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    "<center><h2>Lossless Transmission Line Vpython</h2></center>\n",
    "<p>\n",
    " The telegraph equation describing lossles propagation on a \n",
    " transmission line is solved and visualized with Vpython:\n",
    " \n",
    " $$\n",
    "\\frac{\\partial^2 V}{\\partial t^2}-v_p^2\\frac{\\partial^2 V}{\\partial x^2}=0, \\quad v_p= \\frac{1}{\\sqrt{LC}}.\n",
    "$$ "
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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, 2017. \n",
    "    Please respect copyright & acknowledge our work.\"\"\"\n",
    "   \n",
    "# TelegraphViz.py:  Lossless transmission line animation, Vpython\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "from vpython import *\n",
    "import numpy as np\n",
    "\n",
    "g = display(width = 600, height = 300, title='Telegrapher`s Eqnt')\n",
    "vibst = curve(x=list(range(0,101)), color=color.yellow,radius=0.5)\n",
    "L = 0.1; C = 2.5; c = 1/sqrt(L*C); dt = 0.025; dx = 0.05 \n",
    "R = (c*dt/dx)**2                       # R  = 1 for stabiity\n",
    "V = np.zeros( (101, 3), float)                  # Declare array\n",
    "xx = 0\n",
    "\n",
    "for i in arange (0,100):\n",
    "    V[i,0] =  10*exp(-(xx**2)/0.1)   \n",
    "    xx = xx+dx    \n",
    "for i in range(1, 100):   V[i, 2] = V[i,0] + R*(V[i+1,1] + V[i-1,1] - 2*V[i,1])\n",
    "    \n",
    "rate(100)\n",
    "vibst.visible=True\n",
    "V[: ,0] = V[: ,1];  V[: ,1] = V[: ,2]            # Recycle array#\n",
    "   \n",
    "for j in range(0,250):\n",
    "    rate(20)                        # Delay plot, large = slow\n",
    "    vibst.clear()\n",
    "    for i in range(1, 100):   \n",
    "        V[i, 2] = 2.*V[i,1]-V[i,0]+R*(V[i+1,1]+V[i-1,1]-2*V[i,1])\n",
    "        vibst.append(pos=vec( 2.*i - 100.0 , V[i, 2],0))\n",
    "        vibst.visible=True\n",
    "    V[: ,0] = V[: ,1]; V[: ,1] = V[: ,2]          # Recycle array"
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