HotSpots.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5304b35f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Thanks for using AART\n",
      "Copyright (C) 2024, A. Cardenas-Avendano, H. Zhu & A. Lupsasca\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from aart_func import *\n",
    "from params import * "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a27a5311",
   "metadata": {},
   "source": [
    "As usual, let us get the geometry. From Examples.ipynb, we know how AART works. We need to get lensing bands and the ratracing information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ba8c94b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n",
      "\n",
      "Thanks for using AART\n",
      "Copyright (C) 2024, A. Cardenas-Avendano, H. Zhu & A. Lupsasca\n",
      "\n",
      "Computing the lensing bands\n",
      "Number of points in the n=0 grid  6250000\n",
      "Number of points in the n=1 grid  6250000\n",
      "Number of points in the n=2 grid  6250000\n",
      "File  ./Results/LensingBands_a_0.94_i_17.h5  created.\n",
      "CPU times: user 187 ms, sys: 78 ms, total: 265 ms\n",
      "Wall time: 37.5 s\n"
     ]
    }
   ],
   "source": [
    "%time !python lensingbands.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "520b29c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n",
      "\n",
      "Thanks for using AART\n",
      "Copyright (C) 2024, A. Cardenas-Avendano, H. Zhu & A. Lupsasca\n",
      "\n",
      "Ray-tracing\n",
      "Reading file:  ./Results/LensingBands_a_0.94_i_17.h5\n",
      "Analytical ray-tracing of the n=0 band points\n",
      "Analytical ray-tracing of the n=1 band points\n",
      "Analytical ray-tracing of the n=2 band points\n",
      "File  ./Results/Rays_a_0.94_i_17.h5  created.\n",
      "\n",
      "A total of 18750000 photons were ray-traced\n",
      "CPU times: user 319 ms, sys: 133 ms, total: 452 ms\n",
      "Wall time: 1min\n"
     ]
    }
   ],
   "source": [
    "%time !python raytracing.py"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ce6f0aa",
   "metadata": {},
   "source": [
    "We will now load what we need. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "37fc028a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading file:  ./Results/LensingBands_a_0.94_i_17.h5\n"
     ]
    }
   ],
   "source": [
    "fnbands=\"./Results/LensingBands_a_%s_i_%s.h5\"%(spin_case,i_case)\n",
    "\n",
    "print(\"Reading file: \",fnbands)\n",
    "\n",
    "h5f = h5py.File(fnbands,'r')\n",
    "\n",
    "#Points for the boundary of the BH shadow\n",
    "alpha_critc=h5f['alpha'][:]\n",
    "beta_critc=h5f['beta'][:]\n",
    "\n",
    "#The concave hulls for the lensing bands\n",
    "hull_0i=h5f['hull_0i'][:]\n",
    "\n",
    "#The grid points for each lensing band\n",
    "N0=int(h5f[\"N0\"][0])\n",
    "lim0=int(h5f[\"lim0\"][0])\n",
    "\n",
    "h5f.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a64a587c",
   "metadata": {},
   "source": [
    "# From an analytical prescribed hotspot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39bce4b5",
   "metadata": {},
   "source": [
    "Let us start by raytracing a hotspot that is prescribed analytically. We will assume it is a Gaussian blob at radius=radhs with angular frequency=velhs, moving on a circular orbit. All the parameters are specified in *intensity_f.py*. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "07d64e6b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n",
      "\n",
      "Thanks for using AART\n",
      "Copyright (C) 2024, A. Cardenas-Avendano, H. Zhu & A. Lupsasca\n",
      "\n",
      "Intensity for a Flare\n",
      "Reading file:  ./Results/LensingBands_a_0.94_i_17.h5\n",
      "Reading file:  ./Results/Rays_a_0.94_i_17.h5\n",
      "Calculating an image at time t=2.18182 (M)\n",
      "Calculating an image at time t=0.0 (M)\n",
      "Calculating an image at time t=1.09091 (M)\n",
      "Calculating an image at time t=3.27273 (M)\n",
      "Calculating an image at time t=4.36364 (M)\n",
      "Calculating an image at time t=5.45455 (M)\n",
      "Calculating an image at time t=6.54545 (M)\n",
      "Calculating an image at time t=7.63636 (M)\n",
      "Calculating an image at time t=8.72727 (M)\n",
      "Calculating an image at time t=9.81818 (M)\n",
      "Calculating an image at time t=10.90909 (M)\n",
      "Calculating an image at time t=12.0 (M)\n",
      "File  ./Results/Intensities_a_0.94_i_17_rhs_8_velhs_0.05_rwidth_0.5.h5  created.\n",
      "CPU times: user 69.9 ms, sys: 36.1 ms, total: 106 ms\n",
      "Wall time: 7.17 s\n"
     ]
    }
   ],
   "source": [
    "%time !python hotspot.py"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa514882",
   "metadata": {},
   "source": [
    "Let us now load the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "acd51b5c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading file:  ./Results/Intensities_a_0.94_i_17_rhs_8_velhs_0.05_rwidth_0.5.h5\n"
     ]
    }
   ],
   "source": [
    "fimages=\"./Results/Intensities_a_%s_i_%s_rhs_%s_velhs_%s_rwidth_%s.h5\"%(spin_case,i_case,radhs,velhs,rwidth)\n",
    "\n",
    "print(\"Reading file: \",fimages)\n",
    "\n",
    "h5f = h5py.File(fimages,'r')\n",
    "\n",
    "Is0=h5f['bghts0'][:]\n",
    "Is1=h5f['bghts1'][:]\n",
    "Is2=h5f['bghts2'][:]\n",
    "\n",
    "h5f.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "213e4797",
   "metadata": {},
   "source": [
    "And visualize a single snapshot, the first one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "db094bc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "tsnap=0\n",
    "VMAX=np.max(Is0+Is1+Is2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d4d2cc72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\beta$ (M)')"
      ]
     },
     "execution_count": 8,
     "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": [
    "plt.fill(hull_0i[:,0],hull_0i[:,1],color=\"k\")\n",
    "\n",
    "plt.imshow(Is0[tsnap,:,:]+Is1[tsnap,:,:]+Is2[tsnap,:,:],vmax=VMAX,origin=\"lower\",cmap=\"plasma\",extent=[-lim0,lim0,-lim0,lim0])\n",
    "\n",
    "plt.xlim(-10,10)\n",
    "plt.ylim(-10,10)\n",
    "\n",
    "plt.xlabel(r\"$\\alpha$\"+\" \"+\"(M)\")\n",
    "plt.ylabel(r\"$\\beta$\"+\" \"+\"(M)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5f55f5a",
   "metadata": {},
   "source": [
    "And produce a movie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "20be8130",
   "metadata": {},
   "outputs": [],
   "source": [
    "fignames=[]\n",
    "VMAX=np.max(Is0+Is1+Is2)\n",
    "for tsnap in np.arange(snapshots)[::-1]:\n",
    "    fig, ax = plt.subplots()\n",
    "    \n",
    "    ax.fill(hull_0i[:,0],hull_0i[:,1],color=\"k\")\n",
    "    \n",
    "    ax.imshow(Is0[tsnap,:,:]+Is1[tsnap,:,:]+Is2[tsnap,:,:],vmax=VMAX,origin=\"lower\",cmap=\"plasma\",extent=[-lim0,lim0,-lim0,lim0])\n",
    "    ax.set_xlim(-10,10)\n",
    "    ax.set_ylim(-10,10)\n",
    "    \n",
    "    ax.set_xlabel(r\"$\\alpha$\"+\" \"+\"(M)\")\n",
    "    ax.set_ylabel(r\"$\\beta$\"+\" \"+\"(M)\")\n",
    "    \n",
    "    fignames.append('Fig%s.png'%tsnap)\n",
    "    plt.savefig('Fig%s.png'%tsnap,dpi=400,bbox_inches='tight')\n",
    "    plt.close(fig)\n",
    "\n",
    "with imageio.get_writer('HotSpotMovie_Analytical.gif', mode='I') as writer:\n",
    "    for filename in fignames:\n",
    "        image = imageio.imread(filename)\n",
    "        writer.append_data(image)\n",
    "\n",
    "# We delete the created images and just keep the GIF\n",
    "for filename in set(fignames):\n",
    "    os.remove(filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3c1fe1c",
   "metadata": {},
   "source": [
    "# From a file containing a hotspot movie"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da2f72ae",
   "metadata": {},
   "source": [
    "Let us now start by exploring the precomputed hot spot movie (dataset)first. Make <span style=\"color:blue\">**sure**</span> to change the name of the inoisy file in *params.py* to \"hotspot.h5\". I thank **Sreehari Harikesh** for providing this example data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3287d857",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading file:  hotspot.h5\n"
     ]
    }
   ],
   "source": [
    "inoisyfile=\"hotspot.h5\"\n",
    "\n",
    "print(\"Reading file: \",inoisyfile)\n",
    "\n",
    "h5f = h5py.File(inoisyfile,'r')\n",
    "\n",
    "inoisy=np.array(h5f['data/data_env'])\n",
    "\n",
    "xtstart = np.array(h5f['params/x0start'])\n",
    "xtend = np.array(h5f['params/x0end'])\n",
    "\n",
    "x1start = np.array(h5f['params/x1start'])\n",
    "x2start = np.array(h5f['params/x2start'])\n",
    "x1end = np.array(h5f['params/x1end'])\n",
    "x2end = np.array(h5f['params/x2end'])\n",
    "\n",
    "h5f.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8bcdae0",
   "metadata": {},
   "source": [
    "And visualize a single snapshot. This is to get a sense where the hotspot is and how it is moving, in case we want to compare to an implementation that prescribes the hotspot analytically. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cd5d231f",
   "metadata": {},
   "outputs": [],
   "source": [
    "snap=15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "aa918c1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$Y$ (M)')"
      ]
     },
     "execution_count": 12,
     "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": [
    "plt.imshow(inoisy[snap],origin=\"lower\",extent=[x1start,np.abs(x1start),x2start,np.abs(x2start)])\n",
    "\n",
    "plt.fill(hull_0i[:,0],hull_0i[:,1],color=\"k\")\n",
    "\n",
    "plt.axvline(2.2,color=\"w\",linestyle=\"--\",alpha=0.2)\n",
    "plt.axhline(-2.2,color=\"w\",linestyle=\"--\",alpha=0.2)\n",
    "\n",
    "plt.xlabel(r\"$X$\"+\" \"+\"(M)\")\n",
    "plt.ylabel(r\"$Y$\"+\" \"+\"(M)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bda6928",
   "metadata": {},
   "source": [
    "And a movie, just for fun!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a875231b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "fignames=[]\n",
    "for tsnap in np.arange(0,int(inoisy.shape[0]),1):\n",
    "    \n",
    "    fig, ax = plt.subplots()\n",
    "    \n",
    "    ax.fill(hull_0i[:,0],hull_0i[:,1],color=\"k\")\n",
    "    \n",
    "    ax.imshow(inoisy[tsnap],origin=\"lower\",extent=[x1start,np.abs(x1start),x2start,np.abs(x2start)])\n",
    "    ax.set_xlim(-10,10)\n",
    "    ax.set_ylim(-10,10)\n",
    "    \n",
    "    ax.set_xlabel(r\"$X$\"+\" \"+\"(M)\")\n",
    "    ax.set_ylabel(r\"$Y$\"+\" \"+\"(M)\")\n",
    "    \n",
    "    fignames.append('Fig%s.png'%tsnap)\n",
    "    plt.savefig('Fig%s.png'%tsnap,dpi=400,bbox_inches='tight')\n",
    "    plt.close(fig)\n",
    "\n",
    "with imageio.get_writer('inoisyMovie.gif', mode='I') as writer:\n",
    "    for filename in fignames:\n",
    "        image = imageio.imread(filename)\n",
    "        writer.append_data(image)\n",
    "\n",
    "# We delete the created images and just keep the GIF\n",
    "for filename in set(fignames):\n",
    "    os.remove(filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28442307",
   "metadata": {},
   "source": [
    "Let us generate a single image, but in the slow light approximation (we use all the dataset information)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "13ceea22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n",
      "\n",
      "Thanks for using AART\n",
      "Copyright (C) 2024, A. Cardenas-Avendano, H. Zhu & A. Lupsasca\n",
      "\n",
      "Computing a single image \n",
      "\n",
      "Reading file:  ./Results/LensingBands_a_0.94_i_17.h5\n",
      "Reading file:  ./Results/Rays_a_0.94_i_17.h5\n",
      "Reading inoisy file:  hotspot.h5\n",
      "AART starts!\n",
      "Using all the available inoisy frames\n",
      "Computing lensed image using all inoisy frames\n",
      "Images file  ./Results/Dynamical_Image_a_0.94_i_17.h5  created.\n",
      "CPU times: user 30.5 ms, sys: 90.3 ms, total: 121 ms\n",
      "Wall time: 3.58 s\n"
     ]
    }
   ],
   "source": [
    "%time !python iImages.py"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6ab800e",
   "metadata": {},
   "source": [
    "Now we can visualize a single snapshot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cdb05879",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading file:  ./Results/Dynamical_Image_a_0.94_i_17.h5\n"
     ]
    }
   ],
   "source": [
    "fimages=\"./Results/Dynamical_Image_a_%s_i_%s.h5\"%(spin_case,i_case)\n",
    "\n",
    "print(\"Reading file: \",fimages)\n",
    "\n",
    "h5f = h5py.File(fimages,'r')\n",
    "\n",
    "I0=h5f['bghts0'][:]\n",
    "I1=h5f['bghts1'][:]\n",
    "I2=h5f['bghts2'][:]\n",
    "\n",
    "h5f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c7589e1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2000x2000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=[5,5],dpi=400)\n",
    "\n",
    "ax.fill(hull_0i[:,0],hull_0i[:,1],color=\"k\")\n",
    "\n",
    "ax.imshow(I0+I1+I2,origin=\"lower\",cmap=\"plasma\",extent=[-lim0,lim0,-lim0,lim0])\n",
    "\n",
    "ax.set_xlim(-10,10)\n",
    "ax.set_ylim(-10,10)\n",
    "    \n",
    "ax.set_xlabel(r\"$\\alpha$\"+\" \"+\"(M)\")\n",
    "ax.set_ylabel(r\"$\\beta$\"+\" \"+\"(M)\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b90b227a",
   "metadata": {},
   "source": [
    "And now run a movie!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0a563fcb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n",
      "\n",
      "Thanks for using AART\n",
      "Copyright (C) 2024, A. Cardenas-Avendano, H. Zhu & A. Lupsasca\n",
      "\n",
      "Movies\n",
      "Reading file:  ./Results/LensingBands_a_0.94_i_17.h5\n",
      "Reading file:  ./Results/Rays_a_0.94_i_17.h5\n",
      "Reading inoisy file:  hotspot.h5\n",
      "AART starts!\n",
      "Calculating an image at time t=2.18182 (M)\n",
      "Calculating an image at time t=1.09091 (M)\n",
      "Calculating an image at time t=0.0 (M)\n",
      "Calculating an image at time t=3.27273 (M)\n",
      "Calculating an image at time t=4.36364 (M)\n",
      "Calculating an image at time t=5.45455 (M)\n",
      "Calculating an image at time t=6.54545 (M)\n",
      "Calculating an image at time t=7.63636 (M)\n",
      "Calculating an image at time t=8.72727 (M)\n",
      "Calculating an image at time t=9.81818 (M)\n",
      "Calculating an image at time t=10.90909 (M)\n",
      "Calculating an image at time t=12.0 (M)\n",
      "Images  ./Results/Images_a_0.94_i_17.h5  created.\n",
      "\n",
      "CPU times: user 82.3 ms, sys: 70.5 ms, total: 153 ms\n",
      "Wall time: 8.64 s\n"
     ]
    }
   ],
   "source": [
    "%time !python iMovies.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f8e31e21",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading file:  ./Results/Images_a_0.94_i_17.h5\n"
     ]
    }
   ],
   "source": [
    "fimages=\"./Results/Images_a_%s_i_%s.h5\"%(spin_case,i_case)\n",
    "\n",
    "print(\"Reading file: \",fimages)\n",
    "\n",
    "h5f = h5py.File(fimages,'r')\n",
    "\n",
    "Is0=h5f['bghts0'][:]\n",
    "Is1=h5f['bghts1'][:]\n",
    "Is2=h5f['bghts2'][:]\n",
    "\n",
    "h5f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c48ab256",
   "metadata": {},
   "outputs": [],
   "source": [
    "VMAX=np.max(Is0+Is1+Is2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a60dcde",
   "metadata": {},
   "source": [
    "We can still visualize a single snapshot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "514dc3b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\beta$ (M)')"
      ]
     },
     "execution_count": 20,
     "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": [
    "tsnap=0\n",
    "\n",
    "plt.fill(hull_0i[:,0],hull_0i[:,1],color=\"k\")\n",
    "\n",
    "plt.imshow(Is0[tsnap,:,:]+Is1[tsnap,:,:]+Is2[tsnap,:,:],vmax=VMAX,origin=\"lower\",cmap=\"plasma\",extent=[-lim0,lim0,-lim0,lim0])\n",
    "\n",
    "plt.xlim(-10,10)\n",
    "plt.ylim(-10,10)\n",
    "    \n",
    "plt.xlabel(r\"$\\alpha$\"+\" \"+\"(M)\")\n",
    "plt.ylabel(r\"$\\beta$\"+\" \"+\"(M)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9f300f48",
   "metadata": {},
   "outputs": [],
   "source": [
    "fignames=[]\n",
    "for tsnap in np.arange(snapshots)[::-1]:\n",
    "    fig, ax = plt.subplots()\n",
    "    \n",
    "    \n",
    "    ax.fill(hull_0i[:,0],hull_0i[:,1],color=\"k\")\n",
    "    \n",
    "    ax.imshow(Is0[tsnap,:,:]+Is1[tsnap,:,:]+Is2[tsnap,:,:],vmax=VMAX,origin=\"lower\",cmap=\"plasma\",extent=[-lim0,lim0,-lim0,lim0])\n",
    "    ax.set_xlim(-10,10)\n",
    "    ax.set_ylim(-10,10)\n",
    "    \n",
    "    ax.set_xlabel(r\"$\\alpha$\"+\" \"+\"(M)\")\n",
    "    ax.set_ylabel(r\"$\\beta$\"+\" \"+\"(M)\")\n",
    "    \n",
    "    fignames.append('Fig%s.png'%tsnap)\n",
    "    plt.savefig('Fig%s.png'%tsnap,dpi=400,bbox_inches='tight')\n",
    "    plt.close(fig)\n",
    "\n",
    "with imageio.get_writer('HotSpotMovie.gif', mode='I') as writer:\n",
    "    for filename in fignames:\n",
    "        image = imageio.imread(filename)\n",
    "        writer.append_data(image)\n",
    "\n",
    "# We delete the created images and just keep the GIF\n",
    "for filename in set(fignames):\n",
    "    os.remove(filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4324c2bf",
   "metadata": {},
   "source": [
    "## License\n",
    "\n",
    "MIT license\n",
    "\n",
    "Permission is hereby granted, free of charge, to any person obtaining a copy of this \n",
    "software and associated documentation files (the \"Software\"), to deal in the Software \n",
    "without restriction, including without limitation the rights to use, copy, modify, merge, \n",
    "publish, distribute, sublicense, and/or sell copies of the Software, and to permit \n",
    "persons to whom the Software is furnished to do so, subject to the following conditions:\n",
    "\n",
    "The above copyright notice and this permission notice shall be included in all copies \n",
    "or substantial portions of the Software.\n",
    "\n",
    "THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, \n",
    "INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR \n",
    "PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE \n",
    "FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, \n",
    "ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN \n",
    "THE SOFTWARE."
   ]
  }
 ],
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