diff --git a/02_Discrete_Bayes.ipynb b/02_Discrete_Bayes.ipynb
index f3e5b33..02f6f4d 100644
--- a/02_Discrete_Bayes.ipynb
+++ b/02_Discrete_Bayes.ipynb
@@ -252,10 +252,13 @@
    "source": [
     "#format the book\n",
     "%matplotlib inline\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2\n",
+    "\n",
     "from __future__ import division, print_function\n",
     "import matplotlib.pyplot as plt\n",
-    "import book_format\n",
-    "book_format.load_style()"
+    "from book_format import load_style, figsize, set_figsize\n",
+    "load_style()"
    ]
   },
   {
@@ -288,9 +291,9 @@
     "\n",
     "To keep the problem small, we will assume that there are only 10 positions in a single hallway to consider, which we will number 0 to 9, where 1 is to the right of 0, 2 is to the right of 1, and so on. For reasons that will be clear later, we will also assume that the hallway is circular or rectangular. If you move right from position 9, you will be at position 0.  \n",
     "\n",
-    "When I begin listening to the sensor I have no reason to believe that Simon is at any particular position in the hallway. He is equally likely to be in any position. The probability that he is in each position is therefore 1/10. \n",
+    "When I begin listening to the sensor I have no reason to believe that Simon is at any particular position in the hallway. He is equally likely to be in any position. Their are 10 positions, so the probability that he is in any given position is 1/10. \n",
     "\n",
-    "Let us represent our belief of his position at any time in a NumPy array."
+    "Let's represent our belief of his position at any time in a NumPy array."
    ]
   },
   {
@@ -328,7 +331,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "So I start listening to Simon's transmissions on the network, and the first data I get from the sensor is \"door\". From this I conclude that he is in front of a door, but which one? I have no idea. I have no reason to believe is in front of the first, second, or third door. But what I can do is assign a probability to each door. All doors are equally likely, so I assign a probability of 1/3 to each door. "
+    "So I start listening to Simon's transmissions on the network, and the first data I get from the sensor is \"door\". From this I conclude that he is in front of a door, but which one? I have no idea. I have no reason to believe he is is in front of the first, second, or third door. But what I can do is assign a probability to each door. All doors are equally likely, and there are three of them, so I assign a probability of 1/3 to each door. "
    ]
   },
   {
@@ -341,150 +344,133 @@
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+       "VV5ebndZAYVL8VnWvHnzrJiYGGvYsGHWmDFjrPvvv986dOiQ3WXZaseOHVZKSoo1YsQIKykpydq0\n",
+       "aZPdJdlu9+7dVnBwsFVbW2t3KQHhiy++sH72s59Z8fHxlsPhsBITE62nnnrKOnv2rN2l2Wrbtm3W\n",
+       "jTfeaA0fPtyKjo62li5dap06dcrusvqM258DAAAAhgz6c64BAACA/kK4BgAAAAwhXAMAAACGEK4B\n",
+       "AAAAQwjXAAAAgCGEawAAAMAQwjUAAABgCOEaAAAAMIRwDQAAABjyv5O4m5JqfGQjAAAAAElFTkSu\n",
+       "QmCC\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6a80b38>"
+       "<matplotlib.figure.Figure at 0x6b16ba8>"
       ]
      },
      "metadata": {},
@@ -498,6 +484,8 @@
     "import numpy as np\n",
     "\n",
     "pos_belief = np.array([1./3, 1./3, 0, 0, 0, 0, 0, 0, 1./3, 0])\n",
+    "\n",
+    "set_figsize(y=3)\n",
     "bp.bar_plot(pos_belief)"
    ]
   },
@@ -619,152 +607,134 @@
     {
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+       "WgEBAVZAQIAVGBjY9TozM9Pu0mzz7V6c/bNs2TK7S7PN3LlzrTFjxljDhw+3IiIirNtvv90qLy+3\n",
+       "uyy/wq34LGvWrFlWdHS0NWzYMGv06NHWvffea+3fv9/usmy1detWKzk52RoxYoSVmJhorV+/3u6S\n",
+       "bLdjxw4rMDDQqq2ttbsUv/Dll19av/rVr6y4uDjL4XBYCQkJ1pNPPmmdOnXK7tJstXnzZuvaa6+1\n",
+       "hg8fbkVFRVkLFy60jh8/bndZ/cbjzwEAAABDLvk91wAAAMBAIVwDAAAAhhCuAQAAAEMI1wAAAIAh\n",
+       "hGsAAADAEMI1AAAAYAjhGgAAADCEcA0AAAAYQrgGAAAADPk/8V36YlZV3tsAAAAASUVORK5CYII=\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6ac1278>"
+       "<matplotlib.figure.Figure at 0x6bc16a0>"
       ]
      },
      "metadata": {},
@@ -772,7 +742,7 @@
     }
    ],
    "source": [
-    "def update(pos_belief, measure, p_hit, p_miss):\n",
+    "def update(hallway, pos_belief, measure, p_hit, p_miss):\n",
     "    for i in range(len(hallway)):\n",
     "        if hallway[i] == measure:\n",
     "            pos_belief[i] *= p_hit\n",
@@ -781,7 +751,7 @@
     "\n",
     "pos_belief = np.array([0.2] * 10)\n",
     "reading = 1 # 1 is 'door'\n",
-    "update(pos_belief, 1, .6, .2)\n",
+    "update(hallway, pos_belief, 1, .6, .2)\n",
     "\n",
     "print(pos_belief)\n",
     "print('sum =', sum(pos_belief))\n",
@@ -797,7 +767,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
@@ -814,152 +784,134 @@
     {
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+       "/OUvrbi4OMvhcFgJCQnWk08+aZ05c8bu0my1detW68Ybb7SGDx9uRUVFWUuWLLFOnjxpd1n9xuPP\n",
+       "AQAAAEOu+D3XAAAAwEAhXAMAAACGEK4BAAAAQwjXAAAAgCGEawAAAMAQwjUAAABgCOEaAAAAMIRw\n",
+       "DQAAABhCuAYAAAAM+X9QtfQM34Hr6AAAAABJRU5ErkJggg==\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x749b208>"
+       "<matplotlib.figure.Figure at 0x73d8a20>"
       ]
      },
      "metadata": {},
@@ -967,7 +919,7 @@
     }
    ],
    "source": [
-    "def update(pos_belief, measure, p_hit, p_miss):\n",
+    "def update(hallway, pos_belief, measure, p_hit, p_miss):\n",
     "    for i in range(len(hallway)):\n",
     "        if hallway[i] == measure:\n",
     "            pos_belief[i] *= p_hit\n",
@@ -978,7 +930,7 @@
     "\n",
     "pos_belief = np.array([0.2] * 10)\n",
     "reading = 1 # 1 is 'door'\n",
-    "update(pos_belief, 1, .6, .2)\n",
+    "update(hallway, pos_belief, 1, .6, .2)\n",
     "\n",
     "print('sum =', sum(pos_belief))\n",
     "print('probability of door =', pos_belief[0])\n",
@@ -1015,7 +967,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -1031,177 +983,159 @@
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       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6be1ef0>"
+       "<matplotlib.figure.Figure at 0x77e50b8>"
       ]
      },
      "metadata": {},
@@ -1256,7 +1190,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
@@ -1271,141 +1205,125 @@
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       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6c43e48>"
+       "<matplotlib.figure.Figure at 0x72eac18>"
       ]
      },
      "metadata": {},
@@ -1438,7 +1356,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1454,142 +1372,126 @@
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       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6bcb940>"
+       "<matplotlib.figure.Figure at 0x73caf28>"
       ]
      },
      "metadata": {},
@@ -1614,7 +1516,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
@@ -1622,142 +1524,126 @@
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       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6c51ef0>"
+       "<matplotlib.figure.Figure at 0x73cac18>"
       ]
      },
      "metadata": {},
@@ -1777,7 +1663,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
@@ -1792,151 +1678,133 @@
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+       "bXdptvl6L778s3LlSrtLs82CBQuscePGWcOHD7dGjx5t3XbbbVZlZaXdZQUVbsVnWXPnzrViY2Ot\n",
+       "YcOGWWPHjrXuuece69ChQ3aXZasdO3ZYqamp1ogRI6zk5GRr06ZNdpdku927d1uhoaFWfX293aUE\n",
+       "hc8++8z65S9/aSUkJFgOh8NKSkqyHn/8cevMmTN2l2arbdu2Wddee601fPhwKyYmxlqyZIl18uRJ\n",
+       "u8vqNx5/DgAAABhyye+5BgAAAAYK4RoAAAAwhHANAAAAGEK4BgAAAAwhXAMAAACGEK4BAAAAQwjX\n",
+       "AAAAgCGEawAAAMAQwjUAAABgyP8DiED2PiJDenEAAAAASUVORK5CYII=\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6aac7f0>"
+       "<matplotlib.figure.Figure at 0x72d95f8>"
       ]
      },
      "metadata": {},
@@ -1989,7 +1857,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
@@ -2004,13 +1872,13 @@
    ],
    "source": [
     "pos_belief = np.array([.1] * 10)\n",
-    "update(pos_belief, 1, .6, .2)\n",
+    "update(hallway, pos_belief, 1, .6, .2)\n",
     "print(pos_belief)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
@@ -2025,152 +1893,134 @@
     {
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       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6aacd68>"
+       "<matplotlib.figure.Figure at 0x6bc0940>"
       ]
      },
      "metadata": {},
@@ -2192,7 +2042,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
@@ -2207,154 +2057,135 @@
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       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6b2cc88>"
+       "<matplotlib.figure.Figure at 0x780e588>"
       ]
      },
      "metadata": {},
@@ -2362,7 +2193,7 @@
     }
    ],
    "source": [
-    "update(pos_belief, 1, .6, .2)\n",
+    "update(hallway, pos_belief, 1, .6, .2)\n",
     "print(pos_belief)\n",
     "bp.bar_plot(pos_belief)"
    ]
@@ -2376,7 +2207,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
    "metadata": {
     "collapsed": false
    },
@@ -2384,154 +2215,136 @@
     {
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+       "WD//+c+t2NhYy+FwWPHx8dYTTzxhnTlzxu7SbLVt2zbr+uuvt4KCgqzIyEhr6dKl1qlTp+wua8C4\n",
+       "/TkAAABgyGW/5hoAAAAYKoRrAAAAwBDCNQAAAGAI4RoAAAAwhHANAAAAGEK4BgAAAAwhXAMAAACG\n",
+       "EK4BAAAAQwjXAAAAgCH/B3pyCq6hZg7wAAAAAElFTkSuQmCC\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x75c8eb8>"
+       "<matplotlib.figure.Figure at 0x73ca550>"
       ]
      },
      "metadata": {},
@@ -2540,7 +2353,7 @@
    ],
    "source": [
     "predict(pos_belief, 1, .8, .1, .1)\n",
-    "update(pos_belief, 0, .6, .2)\n",
+    "update(hallway, pos_belief, 0, .6, .2)\n",
     "bp.bar_plot(pos_belief)"
    ]
   },
@@ -2553,7 +2366,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false
    },
@@ -2561,155 +2374,136 @@
     {
      "data": {
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+       "is+yFixYYEVERFijRo2yxo0bZ913333WkSNH7C7LVrt27bISEhKs0aNHW3FxcdaWLVvsLsl2e/fu\n",
+       "tXx9fa2amhq7S/EKX3zxhfXzn//cio6OthwOhxUbG2s98cQT1tmzZ+0uzVY7duywbrjhBisgIMAK\n",
+       "Dw+3li9fbp05c8busgaMx58DAAAAhgz7PdcAAADAYCFcAwAAAIYQrgEAAABDCNcAAACAIYRrAAAA\n",
+       "wBDCNQAAAGAI4RoAAAAwhHANAAAAGEK4BgAAAAz5P8inCNIrsxwuAAAAAElFTkSuQmCC\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x74d9208>"
+       "<matplotlib.figure.Figure at 0x7552550>"
       ]
      },
      "metadata": {},
@@ -2718,7 +2512,7 @@
    ],
    "source": [
     "predict(pos_belief, 1, .8, .1, .1)\n",
-    "update(pos_belief, 0, .6, .2)\n",
+    "update(hallway, pos_belief, 0, .6, .2)\n",
     "bp.bar_plot(pos_belief)"
    ]
   },
@@ -2755,7 +2549,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false
    },
@@ -2770,153 +2564,135 @@
     {
      "data": {
       "image/png": [
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+       "/1avXm13abZZtGiRNWHCBGv06NFWRESEddttt1mVlZV2l+VXuBWfZc2fP9+Kjo62Ro0aZY0fP966\n",
+       "5557rIMHD9pdlq127NhhJScnW2PGjLESExOtzZs3212S7Xbv3m0FBgZa9fX1dpfiF7744gvrF7/4\n",
+       "hRUXF2c5HA4rISHBeuKJJ6zTp0/bXZqttm3bZl177bXW6NGjraioKGvZsmXWiRMn7C5rwHj8OQAA\n",
+       "AGDIsL/mGgAAABgshGsAAADAEMI1AAAAYAjhGgAAADCEcA0AAAAYQrgGAAAADCFcAwAAAIYQrgEA\n",
+       "AABDCNcAAACAIf8Hla8BCkseigwAAAAASUVORK5CYII=\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6c9cc88>"
+       "<matplotlib.figure.Figure at 0x7460828>"
       ]
      },
      "metadata": {},
@@ -2929,7 +2705,7 @@
     "measurements = [1, 0, 1, 0, 0]\n",
     "\n",
     "for m in measurements:\n",
-    "    update(pos_belief, m, .6, .2)\n",
+    "    update(hallway, pos_belief, m, .6, .2)\n",
     "    predict(pos_belief, 1, .8, .1, .1)\n",
     "bp.bar_plot(pos_belief)\n",
     "print(pos_belief)"
@@ -2944,7 +2720,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "metadata": {
     "collapsed": false
    },
@@ -2952,152 +2728,134 @@
     {
      "data": {
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+       "Ki8vt7usgMKt+Cxr7ty5VnR0tDV8+HBr7Nix1n333WcdOnTI7rJstWPHDis5OdkaOXKklZiYaG3a\n",
+       "tMnukmy3e/duKzg42KqtrbW7lIDw+eefWz//+c+tuLg4y+FwWAkJCdaTTz5pnT171u7SbLVt2zbr\n",
+       "+uuvt0aMGGFFRUVZS5YssU6dOmV3WX3G488BAAAAQwb9nmsAAACgvxCuAQAAAEMI1wAAAIAhhGsA\n",
+       "AADAEMI1AAAAYAjhGgAAADCEcA0AAAAYQrgGAAAADCFcAwAAAIb8H46f8sXbMZnbAAAAAElFTkSu\n",
+       "QmCC\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6b34c18>"
+       "<matplotlib.figure.Figure at 0x74df2b0>"
       ]
      },
      "metadata": {},
@@ -3105,7 +2863,7 @@
     }
    ],
    "source": [
-    "update(pos_belief, m, .6, .2)\n",
+    "update(hallway, pos_belief, m, .6, .2)\n",
     "predict(pos_belief, 1, .8, .1, .1)\n",
     "bp.bar_plot(pos_belief)"
    ]
@@ -3119,7 +2877,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 24,
    "metadata": {
     "collapsed": false
    },
@@ -3128,463 +2886,466 @@
      "data": {
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+       "Hx8fb/Pad9Zs+Fq+fLnNa8+YMUOCg4PF1dVVfH195bHHHtMseEXUPaFx6tSpEhgYKC4uLhIUFCQT\n",
+       "J06U4uJiVWqLiOzevVvCw8PFzc1N+vXrJ+vWrVOtdm5urjg4OKhy7OXtrl+/LgsXLpSQkBBxd3eX\n",
+       "sLAw+fOf/yw3btxQbQ7bt2+X3r17i6urqwQEBMj8+fPl6tWrqtW3Z1rku71mu4j95rvW2S7CfNci\n",
+       "39XOdt7+nIiIiIhIIe3imGsiIiIiovaAi2siIiIiIoVwcU1EREREpBAuromIiIiIFMLFNRERERGR\n",
+       "Qri4JiIiIiJSCBfXREREREQK4eKaiIiIiEghXFwTERERESnk/wF6xhwA6ik7QQAAAABJRU5ErkJg\n",
+       "gg==\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6aec048>"
+       "<matplotlib.figure.Figure at 0x7baa7f0>"
       ]
      },
      "metadata": {},
@@ -3592,13 +3353,14 @@
     }
    ],
    "source": [
-    "measurements = [0, 1, 0, 1, 0, 0]\n",
+    "with figsize(y=5.5):\n",
+    "    measurements = [0, 1, 0, 1, 0, 0]\n",
     "\n",
-    "for i, m in enumerate(measurements):\n",
-    "    update(pos_belief, m, .6, .2)\n",
-    "    predict(pos_belief, 1, .8, .1, .1)\n",
-    "    plt.subplot(3, 2, i+1)\n",
-    "    bp.bar_plot(pos_belief, title='step{}'.format(i+1))"
+    "    for i, m in enumerate(measurements):\n",
+    "        update(hallway, pos_belief, m, .6, .2)\n",
+    "        predict(pos_belief, 1, .8, .1, .1)\n",
+    "        plt.subplot(3, 2, i+1)\n",
+    "        bp.bar_plot(pos_belief, title='step{}'.format(i+1))"
    ]
   },
   {
@@ -3634,7 +3396,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 25,
    "metadata": {
     "collapsed": false
    },
@@ -3642,153 +3404,135 @@
     {
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       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6b9f898>"
+       "<matplotlib.figure.Figure at 0x6b515c0>"
       ]
      },
      "metadata": {},
@@ -3814,12 +3558,722 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Generalizing to Multiple Dimensions"
+    "## Tracking and Control\n",
+    "\n",
+    "So far we have been tracking an object which is moving independently. But consider this very similar problem. I am automating a warehouse and want to use robots to collect all of the items for a customer's order. Perhaps the easiest way to do this is to have the robots travel on a train track. I want to be able to send the robot a destination and have it go correctly to that point. But train tracks and robot motors are imperfect. Wheel slippage and imperfect motors means that the robot is unlikely to travel to exactly the position you command. \n",
+    "\n",
+    "So, we add sensors. Our budget is limited, and Hall sensors are cheap (they detect when proximity to magnets), so we line the track with magnets in some non-uniform pattern and put a cheap Hall sensor on the robot. You already see where this is going. The hall sensor reports whether the robot is near a magnet or not, and using the code above we can determine the position of our robot.\n",
+    "\n",
+    "But we are not done. A key lesson from the g-h filters chapter is to never throw information away. If you have information you should use it to improve your knowledge. What information are we leaving out? Well, we know what our destination is, and we know what control inputs we are feeding to the wheels of the robot at each moment in time. For example, let's say that once a second we send a movement command to the robot - move left 1 unit, move right 1 unit, or stand still. This is obviously a simplification because I am not taking acceleration into account, but I am not trying to teach control theory here. If I send the command 'move left 1 unit' I expect that in one second from now the robot will be 1 unit to the left of where it is now. But, wheels and motors are imperfect. We will assume that it never makes a mistake and goes right when told to go left, so the errors should be relatively small. Thus the robot might end up 0.9 units away, or maybe 1.2 units away. \n",
+    "\n",
+    "Now the entire solution is clear. For the dog which was moving independently we assumed that he kept moving in whatever direction he was previously moving. That is a dubious assumption for my dog! Robots are far more predictable. Instead of feeding in a dubious prediction based on assumption of behavior we will feed in the command that we sent to the robot! "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
+   "source": [
+    "### Simulating the Train Behavior\n",
+    "\n",
+    "To fully implement this filter we need to simulate an imperfect train. When we command it to move it will sometimes make a small mistake, and it's sensor will sometimes return the incorrect value."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 191,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import random\n",
+    "\n",
+    "class Train(object):\n",
+    "    \n",
+    "    def __init__(self, track, move_error=.1, sense_error=.1, no_sense_error=.05):\n",
+    "        self.track = track \n",
+    "        self.pos = 0\n",
+    "        self.move_error = move_error\n",
+    "        self.sense_error = sense_error\n",
+    "        self.no_sense_error = no_sense_error\n",
+    "        \n",
+    "        \n",
+    "    def move(self, distance=1, left=True):\n",
+    "        \"\"\" move in the specified direction with some small chance of error\"\"\"\n",
+    "        if left:\n",
+    "            self.pos -= distance\n",
+    "        else:\n",
+    "            self.pos += distance\n",
+    "            \n",
+    "        # insert random movement error\n",
+    "        r = random.random()\n",
+    "        if r < self.move_error:\n",
+    "            self.pos -= 1\n",
+    "        elif r > 1 - self.move_error:\n",
+    "            self.pos += 1\n",
+    "            \n",
+    "        self.pos = self.pos % len(track)\n",
+    "        return self.pos\n",
+    "    \n",
+    "    def sense(self):\n",
+    "        at_magnet = (self.track[self.pos] == 1)\n",
+    "        \n",
+    "         # insert random sensor error\n",
+    "        r = random.random()\n",
+    "        \n",
+    "        if at_magnet:\n",
+    "            if r < self.sense_error:\n",
+    "                at_magnet = False\n",
+    "                print('sense error')\n",
+    "        else:\n",
+    "            if r < self.no_sense_error:\n",
+    "                at_magnet = True\n",
+    "                print('sense error')\n",
+    "        return at_magnet"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "With that we are ready to write the simulation. We will put it in a function so that we can run it with different assumptions. I will assume that the robot always starts at the beginning of the track. The track is implemented as being only 10 units long, but this could just represent a track of length, say 10,000, with the magnet pattern repeated every 10 units. I set the magnet pattern to first have a gap of 1 unit, then 2 units, then 3 units to help the algorithm distinguish where the robot is. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 218,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def simulate(iterations, move_error, sense_error, \n",
+    "             no_sense_error, move_distance,\n",
+    "             do_print=True):\n",
+    "    track = [True, False, True, False, False,\n",
+    "             True, False, False, False, True]\n",
+    "\n",
+    "    pos_belief = np.array([0.01] * 10)\n",
+    "    pos_belief[0] = .9\n",
+    "    \n",
+    "    p_correct = 1 - move_error\n",
+    "\n",
+    "    robot = Train(track, move_error, sense_error, no_sense_error)\n",
+    "\n",
+    "    for i in range(iterations):\n",
+    "        robot.move(distance=move_distance, left=False)\n",
+    "        m = robot.sense()\n",
+    "        if do_print:\n",
+    "            print('time {}: pos {}, sense {}, at magnet {}'.format(\n",
+    "                    i, robot.pos, m, track[robot.pos]))\n",
+    "\n",
+    "        predict(pos_belief, move_distance, p_correct, move_error/2., move_error/2.)       \n",
+    "        if do_print:\n",
+    "            print('    predict', pos_belief)\n",
+    "\n",
+    "        update(track, pos_belief, m, 1. - sense_error, no_sense_error)\n",
+    "        if do_print:\n",
+    "            print('    update ', pos_belief)\n",
+    "        ind = np.argmax(pos_belief)\n",
+    "        print('    predicted position is {} with confidence {:.4}%:'.format(\n",
+    "                ind, pos_belief[ind]*100))\n",
+    "\n",
+    "            \n",
+    "    bp.bar_plot(pos_belief)\n",
+    "    print()\n",
+    "    print('final position is    :', robot.pos)\n",
+    "    i = np.argmax(pos_belief)\n",
+    "    print('predicted position is {} with confidence {:.4}%:'.format(\n",
+    "            i, pos_belief[i]*100))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Read the code and make sure you understand it. Now let's do a run with no sensor or movement error. If the code is correct it should be able to locate the robot with no error. The output is a bit tedious to read, but if you are at all unsure of how the update/predict cycle works make sure you read through it carefully to solidify your understanding."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 219,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "time 0: pos 1, sense False, at magnet False\n",
+      "    predict [ 0.05  0.81  0.05  0.01  0.01  0.01  0.01  0.01  0.01  0.01]\n",
+      "    update  [ 0.    0.93  0.    0.01  0.01  0.    0.01  0.01  0.01  0.  ]\n",
+      "    predicted position is 1 with confidence 93.42%:\n",
+      "time 1: pos 2, sense True, at magnet True\n",
+      "    predict [ 0.    0.05  0.84  0.05  0.01  0.01  0.    0.01  0.01  0.01]\n",
+      "    update  [ 0.    0.    0.96  0.    0.    0.01  0.    0.    0.    0.01]\n",
+      "    predicted position is 2 with confidence 96.47%:\n",
+      "time 2: pos 3, sense False, at magnet False\n",
+      "    predict [ 0.01  0.    0.05  0.87  0.05  0.    0.01  0.    0.    0.  ]\n",
+      "    update  [ 0.    0.    0.    0.93  0.05  0.    0.01  0.    0.    0.  ]\n",
+      "    predicted position is 3 with confidence 92.57%:\n",
+      "time 3: pos 3, sense False, at magnet False\n",
+      "    predict [ 0.    0.    0.    0.05  0.84  0.1   0.    0.01  0.    0.  ]\n",
+      "    update  [ 0.    0.    0.    0.05  0.92  0.01  0.    0.01  0.    0.  ]\n",
+      "    predicted position is 4 with confidence 92.17%:\n",
+      "\n",
+      "final position is    : 3\n",
+      "predicted position is 4 with confidence 92.17%:\n"
+     ]
+    },
+    {
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+      ],
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7820240>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "random.seed(3)\n",
+    "np.set_printoptions(precision=2)\n",
+    "simulate(4, move_error=0.1, sense_error=0.1,\n",
+    "         no_sense_error=0.05, move_distance=1,\n",
+    "         do_print=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can see that the code was able to perfectly track the robot so we should feel reasonably confident that the code is working. Now let's see how it fairs with some errors. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 158,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "time 0: pos 3, sense False, at magnet False\n",
+      "    update  [ 0.    0.17  0.    0.17  0.17  0.    0.17  0.17  0.17  0.  ]\n",
+      "predicted position is 1 with confidence 16.67%:\n",
+      "    predict [ 0.17  0.16  0.01  0.01  0.15  0.02  0.16  0.16  0.02  0.16]\n",
+      "time 1: pos 6, sense False, at magnet False\n",
+      "    update  [ 0.    0.24  0.    0.01  0.23  0.    0.24  0.24  0.03  0.  ]\n",
+      "predicted position is 1 with confidence 24.36%:\n",
+      "    predict [ 0.23  0.04  0.    0.01  0.22  0.01  0.02  0.21  0.02  0.23]\n",
+      "time 2: pos 9, sense True, at magnet True\n",
+      "    update  [ 0.49  0.    0.    0.    0.    0.03  0.    0.    0.    0.48]\n",
+      "predicted position is 0 with confidence 48.66%:\n",
+      "    predict [ 0.    0.02  0.46  0.46  0.02  0.    0.    0.    0.02  0.  ]\n",
+      "time 3: pos 2, sense True, at magnet True\n",
+      "    update  [ 0.    0.    0.99  0.    0.    0.01  0.    0.    0.    0.  ]\n",
+      "predicted position is 2 with confidence 99.19%:\n",
+      "    predict [ 0.    0.    0.    0.    0.05  0.89  0.05  0.    0.    0.  ]\n",
+      "time 4: pos 5, sense True, at magnet True\n",
+      "    update  [ 0.  0.  0.  0.  0.  1.  0.  0.  0.  0.]\n",
+      "predicted position is 5 with confidence 99.68%:\n",
+      "    predict [ 0.    0.    0.    0.    0.    0.    0.    0.05  0.9   0.05]\n",
+      "time 5: pos 8, sense False, at magnet False\n",
+      "    update  [ 0.    0.    0.    0.    0.    0.    0.    0.05  0.95  0.  ]\n",
+      "predicted position is 8 with confidence 94.7%:\n",
+      "    predict [ 0.09  0.85  0.05  0.    0.    0.    0.    0.    0.    0.  ]\n",
+      "time 6: pos 1, sense False, at magnet False\n",
+      "    update  [ 0.  1.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
+      "predicted position is 1 with confidence 99.98%:\n",
+      "    predict [ 0.    0.    0.    0.05  0.9   0.05  0.    0.    0.    0.  ]\n",
+      "time 7: pos 4, sense False, at magnet False\n",
+      "    update  [ 0.    0.    0.    0.05  0.95  0.    0.    0.    0.    0.  ]\n",
+      "predicted position is 4 with confidence 94.73%:\n",
+      "    predict [ 0.    0.    0.    0.    0.    0.    0.09  0.86  0.05  0.  ]\n",
+      "time 8: pos 7, sense False, at magnet False\n",
+      "    update  [ 0.    0.    0.    0.    0.    0.    0.09  0.86  0.05  0.  ]\n",
+      "predicted position is 7 with confidence 85.75%:\n",
+      "    predict [ 0.78  0.09  0.    0.    0.    0.    0.    0.    0.    0.13]\n",
+      "time 9: pos 0, sense True, at magnet True\n",
+      "    update  [ 0.86  0.    0.    0.    0.    0.    0.    0.    0.    0.14]\n",
+      "predicted position is 0 with confidence 85.63%:\n",
+      "    predict [ 0.    0.01  0.17  0.78  0.04  0.    0.    0.    0.    0.  ]\n",
+      "\n",
+      "final position is    : 0\n",
+      "predicted position is 3 with confidence 77.77%:\n"
+     ]
+    },
+    {
+     "data": {
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+       "COEaAAAAMIRwDQAAABhCuAYAAAAMIVwDAAAAhvxfYGe+k8gdXYgAAAAASUVORK5CYII=\n"
+      ],
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x6b66a20>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "simulate(10, move_error=0.0, sense_error=.05,\n",
+    "         no_sense_error=0.05, move_distance=3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Ypi "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 126,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "final position is    : 4\n",
+      "predicted position is 1 with confidence 56.3%:\n"
+     ]
+    },
+    {
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+       "AABDCNcAAACAIYRrAAAAwJD/B9Am4+6cNEmnAAAAAElFTkSuQmCC\n"
+      ],
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x6b73978>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "simulate(133, move_error=0.05, sense_error=.05,\n",
+    "         no_sense_error=0.05, move_distance=4, do_print=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
    "source": []
   },
   {