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    "# Interactive Mandelbrot Set\n",
    "\n",
    "Mandelbrot Set is a fractal, which is self-similar. If you zoom in on a fractal object it will look similar, (possibly rotated), or exactly like the original shape. \n",
    "\n",
    "\n",
    "There are many other known  <a href=\"https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension\"> fractals </a>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b96de77a",
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   "source": [
    "from numpy import * # because arrays are defined in numpy\n",
    "from numba import njit  # This is the new line with numba\n",
    "from numba import prange\n",
    "\n",
    "@njit   # this is an alias for @jit(nopython=True)\n",
    "def Mand(z0, max_steps):\n",
    "    z = 0j  # no need to specify type. \n",
    "    # To initialize to complex number, just assign 0j==i*0\n",
    "    for itr in range(max_steps):\n",
    "        if abs(z)>2:\n",
    "            return itr\n",
    "        z = z*z + z0\n",
    "    return max_steps\n",
    "\n",
    "@njit(parallel=True)\n",
    "def Mandelbrot3(data, ext, max_steps):\n",
    "    \"\"\"\n",
    "    ext[4]    -- array of 4 values [min_x,max_x,min_y,max_y]\n",
    "    Nxy       -- int number of points in x and y direction\n",
    "    max_steps -- how many steps we will try at most before we conclude the point is in the set\n",
    "    \"\"\"\n",
    "    Nx,Ny = shape(data) # 2D array should be already allocated we get its size\n",
    "    for i in range(Nx):\n",
    "        for j in prange(Ny):    # note that we used prange instead of range.\n",
    "                                # this switches off parallelization of this loop, so that\n",
    "                                # only the outside loop over i is parallelized.\n",
    "            x = ext[0] + (ext[1]-ext[0])*i/(Nx-1.)\n",
    "            y = ext[2] + (ext[3]-ext[2])*j/(Ny-1.)\n",
    "            # creating complex number of the fly\n",
    "            data[i,j] = Mand(x + y*1j, max_steps)  \n",
    "# data now contains integers. \n",
    "# MandelbrotSet has value 1000, and points not in the set have value <1000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b50cb479",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: MacOSX\n"
     ]
    }
   ],
   "source": [
    "%matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "#from pylab import *    # plotting library\n",
    "# don't use \"%matplotlib inline\"\n",
    "\n",
    "def ax_update(ax):  # actual plotting routine\n",
    "    ax.set_autoscale_on(False) # Otherwise, infinite loop\n",
    "    # Get the range for the new area\n",
    "    xstart, ystart, xdelta, ydelta = ax.viewLim.bounds\n",
    "    xend = xstart + xdelta\n",
    "    yend = ystart + ydelta\n",
    "    ext=array([xstart,xend,ystart,yend])\n",
    "    Mandelbrot3(data, ext, 1000) # actually producing new fractal\n",
    "    \n",
    "    # Update the image object with our new data and extent\n",
    "    im = ax.images[-1]  # take the latest object\n",
    "    im.set_data(-log(data.T))   # update it with new data\n",
    "    im.set_extent(ext)           # change the extent\n",
    "    ax.figure.canvas.draw_idle() # finally redraw\n",
    "\n",
    "\n",
    "data = zeros((1000,1000))\n",
    "ext=[-2,1,-1,1]\n",
    "Mandelbrot3(data, array(ext), 1000)\n",
    "fig,ax = plt.subplots(1,1)\n",
    "ax.imshow(-log(data.T), extent=ext, aspect='equal',origin='lower',cmap=cm.hot)\n",
    "    \n",
    "ax.callbacks.connect('xlim_changed', ax_update)\n",
    "ax.callbacks.connect('ylim_changed', ax_update)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "22f92109",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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