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   "source": [
    "from vpython import *\n",
    "from numpy import arange, clip\n",
    "\n",
    "# David Scherer\n",
    "\n",
    "scene.caption = \"\"\"Right button drag or Ctrl-drag to rotate \"camera\" to view scene.\n",
    "Middle button to drag or Alt-drag to zoom in or out.\n",
    "  On a two-button mouse, middle is left + right.\"\"\"\n",
    "scene.title = \"Lorenz differential equation\"\n",
    "scene.center = vector(25,0,0)\n",
    "scene.background = color.white\n",
    "scene.forward = vector(0,-.2,-1)\n",
    "scene.range = 35\n",
    "\n",
    "lorenz = curve( color = color.black, radius=0.3 )\n",
    "\n",
    "# Draw grid\n",
    "for x in arange(0,51,10):\n",
    "    box(pos=vector(x,0,0), axis=vector(0,0,50), height=0.4, width=0.4, color=color.gray(0.6) )\n",
    "for z in arange(-25,26,10):\n",
    "    box(pos=vector(25,0,z), axis=vector(50,0,0), height=0.4, width=0., color=color.gray(0.6) )\n",
    "\n",
    "dt = 0.01\n",
    "y = vector(35, -10, -7)\n",
    "\n",
    "for t in arange(0,10,dt):\n",
    "    # Integrate a funny differential equation\n",
    "    dydt = vector( - 8.0/3*y.x           +   y.y*y.z,\n",
    "                              - 10*y.y +   10*y.z,\n",
    "                 -  y.y*y.x +   28*y.y -   y.z );\n",
    "    y = y + dydt*dt\n",
    "\n",
    "    # Draw lines colored by speed\n",
    "    c = clip( [mag(dydt) * 0.005], 0, 1 )[0]\n",
    "\n",
    "    lorenz.append( pos=y, color=vector(c,0, 1-c) )\n",
    "\n",
    "    rate( 500 )"
   ]
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