = matplotlib.animation.FuncAnimation(fig, animate, frames=len(frames), interval=100)\n",
    "    return IPython.display.HTML(ani.to_jshtml())"
   ]
  },
  {
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   "execution_count": 11,
   "id": "835b3f5a-b876-49dc-9121-6881f5183c0b",
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