Nonlinear Dynamics - 2-4 Feigenbaum.ipynb

{
 "metadata": {
  "name": "Nonlinear Dynamics - 2-4 Feigenbaum"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Codebase - Run these first"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Logistic Function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$X_{1} = RX_{0} (1-X_{0}) $$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def logisticFunction(R, X0):\n",
      "    return (R * X0 * (1-X0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def logistIterator(R, X0, num):\n",
      "    myVals = [X0]\n",
      "    for i in range(num):\n",
      "        myVals.append(logisticFunction(R, myVals[-1]))\n",
      "    return myVals"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Bifurcation Diagram"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Finished Work\n",
      "\n",
      "# http://www.complexityexplorer.org/online-courses/10-nonlinear-dynamics-mathematical-and-computational-approaches/segments/2465\n",
      "\n",
      "def bifurcationDiagram(x0, rMin, rMax, rStep, n, k):\n",
      "    #Generate all my values for R and store them\n",
      "    myRVals = append(arange(rMin, rMax, rStep), array(rMax))\n",
      "    #Create a list to hold my maps\n",
      "    myMapList = []\n",
      "    #Generare the maps\n",
      "    for myR in myRVals:\n",
      "        myMapList.append(logistIterator(myR, x0, n)[k:])\n",
      "    return myMapList\n",
      "\n",
      "def bifCleaner(myBif):\n",
      "    myRoundMaps = []\n",
      "    for myRawMap in myBif:\n",
      "        myRoundMaps.append([round(a,2) for a in myRawMap])\n",
      "    mySetMaps = []\n",
      "    for myRoundMap in myRoundMaps:\n",
      "        mySetMaps.append(set(myRoundMap))\n",
      "    myUniques = [list(a) for a in mySetMaps]\n",
      "    return myUniques\n",
      "\n",
      "def bifurPlotter(myBifVals, myRVals):\n",
      "    myX = [round(a, 2) for a in myRVals]\n",
      "    myY = myBifVals\n",
      "    myFlatCouplets = sum([[[myX[b], myY[b][a]] for a in range(len(myY[b]))] for b in range(len(myX))])\n",
      "    myX2 = [a[0] for a in myFlatCouplets]\n",
      "    myY2 = [a[1] for a in myFlatCouplets]\n",
      "    matplotlib.pyplot.scatter(myX2,myY2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Finished Work"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exploring SDIC"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#For r=2\n",
      "r2x = logistIterator(2, 0.2, 200)\n",
      "r2xHat = logistIterator(2, 0.200001, 200)\n",
      "\n",
      "#print len(r2x)\n",
      "#print len(r2xHat)\n",
      "\n",
      "r2Diffs = [abs(r2x[i]-r2xHat[i]) for i in range(len(r2x))]\n",
      "r2Diffs[0]\n",
      "#len(r2Diffs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "1.000000000001e-06"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Let's Plot!\n",
      "x = range(len(r2x))\n",
      "y = r2Diffs\n",
      "\n",
      "axis([0.0, 200.0, 0.0, 1.2e-6])\n",
      "plot(x,y, '-o')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7e03ba8>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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QWVmJgwcPJqz31FOP4ZFHHsM3vwm43WkbDhHRkpc0fMxmMwYHB7Xng4ODUSuQ\neHWGhoZgsVgQDofnlJvNZgA3VjvDw8PIyspCIBBAZmZmwr7MZjOGhobmlN9sc/nyZaxZswZTU1O4\ncuWKtur5/PPP8fTTT6Ourk7bsou1b98+7edNm4pw7VpRsmkhIlpSurq60NXVtXAdJntTKBwOS3Z2\ntni9XgkGg0kPHJw5c0Y7cJCobW1trTQ0NIiISH19/ZwDB8FgUC5cuCDZ2dnagYPCwkLp7u6WmZmZ\nOQcOXnjhBREROXz4sHbgIBgMyuOPPy6vvfbavPcXOwWhkMg994jMviQREcWRQnwkbp9KpePHj4vd\nbhdFUaSurk5ERJqamqSpqUmrs3v3blEURQoKCqS3tzdhWxGR0dFRKS4uFlVVxeVyyfj4uHZt//79\noiiK5OTkiNvt1srPnj0reXl5oiiKVFdXa+XXr1+XZ599Vmw2mzidTvF6vSIicujQITEajbJx40bt\n8fHHH0dPQJwJNBpFrl9PZWaIiJamrxo+/HqdOF8R8fWvA+fPAxHnFYiIKMJX/XodfsNBHPffD1y7\nttijICK6ezF84li2DPjii8UeBRHR3YvhE8eyZVz5EBGlE8Mnjvvv58qHiCidGD5xcOVDRJReDJ84\nGD5EROnF8ImD225EROnF8ImDKx8iovRi+MTB8CEiSi+GTxzcdiMiSi+GTxxc+RARpRfDJw5+vQ4R\nUXoxfOLg1+sQEaUXwycObrsREaUXwycObrsREaUXwycObrsREaUXwycObrsREaUXwycOfs6HiCi9\nGD5xcOVDRJReDJ84eOCAiCi9GD5x8MABEVF6MXziuLntJrLYIyEiujsxfOIwGgGDAQiFFnskRER3\nJ4bPPLj1RkSUPgyfefDEGxFR+jB85sETb0RE6cPwmQe33YiI0ofhMw+ufIiI0idp+LjdbuTm5kJV\nVTQ2NsatU1NTA1VV4XA40NfXl7Tt2NgYXC4X7HY7SkpKMDExoV2rr6+HqqrIzc1FZ2enVt7b24v8\n/Hyoqoo9e/Zo5cFgEOXl5VBVFVu2bMGlS5e0a83NzbDb7bDb7Th48GCKUwK0t5/Cf/3XK/jBD/Zh\n69ZX0N5+KuW2RESUAklgampKFEURr9croVBIHA6H9Pf3R9Vpb2+X0tJSERHp7u4Wp9OZtG1tba00\nNjaKiEhDQ4Ps3btXRETOnTsnDodDQqGQeL1eURRFZmZmRERk8+bN4vF4RESktLRUOjo6RETkwIED\nsmvXLhGM7MyHAAAG60lEQVQRaWlpkfLychERGR0dlezsbBkfH5fx8XHt51ixU/Dzn58URfmx3PiU\nz42HovxYfv7zk4mmimZ9+OGHiz2Euwrnc+FwLhdWkvhIKiNRMPX09MBms8FqtQIAKioq0NrainXr\n1ml12traUFVVBQBwOp2YmJjA8PAwvF7vvG3b2tpw8uRJAEBVVRWKiorQ0NCA1tZW7NixA0ajEVar\nFTabDR6PBw8//DAmJydRWFgIAKisrMSxY8fwxBNPoK2tDa+++ioAYPv27fjhD38IAHjvvfdQUlKC\nFStWAABcLhfcbjcqKioShvHrr3fi/Pn9s89OATiI8+evoqysDsuWvYaVK7+G0dFxAPdjZiaMe++9\n964qu3p1Cg88kHHLfdxzzwCmp9feNvdzJ8xZorJg8CKMRnXR7/FOmrP5yq5f/3/42tc23HZzcTvP\nWaKyryph+Ph8Pqxdu1Z7brFY4PF4ktbx+Xzw+/3zth0ZGYHJZAIAmEwmjIyMAAD8fj+2bNkypy+j\n0QiLxaKVm81m+Hy+Oa+fkZGB5cuXY3R0FH6/P6rNzb6SCQZvTskpAM0AsgBUYmbmPUxObsXkZDOA\nRwBsBfAegLup7MZ/R0dvvQ9gz210P3fGnCUuMyEcXnMb3vftPGfzlb2MyckXb7O5uN3nbL6y/QAM\n+CoSvudjMKTWuaTwPTQiErc/g8GQ8uvo4b77pmZ/6gSwGjcmuTPiv3dz2UL08eBtdD93ypwlKjt/\nG9zjnTZn85UV34ZzcbvP2XxlCyDRntyZM2dk69at2vO6ujppaGiIqvP888/L4cOHtec5OTkyPDyc\nsG1OTo4EAgEREfH7/ZKTkyMiIvX19VJfX6+12bp1q3R3d0sgEJDc3Fyt/F/+5V/khRde0OqcOXNG\nRETC4bD8+q//uoiIHD58WJ5//nmtzR//8R9LS0vLnHtUFEUA8MEHH3zw8aUeSqL4SCph+ITDYcnO\nzhav1yvBYDDpgYMzZ85oBw4Sta2trdWCqL6+fs6Bg2AwKBcuXJDs7GztwEFhYaF0d3fLzMzMnAMH\nN4Po8OHDUQcOvvGNb8j4+LiMjY1pPxMR0eJLelzh+PHjYrfbRVEUqaurExGRpqYmaWpq0urs3r1b\nFEWRgoIC6e3tTdhW5EYwFBcXi6qq4nK5okJh//79oiiK5OTkiNvt1srPnj0reXl5oiiKVFdXa+XX\nr1+XZ599Vmw2mzidTvF6vdq1t99+W2w2m9hsNnnnnXe+5NQQEVG6GET4DwcQEZG+lvQ3HKTyAVqa\nn9VqRUFBAR555BHtGHyiDxBTtO9///swmUzIz8/Xym7lA9h0Q7z53LdvHywWCx555BE88sgj6Ojo\n0K5xPuc3ODiI3/3d38WGDRuQl5eH119/HcAC/34u9tJrsaTyAVpKzGq1yujoaFTZfB8gprlOnTol\n//Ef/yF5eXla2Zf5APb09PSijPt2FW8+9+3bJz/96U/n1OV8JhYIBKSvr09ERCYnJ8Vut0t/f/+C\n/n4u2ZVP5AdojUaj9iFY+nIkZtc28kPHVVVVOHbs2GIM647wO7/zO/j6178eVTbf/MX7AHZPT4/u\nY76dxZtPYO7vKMD5TCYrKwsbN24EADzwwANYt24dfD7fgv5+Ltnwme/DsZQ6g8GA3/u938OmTZvw\nj//4jwDm/wAxpSbRB7Bv5UPTBLzxxhtwOBzYuXOntk3E+UzdxYsX0dfXB6fTuaC/n0s2fG6nD7be\nqf7t3/4NfX196OjowIEDB3D69Omo67fbB4jvNMnmj3Ob3K5du+D1evHRRx9h9erVeOmll+aty/mc\n6+rVq9i+fTv+9m//Fg8++GDUta/6+7lkw8dsNmNwcFB7Pjg4GJXclNzq1asBAL/xG7+B73znO+jp\n6YHJZMLw8DAAIBAIIDMzczGHeMeZb/5if1+HhoZgNpsXZYx3kszMTO2P5B/90R9pW0Gcz+TC4TC2\nb9+O5557Dtu2bQOwsL+fSzZ8Nm3ahIGBAVy8eBGhUAhHjhxBWVnZYg/rjvHFF19gcnISAHDt2jV0\ndnYiPz8fZWVlaG5uBnDjn7S4+UtLqZlv/srKytDS0oJQKASv14uBgQHthCHNLxAIaD//67/+q3YS\njvOZmIhg586dWL9+PV588UWtfEF/P9N4YOK2N9+HYCm5CxcuiMPhEIfDIRs2bNDmL9EHiClaRUWF\nrF69WoxGo1gsFnn77bdv6QPYdEPsfL711lvy3HPPSX5+vhQUFMgzzzwjw8PDWn3O5/xOnz4tBoNB\nHA6HbNy4UTZu3CgdHR0L+vvJD5kSEZHuluy2GxERLR6GDxER6Y7hQ0REumP4EBGR7hg+RESkO4YP\nERHpjuFDRES6Y/gQEZHu/j+pCT0LgTyRywAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def SDICDiffs(R, X0 ,XHat0, num):\n",
      "    myFirst = logistIterator(R, X0, num)\n",
      "    mySecond = logistIterator(R, XHat0, num)\n",
      "    myDiffs = [abs(myFirst[i]-mySecond[i]) for i in range(len(myFirst))]\n",
      "    return myDiffs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "201"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r34Diffs = SDICDiffs(3.4, 0.2 ,0.200001, 200)\n",
      "\n",
      "x = range(len(r34Diffs))\n",
      "y = r34Diffs\n",
      "\n",
      "axis([0.0, 200.0, 0.0, 2.5e-6])\n",
      "plot(x,y, '-o')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "[<matplotlib.lines.Line2D at 0x88753c8>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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srjjLzMzEkSNH4Ha74XQ6UVtbi6SkJERFRWHq1KmorKyEiODVV19Vp8289/Xm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\nFFQMHiIiCioGDxERBRWDh4iIgur/AwcL6GjxDraFAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r372Diffs = SDICDiffs(3.72, 0.2 ,0.200001, 200)\n",
      "\n",
      "x = range(len(r372Diffs))\n",
      "y = r372Diffs\n",
      "\n",
      "axis([0.0, 200.0, 0.0, 0.7])\n",
      "plot(x,y, '-o')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "[<matplotlib.lines.Line2D at 0x8bd85c0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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PMRImSSH3HAFRwaeCTK1C/gDa0SeqRtMxE1AKk5QreDVlGo2SQZin4K1G0uhJ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\nD0KrFQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "SDICDiffs(2, 0.2 ,0.200001, 500)[-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "5.551115123125783e-17"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "SDICDiffs(3.4, 0.2 ,0.200001, 500)[-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "0.0"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mean(array(SDICDiffs(3.72, 0.2 ,0.200001, 5000)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "0.24360764898900683"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mean(array(SDICDiffs(3.72, 0.2 ,0.200001, 500000)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "0.24406684960583536"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Bifurcation Diagram"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Finished Work\n",
      "\n",
      "# http://www.complexityexplorer.org/online-courses/10-nonlinear-dynamics-mathematical-and-computational-approaches/segments/2465\n",
      "\n",
      "def bifurcationDiagram(x0, rMin, rMax, rStep, n, k):\n",
      "    #Generate all my values for R and store them\n",
      "    myRVals = append(arange(rMin, rMax, rStep), array(rMax))\n",
      "    #Create a list to hold my maps\n",
      "    myMapList = []\n",
      "    #Generare the maps\n",
      "    for myR in myRVals:\n",
      "        myMapList.append(logistIterator(myR, x0, n)[k:])\n",
      "    return myMapList\n",
      "\n",
      "def bifCleaner(myBif):\n",
      "    myRoundMaps = []\n",
      "    for myRawMap in myBif:\n",
      "        myRoundMaps.append([round(a,2) for a in myRawMap])\n",
      "    mySetMaps = []\n",
      "    for myRoundMap in myRoundMaps:\n",
      "        mySetMaps.append(set(myRoundMap))\n",
      "    myUniques = [list(a) for a in mySetMaps]\n",
      "    return myUniques\n",
      "\n",
      "def bifurPlotter(myBifVals, myRVals):\n",
      "    myX = [round(a, 2) for a in myRVals]\n",
      "    myY = myBifVals\n",
      "    myFlatCouplets = sum([[[x[b], y[b][a]] for a in range(len(y[b]))] for b in range(len(x))])\n",
      "    myX2 = [a[0] for a in myFlatCouplets]\n",
      "    myY2 = [a[1] for a in myFlatCouplets]\n",
      "    matplotlib.pyplot.scatter(myX2,myY2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "testRs = [2.0, 2.4, 2.8]\n",
      "testMapList = []\n",
      "for i in testRs:\n",
      "    testMapList.append(logistIterator(i, 2.0, 5))\n",
      "\n",
      "#print testMapList\n",
      "\n",
      "#append(arange(2.4, 4.0, 0.01), array(4.0))\n",
      "\n",
      "\n",
      "\n",
      "#range(240, 401, 1)\n",
      "#[float(a)/100.0 for a in range(240, 401, 1)]\n",
      "#print \"blah\"\n",
      "\n",
      "#round(logistIterator(2.8, 0.6, 25)[8], 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# http://www.complexityexplorer.org/online-courses/10-nonlinear-dynamics-mathematical-and-computational-approaches/segments/2465\n",
      "\n",
      "def bifurcationDiagram(x0, rMin, rMax, rStep, n, k):\n",
      "    #Generate all my values for R and store them\n",
      "    myRVals = append(arange(rMin, rMax, rStep), array(rMax))\n",
      "    #Create a list to hold my maps\n",
      "    myMapList = []\n",
      "    #Generare the maps\n",
      "    for myR in myRVals:\n",
      "        myMapList.append(logistIterator(myR, x0, n)[k:])\n",
      "    return myMapList\n",
      "\n",
      "#bifurcationDiagram(0.2, 2.4, 4.0, 0.01, 25, 1)\n",
      "\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Scratch\n",
      "#myTestBif = bifurcationDiagram(0.2, 2.4, 4.0, 0.01, 25, 1)\n",
      "\n",
      "#len(myTestBif[0])\n",
      "\n",
      "#roundedMaps = []\n",
      "\n",
      "#for myDumbMap in myTestBif:\n",
      "#    roundedMaps.append([round(a,2) for a in myDumbMap])\n",
      "\n",
      "#setMaps = []\n",
      "\n",
      "#for myRoundedMap in roundedMaps:\n",
      "#    setMaps.append(set(myRoundedMap))\n",
      "    \n",
      "#setMaps"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def bifCleaner(myBif):\n",
      "    myRoundMaps = []\n",
      "    for myRawMap in myBif:\n",
      "        myRoundMaps.append([round(a,2) for a in myRawMap])\n",
      "    mySetMaps = []\n",
      "    for myRoundMap in myRoundMaps:\n",
      "        mySetMaps.append(set(myRoundMap))\n",
      "    myUniques = [list(a) for a in mySetMaps]\n",
      "    return myUniques\n",
      "\n",
      "#bifCleaner(bifurcationDiagram(0.2, 2.4, 4.0, 0.01, 1000, 5))[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "[0.58]"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#The Homework Itself\n",
      "\n",
      "homeworkBif = bifCleaner(bifurcationDiagram(0.2, 2.4, 4.0, 0.01, 1000, 500))\n",
      "\n",
      "homeworkRs = append(arange(2.4, 4.0, 0.01), array(4.0))\n",
      "\n",
      "\n",
      "#print len(homeworkBif)\n",
      "#print len(homeworkRs)\n",
      "\n",
      "[(len(homeworkBif[i]), homeworkRs[i]) for i in range(len(homeworkBif))]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "[(1, 2.3999999999999999),\n",
        " (1, 2.4099999999999997),\n",
        " (1, 2.4199999999999995),\n",
        " (1, 2.4299999999999993),\n",
        " (1, 2.4399999999999991),\n",
        " (1, 2.4499999999999988),\n",
        " (1, 2.4599999999999986),\n",
        " (1, 2.4699999999999984),\n",
        " (1, 2.4799999999999982),\n",
        " (1, 2.489999999999998),\n",
        " (1, 2.4999999999999978),\n",
        " (1, 2.5099999999999976),\n",
        " (1, 2.5199999999999974),\n",
        " (1, 2.5299999999999971),\n",
        " (1, 2.5399999999999969),\n",
        " (1, 2.5499999999999967),\n",
        " (1, 2.5599999999999965),\n",
        " (1, 2.5699999999999963),\n",
        " (1, 2.5799999999999961),\n",
        " (1, 2.5899999999999959),\n",
        " (1, 2.5999999999999956),\n",
        " (1, 2.6099999999999954),\n",
        " (1, 2.6199999999999952),\n",
        " (1, 2.629999999999995),\n",
        " (1, 2.6399999999999948),\n",
        " (1, 2.6499999999999946),\n",
        " (1, 2.6599999999999944),\n",
        " (1, 2.6699999999999942),\n",
        " (1, 2.6799999999999939),\n",
        " (1, 2.6899999999999937),\n",
        " (1, 2.6999999999999935),\n",
        " (1, 2.7099999999999933),\n",
        " (1, 2.7199999999999931),\n",
        " (1, 2.7299999999999929),\n",
        " (1, 2.7399999999999927),\n",
        " (1, 2.7499999999999925),\n",
        " (1, 2.7599999999999922),\n",
        " (1, 2.769999999999992),\n",
        " (1, 2.7799999999999918),\n",
        " (1, 2.7899999999999916),\n",
        " (1, 2.7999999999999914),\n",
        " (1, 2.8099999999999912),\n",
        " (1, 2.819999999999991),\n",
        " (1, 2.8299999999999907),\n",
        " (1, 2.8399999999999905),\n",
        " (1, 2.8499999999999903),\n",
        " (1, 2.8599999999999901),\n",
        " (1, 2.8699999999999899),\n",
        " (1, 2.8799999999999897),\n",
        " (1, 2.8899999999999895),\n",
        " (1, 2.8999999999999893),\n",
        " (1, 2.909999999999989),\n",
        " (1, 2.9199999999999888),\n",
        " (1, 2.9299999999999886),\n",
        " (1, 2.9399999999999884),\n",
        " (1, 2.9499999999999882),\n",
        " (1, 2.959999999999988),\n",
        " (1, 2.9699999999999878),\n",
        " (1, 2.9799999999999875),\n",
        " (1, 2.9899999999999873),\n",
        " (3, 2.9999999999999871),\n",
        " (2, 3.0099999999999869),\n",
        " (2, 3.0199999999999867),\n",
        " (2, 3.0299999999999865),\n",
        " (2, 3.0399999999999863),\n",
        " (2, 3.0499999999999861),\n",
        " (2, 3.0599999999999858),\n",
        " (2, 3.0699999999999856),\n",
        " (2, 3.0799999999999854),\n",
        " (2, 3.0899999999999852),\n",
        " (2, 3.099999999999985),\n",
        " (2, 3.1099999999999848),\n",
        " (2, 3.1199999999999846),\n",
        " (2, 3.1299999999999844),\n",
        " (2, 3.1399999999999841),\n",
        " (2, 3.1499999999999839),\n",
        " (2, 3.1599999999999837),\n",
        " (2, 3.1699999999999835),\n",
        " (2, 3.1799999999999833),\n",
        " (2, 3.1899999999999831),\n",
        " (2, 3.1999999999999829),\n",
        " (2, 3.2099999999999826),\n",
        " (2, 3.2199999999999824),\n",
        " (2, 3.2299999999999822),\n",
        " (2, 3.239999999999982),\n",
        " (2, 3.2499999999999818),\n",
        " (2, 3.2599999999999816),\n",
        " (2, 3.2699999999999814),\n",
        " (2, 3.2799999999999812),\n",
        " (2, 3.2899999999999809),\n",
        " (2, 3.2999999999999807),\n",
        " (2, 3.3099999999999805),\n",
        " (2, 3.3199999999999803),\n",
        " (2, 3.3299999999999801),\n",
        " (2, 3.3399999999999799),\n",
        " (2, 3.3499999999999797),\n",
        " (2, 3.3599999999999794),\n",
        " (2, 3.3699999999999792),\n",
        " (2, 3.379999999999979),\n",
        " (2, 3.3899999999999788),\n",
        " (2, 3.3999999999999786),\n",
        " (2, 3.4099999999999784),\n",
        " (2, 3.4199999999999782),\n",
        " (2, 3.429999999999978),\n",
        " (2, 3.4399999999999777),\n",
        " (3, 3.4499999999999775),\n",
        " (4, 3.4599999999999773),\n",
        " (4, 3.4699999999999771),\n",
        " (4, 3.4799999999999769),\n",
        " (4, 3.4899999999999767),\n",
        " (4, 3.4999999999999765),\n",
        " (4, 3.5099999999999763),\n",
        " (4, 3.519999999999976),\n",
        " (4, 3.5299999999999758),\n",
        " (4, 3.5399999999999756),\n",
        " (8, 3.5499999999999754),\n",
        " (8, 3.5599999999999752),\n",
        " (17, 3.569999999999975),\n",
        " (27, 3.5799999999999748),\n",
        " (39, 3.5899999999999745),\n",
        " (41, 3.5999999999999743),\n",
        " (42, 3.6099999999999741),\n",
        " (45, 3.6199999999999739),\n",
        " (6, 3.6299999999999737),\n",
        " (53, 3.6399999999999735),\n",
        " (57, 3.6499999999999733),\n",
        " (59, 3.6599999999999731),\n",
        " (62, 3.6699999999999728),\n",
        " (66, 3.6799999999999726),\n",
        " (67, 3.6899999999999724),\n",
        " (67, 3.6999999999999722),\n",
        " (68, 3.709999999999972),\n",
        " (68, 3.7199999999999718),\n",
        " (68, 3.7299999999999716),\n",
        " (5, 3.7399999999999713),\n",
        " (73, 3.7499999999999711),\n",
        " (74, 3.7599999999999709),\n",
        " (75, 3.7699999999999707),\n",
        " (73, 3.7799999999999705),\n",
        " (76, 3.7899999999999703),\n",
        " (76, 3.7999999999999701),\n",
        " (79, 3.8099999999999699),\n",
        " (80, 3.8199999999999696),\n",
        " (3, 3.8299999999999694),\n",
        " (3, 3.8399999999999692),\n",
        " (10, 3.849999999999969),\n",
        " (83, 3.8599999999999688),\n",
        " (83, 3.8699999999999686),\n",
        " (87, 3.8799999999999684),\n",
        " (87, 3.8899999999999681),\n",
        " (86, 3.8999999999999679),\n",
        " (89, 3.9099999999999677),\n",
        " (91, 3.9199999999999675),\n",
        " (91, 3.9299999999999673),\n",
        " (92, 3.9399999999999671),\n",
        " (95, 3.9499999999999669),\n",
        " (93, 3.9599999999999667),\n",
        " (97, 3.9699999999999664),\n",
        " (94, 3.9799999999999662),\n",
        " (99, 3.989999999999966),\n",
        " (100, 4.0)]"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = [round(a, 2) for a in homeworkRs]\n",
      "y = homeworkBif\n",
      "\n",
      "#[len(a) for a in homeworkBif]\n",
      "\n",
      "print len(x)\n",
      "print len(y)\n",
      "\n",
      "#print x\n",
      "\n",
      "#axis([2.4, 4.0, 0.0, 1.0])\n",
      "#plot(x[0],y[0][0], 'c.', x[0],y[0][1], 'c.')\n",
      "#plot(2.41, 0.59, '-o')\n",
      "#plot(2.41, 0.58, '-o')\n",
      "\n",
      "#matplotlib.pyplot.scatter(x,y)\n",
      "\n",
      "#matplotlib.pyplot.show()\n",
      "\n",
      "#y[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "161\n",
        "161\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(sum([[[x[b], y[b][a]] for a in range(len(y[b]))] for b in range(len(x))]))\n",
      "sum([[[x[b], y[b][a]] for a in range(len(y[b]))] for b in range(len(x))])[1]\n",
      "\n",
      "testCouplets = sum([[[x[b], y[b][a]] for a in range(len(y[b]))] for b in range(len(x))])\n",
      "\n",
      "\n",
      "testX = [a[0] for a in testCouplets]\n",
      "testY = [a[1] for a in testCouplets]\n",
      "\n",
      "matplotlib.pyplot.scatter(testX,testY)\n",
      "\n",
      "#print len(testX)\n",
      "#print len(testY)\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.collections.PathCollection at 0x7b1ae48>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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H74jf4VDF0qVLOfLIQcTjFyFpJw3p1tcCDxCJ/IHBg0/cXSph2LBhjvT/DYsX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\nRsj4/8HzhpyVacCyAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Increase k to 500\n",
      "\n",
      "homeworkBif2 = bifCleaner(bifurcationDiagram(0.2, 2.4, 4.0, 0.01, 1000, 500))\n",
      "\n",
      "homeworkRs = append(arange(2.4, 4.0, 0.01), array(4.0))\n",
      "\n",
      "x2 = [round(a, 2) for a in homeworkRs]\n",
      "y2 = homeworkBif2\n",
      "\n",
      "flatCouplets = sum([[[x[b], y[b][a]] for a in range(len(y[b]))] for b in range(len(x))])\n",
      "\n",
      "\n",
      "x2 = [a[0] for a in flatCouplets]\n",
      "y2 = [a[1] for a in flatCouplets]\n",
      "\n",
      "matplotlib.pyplot.scatter(x2,y2,marker=\",\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<matplotlib.collections.PathCollection at 0x8a69d68>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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mk0gmk0EOjYhCNDk5ofn/Ls62qUr1APbUjdzebXskSqVSSKVSgbcTKPAnEgmM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\n"
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#homeworkBif2 = bifCleaner(bifurcationDiagram(0.2, 2.8, 3.6, 0.01, 1000, 500))\n",
      "\n",
      "#homeworkRs2 = append(arange(2.8, 3.6, 0.01), array(3.6))\n",
      "\n",
      "bifurPlotter(bifCleaner(bifurcationDiagram(0.2, 2.8, 3.6, 0.01, 1000, 500)), append(arange(2.8, 3.6, 0.01), array(3.6)))\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ch8+3DJFPsVjCsFob8uCDw3Xg1rSzRKdNtNPyer0888wLfPrpbPLzD+D13uLf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\nAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "2-4 Feigenbaum Stuff"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Q1(D):\n",
      "#The Homework Itself\n",
      "\n",
      "homeworkBif = bifCleaner(bifurcationDiagram(0.2, 2.4, 4.0, 0.01, 1000, 500))\n",
      "\n",
      "homeworkRs = append(arange(2.4, 4.0, 0.01), array(4.0))\n",
      "\n",
      "\n",
      "#print len(homeworkBif)\n",
      "#print len(homeworkRs)\n",
      "\n",
      "[(len(homeworkBif[i]), homeworkRs[i]) for i in range(len(homeworkBif))]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "[(1, 2.3999999999999999),\n",
        " (1, 2.4099999999999997),\n",
        " (1, 2.4199999999999995),\n",
        " (1, 2.4299999999999993),\n",
        " (1, 2.4399999999999991),\n",
        " (1, 2.4499999999999988),\n",
        " (1, 2.4599999999999986),\n",
        " (1, 2.4699999999999984),\n",
        " (1, 2.4799999999999982),\n",
        " (1, 2.489999999999998),\n",
        " (1, 2.4999999999999978),\n",
        " (1, 2.5099999999999976),\n",
        " (1, 2.5199999999999974),\n",
        " (1, 2.5299999999999971),\n",
        " (1, 2.5399999999999969),\n",
        " (1, 2.5499999999999967),\n",
        " (1, 2.5599999999999965),\n",
        " (1, 2.5699999999999963),\n",
        " (1, 2.5799999999999961),\n",
        " (1, 2.5899999999999959),\n",
        " (1, 2.5999999999999956),\n",
        " (1, 2.6099999999999954),\n",
        " (1, 2.6199999999999952),\n",
        " (1, 2.629999999999995),\n",
        " (1, 2.6399999999999948),\n",
        " (1, 2.6499999999999946),\n",
        " (1, 2.6599999999999944),\n",
        " (1, 2.6699999999999942),\n",
        " (1, 2.6799999999999939),\n",
        " (1, 2.6899999999999937),\n",
        " (1, 2.6999999999999935),\n",
        " (1, 2.7099999999999933),\n",
        " (1, 2.7199999999999931),\n",
        " (1, 2.7299999999999929),\n",
        " (1, 2.7399999999999927),\n",
        " (1, 2.7499999999999925),\n",
        " (1, 2.7599999999999922),\n",
        " (1, 2.769999999999992),\n",
        " (1, 2.7799999999999918),\n",
        " (1, 2.7899999999999916),\n",
        " (1, 2.7999999999999914),\n",
        " (1, 2.8099999999999912),\n",
        " (1, 2.819999999999991),\n",
        " (1, 2.8299999999999907),\n",
        " (1, 2.8399999999999905),\n",
        " (1, 2.8499999999999903),\n",
        " (1, 2.8599999999999901),\n",
        " (1, 2.8699999999999899),\n",
        " (1, 2.8799999999999897),\n",
        " (1, 2.8899999999999895),\n",
        " (1, 2.8999999999999893),\n",
        " (1, 2.909999999999989),\n",
        " (1, 2.9199999999999888),\n",
        " (1, 2.9299999999999886),\n",
        " (1, 2.9399999999999884),\n",
        " (1, 2.9499999999999882),\n",
        " (1, 2.959999999999988),\n",
        " (1, 2.9699999999999878),\n",
        " (1, 2.9799999999999875),\n",
        " (1, 2.9899999999999873),\n",
        " (3, 2.9999999999999871),\n",
        " (2, 3.0099999999999869),\n",
        " (2, 3.0199999999999867),\n",
        " (2, 3.0299999999999865),\n",
        " (2, 3.0399999999999863),\n",
        " (2, 3.0499999999999861),\n",
        " (2, 3.0599999999999858),\n",
        " (2, 3.0699999999999856),\n",
        " (2, 3.0799999999999854),\n",
        " (2, 3.0899999999999852),\n",
        " (2, 3.099999999999985),\n",
        " (2, 3.1099999999999848),\n",
        " (2, 3.1199999999999846),\n",
        " (2, 3.1299999999999844),\n",
        " (2, 3.1399999999999841),\n",
        " (2, 3.1499999999999839),\n",
        " (2, 3.1599999999999837),\n",
        " (2, 3.1699999999999835),\n",
        " (2, 3.1799999999999833),\n",
        " (2, 3.1899999999999831),\n",
        " (2, 3.1999999999999829),\n",
        " (2, 3.2099999999999826),\n",
        " (2, 3.2199999999999824),\n",
        " (2, 3.2299999999999822),\n",
        " (2, 3.239999999999982),\n",
        " (2, 3.2499999999999818),\n",
        " (2, 3.2599999999999816),\n",
        " (2, 3.2699999999999814),\n",
        " (2, 3.2799999999999812),\n",
        " (2, 3.2899999999999809),\n",
        " (2, 3.2999999999999807),\n",
        " (2, 3.3099999999999805),\n",
        " (2, 3.3199999999999803),\n",
        " (2, 3.3299999999999801),\n",
        " (2, 3.3399999999999799),\n",
        " (2, 3.3499999999999797),\n",
        " (2, 3.3599999999999794),\n",
        " (2, 3.3699999999999792),\n",
        " (2, 3.379999999999979),\n",
        " (2, 3.3899999999999788),\n",
        " (2, 3.3999999999999786),\n",
        " (2, 3.4099999999999784),\n",
        " (2, 3.4199999999999782),\n",
        " (2, 3.429999999999978),\n",
        " (2, 3.4399999999999777),\n",
        " (3, 3.4499999999999775),\n",
        " (4, 3.4599999999999773),\n",
        " (4, 3.4699999999999771),\n",
        " (4, 3.4799999999999769),\n",
        " (4, 3.4899999999999767),\n",
        " (4, 3.4999999999999765),\n",
        " (4, 3.5099999999999763),\n",
        " (4, 3.519999999999976),\n",
        " (4, 3.5299999999999758),\n",
        " (4, 3.5399999999999756),\n",
        " (8, 3.5499999999999754),\n",
        " (8, 3.5599999999999752),\n",
        " (17, 3.569999999999975),\n",
        " (27, 3.5799999999999748),\n",
        " (39, 3.5899999999999745),\n",
        " (41, 3.5999999999999743),\n",
        " (42, 3.6099999999999741),\n",
        " (45, 3.6199999999999739),\n",
        " (6, 3.6299999999999737),\n",
        " (53, 3.6399999999999735),\n",
        " (57, 3.6499999999999733),\n",
        " (59, 3.6599999999999731),\n",
        " (62, 3.6699999999999728),\n",
        " (66, 3.6799999999999726),\n",
        " (67, 3.6899999999999724),\n",
        " (67, 3.6999999999999722),\n",
        " (68, 3.709999999999972),\n",
        " (68, 3.7199999999999718),\n",
        " (68, 3.7299999999999716),\n",
        " (5, 3.7399999999999713),\n",
        " (73, 3.7499999999999711),\n",
        " (74, 3.7599999999999709),\n",
        " (75, 3.7699999999999707),\n",
        " (73, 3.7799999999999705),\n",
        " (76, 3.7899999999999703),\n",
        " (76, 3.7999999999999701),\n",
        " (79, 3.8099999999999699),\n",
        " (80, 3.8199999999999696),\n",
        " (3, 3.8299999999999694),\n",
        " (3, 3.8399999999999692),\n",
        " (10, 3.849999999999969),\n",
        " (83, 3.8599999999999688),\n",
        " (83, 3.8699999999999686),\n",
        " (87, 3.8799999999999684),\n",
        " (87, 3.8899999999999681),\n",
        " (86, 3.8999999999999679),\n",
        " (89, 3.9099999999999677),\n",
        " (91, 3.9199999999999675),\n",
        " (91, 3.9299999999999673),\n",
        " (92, 3.9399999999999671),\n",
        " (95, 3.9499999999999669),\n",
        " (93, 3.9599999999999667),\n",
        " (97, 3.9699999999999664),\n",
        " (94, 3.9799999999999662),\n",
        " (99, 3.989999999999966),\n",
        " (100, 4.0)]"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "So, I think 3.56 or so?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Q1 E:\n",
      "$$\\frac{b_{2} - b_{1}}{b_{3} - b_{2}} = \\delta_{1} $$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(3.4494897 - 3) / (3.5440903 - 3.4494897)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "4.75144660816104"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Q1F and beyond\n",
      "homeworkBif = bifCleaner(bifurcationDiagram(0.2, 2.4, 4.0, 0.01, 3000, 1000))\n",
      "\n",
      "homeworkRs = append(arange(2.4, 4.0, 0.01), array(4.0))\n",
      "\n",
      "\n",
      "#print len(homeworkBif)\n",
      "#print len(homeworkRs)\n",
      "\n",
      "[(len(homeworkBif[i]), homeworkRs[i]) for i in range(len(homeworkBif))]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "[(1, 2.3999999999999999),\n",
        " (1, 2.4099999999999997),\n",
        " (1, 2.4199999999999995),\n",
        " (1, 2.4299999999999993),\n",
        " (1, 2.4399999999999991),\n",
        " (1, 2.4499999999999988),\n",
        " (1, 2.4599999999999986),\n",
        " (1, 2.4699999999999984),\n",
        " (1, 2.4799999999999982),\n",
        " (1, 2.489999999999998),\n",
        " (1, 2.4999999999999978),\n",
        " (1, 2.5099999999999976),\n",
        " (1, 2.5199999999999974),\n",
        " (1, 2.5299999999999971),\n",
        " (1, 2.5399999999999969),\n",
        " (1, 2.5499999999999967),\n",
        " (1, 2.5599999999999965),\n",
        " (1, 2.5699999999999963),\n",
        " (1, 2.5799999999999961),\n",
        " (1, 2.5899999999999959),\n",
        " (1, 2.5999999999999956),\n",
        " (1, 2.6099999999999954),\n",
        " (1, 2.6199999999999952),\n",
        " (1, 2.629999999999995),\n",
        " (1, 2.6399999999999948),\n",
        " (1, 2.6499999999999946),\n",
        " (1, 2.6599999999999944),\n",
        " (1, 2.6699999999999942),\n",
        " (1, 2.6799999999999939),\n",
        " (1, 2.6899999999999937),\n",
        " (1, 2.6999999999999935),\n",
        " (1, 2.7099999999999933),\n",
        " (1, 2.7199999999999931),\n",
        " (1, 2.7299999999999929),\n",
        " (1, 2.7399999999999927),\n",
        " (1, 2.7499999999999925),\n",
        " (1, 2.7599999999999922),\n",
        " (1, 2.769999999999992),\n",
        " (1, 2.7799999999999918),\n",
        " (1, 2.7899999999999916),\n",
        " (1, 2.7999999999999914),\n",
        " (1, 2.8099999999999912),\n",
        " (1, 2.819999999999991),\n",
        " (1, 2.8299999999999907),\n",
        " (1, 2.8399999999999905),\n",
        " (1, 2.8499999999999903),\n",
        " (1, 2.8599999999999901),\n",
        " (1, 2.8699999999999899),\n",
        " (1, 2.8799999999999897),\n",
        " (1, 2.8899999999999895),\n",
        " (1, 2.8999999999999893),\n",
        " (1, 2.909999999999989),\n",
        " (1, 2.9199999999999888),\n",
        " (1, 2.9299999999999886),\n",
        " (1, 2.9399999999999884),\n",
        " (1, 2.9499999999999882),\n",
        " (1, 2.959999999999988),\n",
        " (1, 2.9699999999999878),\n",
        " (1, 2.9799999999999875),\n",
        " (1, 2.9899999999999873),\n",
        " (2, 2.9999999999999871),\n",
        " (2, 3.0099999999999869),\n",
        " (2, 3.0199999999999867),\n",
        " (2, 3.0299999999999865),\n",
        " (2, 3.0399999999999863),\n",
        " (2, 3.0499999999999861),\n",
        " (2, 3.0599999999999858),\n",
        " (2, 3.0699999999999856),\n",
        " (2, 3.0799999999999854),\n",
        " (2, 3.0899999999999852),\n",
        " (2, 3.099999999999985),\n",
        " (2, 3.1099999999999848),\n",
        " (2, 3.1199999999999846),\n",
        " (2, 3.1299999999999844),\n",
        " (2, 3.1399999999999841),\n",
        " (2, 3.1499999999999839),\n",
        " (2, 3.1599999999999837),\n",
        " (2, 3.1699999999999835),\n",
        " (2, 3.1799999999999833),\n",
        " (2, 3.1899999999999831),\n",
        " (2, 3.1999999999999829),\n",
        " (2, 3.2099999999999826),\n",
        " (2, 3.2199999999999824),\n",
        " (2, 3.2299999999999822),\n",
        " (2, 3.239999999999982),\n",
        " (2, 3.2499999999999818),\n",
        " (2, 3.2599999999999816),\n",
        " (2, 3.2699999999999814),\n",
        " (2, 3.2799999999999812),\n",
        " (2, 3.2899999999999809),\n",
        " (2, 3.2999999999999807),\n",
        " (2, 3.3099999999999805),\n",
        " (2, 3.3199999999999803),\n",
        " (2, 3.3299999999999801),\n",
        " (2, 3.3399999999999799),\n",
        " (2, 3.3499999999999797),\n",
        " (2, 3.3599999999999794),\n",
        " (2, 3.3699999999999792),\n",
        " (2, 3.379999999999979),\n",
        " (2, 3.3899999999999788),\n",
        " (2, 3.3999999999999786),\n",
        " (2, 3.4099999999999784),\n",
        " (2, 3.4199999999999782),\n",
        " (2, 3.429999999999978),\n",
        " (2, 3.4399999999999777),\n",
        " (3, 3.4499999999999775),\n",
        " (4, 3.4599999999999773),\n",
        " (4, 3.4699999999999771),\n",
        " (4, 3.4799999999999769),\n",
        " (4, 3.4899999999999767),\n",
        " (4, 3.4999999999999765),\n",
        " (4, 3.5099999999999763),\n",
        " (4, 3.519999999999976),\n",
        " (4, 3.5299999999999758),\n",
        " (4, 3.5399999999999756),\n",
        " (8, 3.5499999999999754),\n",
        " (8, 3.5599999999999752),\n",
        " (17, 3.569999999999975),\n",
        " (27, 3.5799999999999748),\n",
        " (39, 3.5899999999999745),\n",
        " (41, 3.5999999999999743),\n",
        " (43, 3.6099999999999741),\n",
        " (46, 3.6199999999999739),\n",
        " (6, 3.6299999999999737),\n",
        " (53, 3.6399999999999735),\n",
        " (57, 3.6499999999999733),\n",
        " (59, 3.6599999999999731),\n",
        " (63, 3.6699999999999728),\n",
        " (66, 3.6799999999999726),\n",
        " (67, 3.6899999999999724),\n",
        " (67, 3.6999999999999722),\n",
        " (69, 3.709999999999972),\n",
        " (70, 3.7199999999999718),\n",
        " (71, 3.7299999999999716),\n",
        " (5, 3.7399999999999713),\n",
        " (73, 3.7499999999999711),\n",
        " (74, 3.7599999999999709),\n",
        " (75, 3.7699999999999707),\n",
        " (75, 3.7799999999999705),\n",
        " (77, 3.7899999999999703),\n",
        " (78, 3.7999999999999701),\n",
        " (79, 3.8099999999999699),\n",
        " (80, 3.8199999999999696),\n",
        " (3, 3.8299999999999694),\n",
        " (3, 3.8399999999999692),\n",
        " (10, 3.849999999999969),\n",
        " (84, 3.8599999999999688),\n",
        " (86, 3.8699999999999686),\n",
        " (87, 3.8799999999999684),\n",
        " (88, 3.8899999999999681),\n",
        " (88, 3.8999999999999679),\n",
        " (90, 3.9099999999999677),\n",
        " (91, 3.9199999999999675),\n",
        " (92, 3.9299999999999673),\n",
        " (93, 3.9399999999999671),\n",
        " (95, 3.9499999999999669),\n",
        " (96, 3.9599999999999667),\n",
        " (97, 3.9699999999999664),\n",
        " (98, 3.9799999999999662),\n",
        " (100, 3.989999999999966),\n",
        " (101, 4.0)]"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b1 = 3.4494897\n",
      "b2 = 3.5440903\n",
      "b3 = 3.5699999\n",
      "\n",
      "(b2 - b1) / (b3 - b2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "3.651179485596097"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Exam 2, Question 15\n",
      "\n",
      "bifurPlotter(bifCleaner(bifurcationDiagram(0.2, 3.84, 3.8571, 0.01, 1000, 500)), append(arange(3.84, 3.8571, 0.01), array(3.8571)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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LwtC5c2cSE7/m8GE/of8N/onLFUNCQoLV0SQMPl8N0A3YB3iBYdTU+KwNZRMq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\ni4hEEZW+iEgUUemLiESR/w/mzSmSGArEkgAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bifurPlotter(bifCleaner(bifurcationDiagram(0.2, 0.4, 0.6, 0.01, 1000, 500)), append(arange(0.4, 0.6, 0.01), array(0.6)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "TypeError",
       "evalue": "'numpy.float64' object is not iterable",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-32-28258f7e6d00>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mbifurPlotter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbifCleaner\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbifurcationDiagram\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.01\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1000\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m500\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.01\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;32m<ipython-input-19-3a288cdd1cfb>\u001b[0m in \u001b[0;36mbifurPlotter\u001b[1;34m(myBifVals, myRVals)\u001b[0m\n\u001b[0;32m     27\u001b[0m     \u001b[0mmyY\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmyBifVals\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     28\u001b[0m     \u001b[0mmyFlatCouplets\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mmyX\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmyY\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmyY\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mb\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmyX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 29\u001b[1;33m     \u001b[0mmyX2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mmyFlatCouplets\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     30\u001b[0m     \u001b[0mmyY2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mmyFlatCouplets\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     31\u001b[0m     \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmyX2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmyY2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mTypeError\u001b[0m: 'numpy.float64' object is not iterable"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}