source-code/diffusion_limited_aggregation.ipynb

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   "cell_type": "markdown",
   "id": "99e4613c-1de4-4626-884d-916f474d2f6a",
   "metadata": {},
   "source": [
    "# Requirements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7d29969a-5c81-45bd-9b4e-0ebe5db5bbe3",
   "metadata": {
    "tags": []
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   "outputs": [],
   "source": [
    "import itertools\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from operator import attrgetter\n",
    "import random\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0081f193-a617-40a2-be55-5fa90081e160",
   "metadata": {},
   "source": [
    "# Problem setting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0975375-0802-4ab7-9427-49398da480cd",
   "metadata": {},
   "source": [
    "For diffusion-limited aggregation, we start with a set of particles at fixed postions, and a number of particles that can move. Once a moving particle collides with a fixed particle, it \"sticks\", i.e., it will no longer be able to move.  Motion is Brownian.  The simulation ends when all particles are fixed.  The total number of particles remains the same during the entire simulation.\n",
    "\n",
    "For simplicity, particles move on a square grid, they collide when they are at neighboring grid positions, i.e., when for a particle there is another particle in any of the 8 grid positions around it.  The grid has a finite size, and particles can not move beyond its limits, i.e., the particles move in a box.\n",
    "\n",
    "A typical initial condition is that the simulation starts out with a single fixed particle in the middle of the grid.  The moving particles start at the edges of the grid, and gradually diffuse inward."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd311d43-6571-4693-91cd-a5eb5e7856b8",
   "metadata": {},
   "source": [
    "# Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b6aff79-221b-423d-8af9-caa5b157848c",
   "metadata": {},
   "source": [
    "The following class implements such a simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "894055e9-48dd-4cef-96b1-9bb054fade8d",
   "metadata": {
    "tags": []
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   "source": [
    "class System:\n",
    "    \n",
    "    def __init__(self, grid_size, nr_particles=None, fixed_particles=None, measures=None):\n",
    "        '''Initialize a new system\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        grid_size: int\n",
    "            Size of the grid, i.e., there will be grid_size x grid_size positions in the\n",
    "            simulation\n",
    "        nr_particles: int\n",
    "            The number of moving particles initially in the simulation, the default is\n",
    "            4*(grid_size - 1), i.e., all the positions at the edge of the grid are taken.\n",
    "        fixed_particle: list[tuple]\n",
    "            Coordinates [1, grid_size - 2] of the fixed points, by default the point in the\n",
    "            middle of the grid.  Note that fixed points can not be on the edge of the grid.\n",
    "        measures: list[Measure]\n",
    "            List of measures to be computed at each time step.\n",
    "        Returns\n",
    "        -------\n",
    "        System:\n",
    "            The initialized system\n",
    "            \n",
    "        Except\n",
    "        ------\n",
    "        ValueError:\n",
    "            A ValueError is thrown if the number of particles exceeds 4*(grid_size - 1) as well\n",
    "            as when invalid coordinates are specified for a fixed particle.\n",
    "        '''\n",
    "        if nr_particles is None:\n",
    "            nr_particles = 4*(grid_size - 1)\n",
    "        if nr_particles > 4*(grid_size - 1):\n",
    "            raise ValueError(f'too many particles, {nr_particles} exceeds {4*(grid_size - 1)}')\n",
    "        self._empty = ' '\n",
    "        self._moving = '*'\n",
    "        self._fixed = 'x'\n",
    "        self._grid = [[self._empty]*grid_size for _ in range(grid_size)]\n",
    "        if fixed_particles is None:\n",
    "            self._fixed_particles = [(self.nr_rows//2, self.nr_cols//2)]\n",
    "        else:\n",
    "            self._fixed_particles = fixed_particles.copy()\n",
    "        for row, col in self._fixed_particles:\n",
    "            if 0 < row < self.nr_rows - 1 and 0 < col < self.nr_cols - 1:\n",
    "                self._grid[row][col] = self._fixed\n",
    "            else:\n",
    "                raise ValueError(f'fixed particles can not be on the border: ({row}, {col})')\n",
    "        self._moving_particles = self._place_particles(nr_particles)\n",
    "        self._nr_particles = len(self._moving_particles) + len(self._fixed_particles)\n",
    "        self._step = 0\n",
    "        if measures is None:\n",
    "            self._measures = []\n",
    "        else:\n",
    "            self._measures = measures\n",
    "\n",
    "    @property\n",
    "    def nr_particles(self):\n",
    "        '''Returs the total number of particles, both moving and fixed.'''\n",
    "        return self._nr_particles\n",
    "    \n",
    "    @property\n",
    "    def shape(self):\n",
    "        '''Returns the shape of the grid as a tuple.'''\n",
    "        return (len(self._grid), len(self._grid[0]))\n",
    "    \n",
    "    @property\n",
    "    def nr_rows(self):\n",
    "        '''Returns the number of rows in the grid.'''\n",
    "        return self.shape[0]\n",
    "    \n",
    "    @property\n",
    "    def nr_cols(self):\n",
    "        '''Returns the number of columns in the grid.'''\n",
    "        return self.shape[1]\n",
    "    \n",
    "    def _place_particles(self, nr_particles):\n",
    "        '''Places the specified number of moving particles on the edge of the grid\n",
    "        randomly.'''\n",
    "        moving_particles = []\n",
    "        while nr_particles > 0:\n",
    "            side = random.choice(('top', 'right', 'bottom', 'left'))\n",
    "            if side == 'top':\n",
    "                pos = random.randrange(0, self.nr_cols - 1)\n",
    "                if self._grid[0][pos] == self._empty:\n",
    "                    self._grid[0][pos] = self._moving\n",
    "                    moving_particles.append((0, pos))\n",
    "                    nr_particles -= 1\n",
    "            elif side == 'right':\n",
    "                pos = random.randrange(0, self.nr_rows - 1)\n",
    "                if self._grid[pos][self.nr_cols - 1] == self._empty:\n",
    "                    self._grid[pos][self.nr_cols - 1] = self._moving\n",
    "                    moving_particles.append((pos, self.nr_cols - 1))\n",
    "                    nr_particles -= 1\n",
    "            elif side == 'bottom':\n",
    "                pos = random.randrange(1, self.nr_cols)\n",
    "                if self._grid[self.nr_rows - 1][pos] == self._empty:\n",
    "                    self._grid[self.nr_rows - 1][pos] = self._moving\n",
    "                    moving_particles.append((self.nr_rows - 1, pos))\n",
    "                    nr_particles -= 1\n",
    "            else:\n",
    "                pos = random.randrange(1, self.nr_rows)\n",
    "                if self._grid[pos][0] == self._empty:\n",
    "                    self._grid[pos][0] = self._moving\n",
    "                    moving_particles.append((pos, 0))\n",
    "                    nr_particles -= 1\n",
    "        return moving_particles\n",
    "\n",
    "    def _is_grid_pos(self, coord):\n",
    "        '''Returns True if the specified coordinates are valid grid coordinates.'''\n",
    "        return 0 <= coord[0] < self.nr_rows and 0 <= coord[1] < self.nr_cols\n",
    "    \n",
    "    def _is_free_pos(self, coord):\n",
    "        '''Returns True if the position specified by the coordinates doesn't\n",
    "        contain another particle.'''\n",
    "        return self._grid[coord[0]][coord[1]] == self._empty\n",
    "\n",
    "    def _is_fixed_pos(self, coord):\n",
    "        '''Returns True if there is a fixed particle at the given coordinates.'''\n",
    "        return self._grid[coord[0]][coord[1]] == self._fixed\n",
    "\n",
    "    def _has_fixed_neighbor(self, coord):\n",
    "        '''Returns True if a particle at the specified coordinates has a\n",
    "        neighbour that is a fixed particle.'''\n",
    "        for delta_row in (-1, 0, 1):\n",
    "            for delta_col in (-1, 0, 1):\n",
    "                neighbor = coord[0] + delta_row, coord[1] + delta_col\n",
    "                if self._is_grid_pos(neighbor):\n",
    "                    if self._is_fixed_pos(neighbor):\n",
    "                        return True\n",
    "        return False\n",
    "    \n",
    "    def _move(self):\n",
    "        '''Try to move a particle.\n",
    "        \n",
    "        Particles can not move to positions outside of the grid, neither to\n",
    "        positions that already contain a particle.\n",
    "        '''\n",
    "        particle_idx = random.randrange(0, len(self._moving_particles))\n",
    "        coord = self._moving_particles[particle_idx]\n",
    "        delta_row = random.choice((-1, 0, 1))\n",
    "        delta_col = random.choice((-1, 0, 1))\n",
    "        new_coord = coord[0] + delta_row, coord[1] + delta_col\n",
    "        if self._is_grid_pos(new_coord) and self._is_free_pos(new_coord):\n",
    "            self._step += 1\n",
    "            self._grid[coord[0]][coord[1]] = self._empty\n",
    "            self._grid[new_coord[0]][new_coord[1]] = self._moving\n",
    "            if self._has_fixed_neighbor(new_coord):\n",
    "                self._moving_particles.pop(particle_idx)\n",
    "                self._grid[new_coord[0]][new_coord[1]] = self._fixed\n",
    "                self._fixed_particles.append(new_coord)\n",
    "            else:\n",
    "                self._moving_particles[particle_idx] = new_coord\n",
    "            for measure in self._measures:\n",
    "                measure(self)\n",
    "\n",
    "    def run(self, verbose=False):\n",
    "        '''Run the simulation to conclusion\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        verbose: bool\n",
    "            Print feedback about the progress of the simulation.\n",
    "        '''\n",
    "        while self._moving_particles:\n",
    "            self._move()\n",
    "            if verbose and self._step > 0 and self._step % 100_000 == 0:\n",
    "                print(f'{self._step} steps: {len(self._fixed_particles)} out of {self.nr_particles} fixed')\n",
    "        if verbose:\n",
    "            print(f'{self._step} steps: {len(self._fixed_particles)} out of {self.nr_particles} fixed')\n",
    "\n",
    "    @property\n",
    "    def steps(self):\n",
    "        '''Returns the steps taken, i.e., the number of valid moves.'''\n",
    "        return self._step\n",
    "\n",
    "    @property\n",
    "    def particles(self):\n",
    "        '''Return the positions of the fixed particles\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        list[tuple]\n",
    "            A list of tuples with coordinates\n",
    "        '''\n",
    "        return self._fixed_particles.copy()\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return '\\n'.join(''.join(row) for row in self._grid)                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4e0d725c-e8d2-4cc4-a22f-d15626d2b6e0",
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   "source": [
    "def visualize_system(system):\n",
    "    '''Show the system represented as a heatmap.  Particles that were fixed\n",
    "    early on are bright, particles that got fixed positions late are darker.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    system: System\n",
    "        System to visualize, typically after a run has completed.\n",
    "    '''\n",
    "    image = np.zeros(system.shape, dtype=np.uint64)\n",
    "    for i, coord in enumerate(system.particles):\n",
    "        image[coord] = system.nr_particles - i\n",
    "    plt.imshow(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff54855b-f44e-4099-9ea3-7ea9b241741d",
   "metadata": {},
   "source": [
    "# Runs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c430b701-dc94-4d31-b26d-e06d617262d8",
   "metadata": {},
   "source": [
    "We can do a few runs of various systems."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75708d67-726b-403d-8ef6-1fcca1254238",
   "metadata": {},
   "source": [
    "## Small grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "bbdbf590-042c-475d-8cc0-c7de6b1155f4",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 steps: 2 out of 97 fixed\n",
      "200000 steps: 23 out of 97 fixed\n",
      "300000 steps: 31 out of 97 fixed\n",
      "400000 steps: 58 out of 97 fixed\n",
      "500000 steps: 72 out of 97 fixed\n",
      "597320 steps: 97 out of 97 fixed\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "system = System(100, 96)\n",
    "system.run(verbose=True)\n",
    "visualize_system(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d836a78-2739-40c7-b582-78317a2b0106",
   "metadata": {},
   "source": [
    "## Medium grid with multiple initial fixed particles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "114e1a1c-c2da-40a8-9537-aa78b00a00e1",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 steps: 5 out of 801 fixed\n",
      "200000 steps: 5 out of 801 fixed\n",
      "300000 steps: 5 out of 801 fixed\n",
      "400000 steps: 7 out of 801 fixed\n",
      "500000 steps: 9 out of 801 fixed\n",
      "600000 steps: 11 out of 801 fixed\n",
      "700000 steps: 15 out of 801 fixed\n",
      "800000 steps: 19 out of 801 fixed\n",
      "800000 steps: 19 out of 801 fixed\n",
      "900000 steps: 29 out of 801 fixed\n",
      "1000000 steps: 36 out of 801 fixed\n",
      "1100000 steps: 53 out of 801 fixed\n",
      "1200000 steps: 62 out of 801 fixed\n",
      "1300000 steps: 77 out of 801 fixed\n",
      "1400000 steps: 98 out of 801 fixed\n",
      "1500000 steps: 109 out of 801 fixed\n",
      "1500000 steps: 109 out of 801 fixed\n",
      "1600000 steps: 122 out of 801 fixed\n",
      "1700000 steps: 138 out of 801 fixed\n",
      "1800000 steps: 158 out of 801 fixed\n",
      "1900000 steps: 176 out of 801 fixed\n",
      "2000000 steps: 203 out of 801 fixed\n",
      "2100000 steps: 231 out of 801 fixed\n",
      "2100000 steps: 231 out of 801 fixed\n",
      "2200000 steps: 265 out of 801 fixed\n",
      "2300000 steps: 284 out of 801 fixed\n",
      "2400000 steps: 297 out of 801 fixed\n",
      "2500000 steps: 320 out of 801 fixed\n",
      "2600000 steps: 344 out of 801 fixed\n",
      "2700000 steps: 384 out of 801 fixed\n",
      "2800000 steps: 413 out of 801 fixed\n",
      "2900000 steps: 443 out of 801 fixed\n",
      "2900000 steps: 443 out of 801 fixed\n",
      "2900000 steps: 443 out of 801 fixed\n",
      "2900000 steps: 443 out of 801 fixed\n",
      "3000000 steps: 474 out of 801 fixed\n",
      "3100000 steps: 511 out of 801 fixed\n",
      "3200000 steps: 553 out of 801 fixed\n",
      "3300000 steps: 592 out of 801 fixed\n",
      "3400000 steps: 640 out of 801 fixed\n",
      "3500000 steps: 677 out of 801 fixed\n",
      "3600000 steps: 712 out of 801 fixed\n",
      "3700000 steps: 760 out of 801 fixed\n",
      "3700000 steps: 760 out of 801 fixed\n",
      "3781107 steps: 801 out of 801 fixed\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "system = System(200, fixed_particles=[(50, 50), (100, 100), (50, 150), (150, 50), (150, 150)])\n",
    "system.run(verbose=True)\n",
    "visualize_system(system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "16c8a15b-0e2e-4758-9c08-24e8592939fa",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 steps: 3 out of 1199 fixed\n",
      "200000 steps: 3 out of 1199 fixed\n",
      "300000 steps: 3 out of 1199 fixed\n",
      "400000 steps: 3 out of 1199 fixed\n",
      "400000 steps: 3 out of 1199 fixed\n",
      "500000 steps: 3 out of 1199 fixed\n",
      "600000 steps: 3 out of 1199 fixed\n",
      "700000 steps: 3 out of 1199 fixed\n",
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      "1000000 steps: 3 out of 1199 fixed\n",
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "system = System(300, fixed_particles=[(50, 50), (60, 60), (70, 70)])\n",
    "system.run(verbose=True)\n",
    "visualize_system(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e98bb94f-f082-467f-951d-d7aaa93383ff",
   "metadata": {},
   "source": [
    "Note that the runtime increase with the grid size."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f656ab4-24ea-4ac5-9098-44ac4b83e605",
   "metadata": {},
   "source": [
    "## Fixed particles evolution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "988a1715-fccf-4a9a-9be4-7534116e6f1c",
   "metadata": {},
   "source": [
    "How many particles are fixed after a number of time steps?\n",
    "\n",
    "We define a class that keeps track of the number of fixed particles over time.  Objects of this class should be callable with the grid as an argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fc68b5b4-0d1b-4e6b-9fe5-6676ac379eb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "class NumberFixedParticles:\n",
    "    '''Implementation of a measure that keeps track of the number of\n",
    "    fixed particles over time.\n",
    "    '''\n",
    "    \n",
    "    def __init__(self):\n",
    "        '''constructor for a new measure\n",
    "        '''\n",
    "        self._counts = []\n",
    "    \n",
    "    def __call__(self, grid):\n",
    "        '''makes sure that object is callable\n",
    "    \n",
    "        Parameters\n",
    "        ----------\n",
    "        grid: Grid\n",
    "            all information can be extracted out of the grid\n",
    "        '''\n",
    "        self._counts.append(len(grid._fixed_particles))\n",
    "        \n",
    "    @property\n",
    "    def counts(self):\n",
    "        '''returns the values of the count of fixed particles as\n",
    "        a function of the time step\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        list[int]\n",
    "            count of the number of fixed particles over itme\n",
    "        '''\n",
    "        return self._counts\n",
    "    \n",
    "    @staticmethod\n",
    "    def aggregate(measures):\n",
    "        '''compute the average value of multiple measurements\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        list[NumberFixedParticles]\n",
    "            list of measurements\n",
    "            \n",
    "        Returns\n",
    "        -------\n",
    "        list[float]\n",
    "            list of average values\n",
    "        '''\n",
    "        max_len = max(map(lambda x: len(x.counts), measures))\n",
    "        average = [0]*max_len\n",
    "        for measure in measures:\n",
    "            for i in range(len(average)):\n",
    "                if i < len(measure.counts):\n",
    "                      average[i] += measure.counts[i]\n",
    "                else:\n",
    "                      average[i] +=  measure.counts[-1]\n",
    "        return [value/len(measures) for value in average]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e3f39eb9-045d-4367-8231-b01e1bf35148",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nr_runs = 20\n",
    "size = 25\n",
    "measures = []\n",
    "for _ in range(nr_runs):\n",
    "    measures.append(NumberFixedParticles())\n",
    "    system = System(size, measures=[measures[-1]])\n",
    "    system.run()\n",
    "counts = NumberFixedParticles.aggregate(measures)\n",
    "plt.plot(list(range(len(counts))), counts);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60401acf-0260-4654-b3fd-2d3a3f2b2103",
   "metadata": {},
   "source": [
    "## Time steps versus number of particles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "15e204bb-5bc3-438b-b98e-b5ebde8b52c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MaximumTimeSteps:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self._max_time_step = -1\n",
    "        \n",
    "    def __call__(self, grid):\n",
    "        if not grid._moving_particles:\n",
    "            self._max_time_step = grid.steps\n",
    "    \n",
    "    @property\n",
    "    def max_steps(self):\n",
    "        return self._max_time_step\n",
    "    \n",
    "    @staticmethod\n",
    "    def aggregate(measures):\n",
    "        return sum(map(attrgetter('max_steps'), measures))/len(measures)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "026e3569-6dd9-428f-befd-eeea7616b300",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 27.,  57., 120., 124.,  87.,  54.,  18.,   8.,   3.,   2.]),\n",
       " array([ 6150.,  6791.,  7432.,  8073.,  8714.,  9355.,  9996., 10637.,\n",
       "        11278., 11919., 12560.]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nr_runs = 500\n",
    "size = 25\n",
    "nr_particles = 10\n",
    "measures = []\n",
    "for _ in range(nr_runs):\n",
    "    measures.append(MaximumTimeSteps())\n",
    "    system = System(size, measures=[measures[-1]])\n",
    "    system.run()\n",
    "plt.hist(list(map(attrgetter('max_steps'), measures)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f9aeebc5-61fc-48e0-bc63-1ecd8a18b520",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 16.,  46.,  91., 134.,  90.,  71.,  35.,  10.,   6.,   1.]),\n",
       " array([ 5878. ,  6517.6,  7157.2,  7796.8,  8436.4,  9076. ,  9715.6,\n",
       "        10355.2, 10994.8, 11634.4, 12274. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nr_runs = 500\n",
    "size = 25\n",
    "nr_particles = 20\n",
    "measures = []\n",
    "for _ in range(nr_runs):\n",
    "    measures.append(MaximumTimeSteps())\n",
    "    system = System(size, measures=[measures[-1]])\n",
    "    system.run()\n",
    "plt.hist(list(map(attrgetter('max_steps'), measures)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d2227b14-cdf5-4856-ba38-47821fa233af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 15.,  62., 112., 132., 101.,  52.,  19.,   5.,   1.,   1.]),\n",
       " array([ 5778. ,  6485.6,  7193.2,  7900.8,  8608.4,  9316. , 10023.6,\n",
       "        10731.2, 11438.8, 12146.4, 12854. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nr_runs = 500\n",
    "size = 25\n",
    "nr_particles = 4*(size - 1)\n",
    "measures = []\n",
    "for _ in range(nr_runs):\n",
    "    measures.append(MaximumTimeSteps())\n",
    "    system = System(size, measures=[measures[-1]])\n",
    "    system.run()\n",
    "plt.hist(list(map(attrgetter('max_steps'), measures)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "a82e37de-f81a-4a08-90f3-7c26e9b0b31b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of particles: 1\n",
      "number of particles: 3\n",
      "number of particles: 5\n",
      "number of particles: 7\n",
      "number of particles: 9\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[31], line 12\u001b[0m\n\u001b[1;32m     10\u001b[0m         measures\u001b[38;5;241m.\u001b[39mappend(MaximumTimeSteps())\n\u001b[1;32m     11\u001b[0m         system \u001b[38;5;241m=\u001b[39m System(size, measures\u001b[38;5;241m=\u001b[39m[measures[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m]])\n\u001b[0;32m---> 12\u001b[0m         \u001b[43msystem\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     13\u001b[0m     max_times\u001b[38;5;241m.\u001b[39mappend(MaximumTimeSteps\u001b[38;5;241m.\u001b[39maggregate(measures))\n\u001b[1;32m     14\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(\u001b[38;5;28mlist\u001b[39m(\u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m1\u001b[39m, \u001b[38;5;28mlen\u001b[39m(max_times) \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m)), max_times)\n",
      "Cell \u001b[0;32mIn[2], line 164\u001b[0m, in \u001b[0;36mSystem.run\u001b[0;34m(self, verbose)\u001b[0m\n\u001b[1;32m    156\u001b[0m \u001b[38;5;124;03m'''Run the simulation to conclusion\u001b[39;00m\n\u001b[1;32m    157\u001b[0m \u001b[38;5;124;03m\u001b[39;00m\n\u001b[1;32m    158\u001b[0m \u001b[38;5;124;03mParameters\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    161\u001b[0m \u001b[38;5;124;03m    Print feedback about the progress of the simulation.\u001b[39;00m\n\u001b[1;32m    162\u001b[0m \u001b[38;5;124;03m'''\u001b[39;00m\n\u001b[1;32m    163\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_moving_particles:\n\u001b[0;32m--> 164\u001b[0m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_move\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    165\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m verbose \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_step \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_step \u001b[38;5;241m%\u001b[39m \u001b[38;5;241m100_000\u001b[39m \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[1;32m    166\u001b[0m         \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_step\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m steps: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_fixed_particles)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m out of \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mnr_particles\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m fixed\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "Cell \u001b[0;32mIn[2], line 139\u001b[0m, in \u001b[0;36mSystem._move\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    137\u001b[0m particle_idx \u001b[38;5;241m=\u001b[39m random\u001b[38;5;241m.\u001b[39mrandrange(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_moving_particles))\n\u001b[1;32m    138\u001b[0m coord \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_moving_particles[particle_idx]\n\u001b[0;32m--> 139\u001b[0m delta_row \u001b[38;5;241m=\u001b[39m \u001b[43mrandom\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mchoice\u001b[49m\u001b[43m(\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    140\u001b[0m delta_col \u001b[38;5;241m=\u001b[39m random\u001b[38;5;241m.\u001b[39mchoice((\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m))\n\u001b[1;32m    141\u001b[0m new_coord \u001b[38;5;241m=\u001b[39m coord[\u001b[38;5;241m0\u001b[39m] \u001b[38;5;241m+\u001b[39m delta_row, coord[\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m+\u001b[39m delta_col\n",
      "File \u001b[0;32m~/mambaforge/envs/scientific_python/lib/python3.10/random.py:378\u001b[0m, in \u001b[0;36mRandom.choice\u001b[0;34m(self, seq)\u001b[0m\n\u001b[1;32m    376\u001b[0m \u001b[38;5;124;03m\"\"\"Choose a random element from a non-empty sequence.\"\"\"\u001b[39;00m\n\u001b[1;32m    377\u001b[0m \u001b[38;5;66;03m# raises IndexError if seq is empty\u001b[39;00m\n\u001b[0;32m--> 378\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m seq[\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_randbelow\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mlen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mseq\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m]\n",
      "File \u001b[0;32m~/mambaforge/envs/scientific_python/lib/python3.10/random.py:245\u001b[0m, in \u001b[0;36mRandom._randbelow_with_getrandbits\u001b[0;34m(self, n)\u001b[0m\n\u001b[1;32m    243\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;241m0\u001b[39m\n\u001b[1;32m    244\u001b[0m getrandbits \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mgetrandbits\n\u001b[0;32m--> 245\u001b[0m k \u001b[38;5;241m=\u001b[39m \u001b[43mn\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbit_length\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m  \u001b[38;5;66;03m# don't use (n-1) here because n can be 1\u001b[39;00m\n\u001b[1;32m    246\u001b[0m r \u001b[38;5;241m=\u001b[39m getrandbits(k)  \u001b[38;5;66;03m# 0 <= r < 2**k\u001b[39;00m\n\u001b[1;32m    247\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m r \u001b[38;5;241m>\u001b[39m\u001b[38;5;241m=\u001b[39m n:\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "nr_runs = 20\n",
    "size = 10\n",
    "size_delta = 2\n",
    "max_size = 4*(size - 1)\n",
    "max_times = []\n",
    "for nr_particles in range(1, max_size + 1, size_delta):\n",
    "    print(f'number of particles: {nr_particles}')\n",
    "    measures = []\n",
    "    for _ in range(nr_runs):\n",
    "        measures.append(MaximumTimeSteps())\n",
    "        system = System(size, measures=[measures[-1]])\n",
    "        system.run()\n",
    "    max_times.append(MaximumTimeSteps.aggregate(measures))\n",
    "plt.plot(list(range(1, len(max_times) + 1)), max_times);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3acde11-1bc1-427e-8e65-fd1aa2f212ee",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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