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    "<center><h2>Sierpinski Gasket</h2></center>\n",
    "<p>\n",
    "    The fractal \"Sierpinski Gasket\"  is generated according to the rules:  \n",
    "<ol>\n",
    "<li>\n",
    "Draw an equilateral triangle with:\n",
    "$\n",
    "\\mbox{vertex } 1\\colon (a_1,b_1);\\enspace \\mbox{vertex } 2\\colon\n",
    "(a_2,b_2);\\enspace \\mbox{vertex } 3\\colon (a_3,b_3).\n",
    "$\n",
    "    </li>\n",
    "<li>Place a dot at random point $P=(x_0,y_0)$ within this\n",
    "triangle.</li>\n",
    "<li>Find next point by randomly selecting  either $1$,\n",
    "$2$, or $3$:\n",
    "    </li>\n",
    "<ol>\n",
    "    <li> If $1$, place a dot halfway between $P$ and vertex 1.</li>\n",
    "\n",
    "<li> If $2$, place a dot halfway between $P$ and vertex 2.</li>\n",
    "\n",
    "<li> If $3$, place a dot halfway between $P$ and vertex 3.</li>\n",
    "</ol>\n",
    "<li>Repeat the process using the last dot as the new $P$.</li>\n",
    "</ol>"
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    "\"\"\" From \"COMPUTATIONAL PHYSICS\" & \"COMPUTER PROBLEMS in PHYSICS\"\n",
    "    by RH Landau, MJ Paez, and CC Bordeianu (deceased)\n",
    "    Copyright R Landau, Oregon State Unv, MJ Paez, Univ Antioquia, \n",
    "    C Bordeianu, Univ Bucharest, 2020. \n",
    "    Please respect copyright & acknowledge our work.\"\"\"\n",
    "\n",
    "# Sierpin.py:            Sierpinski gasket\n",
    "\n",
    "from vpython import * \n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "imax = 15000\n",
    "i  = 0\n",
    "a1 = - 0.5             #                 (a3, b3)\n",
    "b1 = - 0.433           #                   /\\\n",
    "a2 = 0.5               #                  /  \\\n",
    "b2 = - 0.433           #                 /    \\\n",
    "a3 = 0.0               #                /      \\\n",
    "b3 = 0.433             #               /________\\\n",
    "x  = 0.0               #      (a1, b1)           (a2, b2)\n",
    "y  = 0.3               # \n",
    "graph1 = display(width = 500, height = 500, title = 'Sierpinski Gasket', \n",
    "                 range = 0.5, background = vec(0.87, 0.93, 0.87) )\n",
    "\n",
    "for i in range(1, imax):\n",
    "    r = random.random();\n",
    "    if (r <= 1.0/3.0):\n",
    "         x = 0.5 * (x + a1)\n",
    "         y = 0.5 * (y + b1)\n",
    "    else:\n",
    "        if( r > 1.0/3.0 and r <= 2.0/3.0):\n",
    "             x = 0.5*(x + a2)\n",
    "             y = 0.5*(y + b2)\n",
    "        else:\n",
    "            x = 0.5 * (x + a3)\n",
    "            y = 0.5 * (y + b3)\n",
    "    xc = x\n",
    "    yc = y\n",
    "    curve(pos = [vec(xc,yc,0), vec(xc+0.002, yc,0)], color=color.red)  # Thin line"
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