Infinite Resistors.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## In the spirit of\n",
    "https://xkcd.com/356/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import altair as alt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RendererRegistry.enable('notebook')"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alt.renderers.enable('notebook')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1/x = 1/1 + 2/3 + 2/5 + 2/7 + ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "partial_series = [2/(2 + 1)]\n",
    "partial_sum = [sum(partial_series)]\n",
    "resistance = [1 / (1 + partial_sum[-1])]\n",
    "convergence_array = [0]\n",
    "iteration = [1]\n",
    "\n",
    "while iteration[-1] < 50000000:\n",
    "    iteration += [iteration[-1] + 1]\n",
    "    partial_series += [2/(2 * iteration[-1] + 1)]\n",
    "    partial_sum += [partial_sum[-1] + partial_series[-1]]\n",
    "    resistance += [1 / (1 + partial_sum[-1])]\n",
    "    convergence_array += [np.abs(resistance[-1] - resistance[-2])]\n",
    "    #if convergence_array[-1] < 0.0000001:\n",
    "    #    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05350156047445599"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resistance[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50000000"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(partial_sum)\n",
    "len(convergence_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "range_indices = range(0, \n",
    "                      graph_data.shape[0],\n",
    "                      graph_data.shape[0] // 1000)\n",
    "iteration = [iteration[i] for i in range_indices]\n",
    "partial_series = [partial_series[i] for i in range_indices]\n",
    "partial_sum = [partial_sum[i] for i in range_indices]\n",
    "resistance = [resistance[i] for i in range_indices]\n",
    "convergence_array = [convergence_array[i] for i in range_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph_data = pd.DataFrame({'iteration': iteration,\n",
    "                           'partial_series': partial_series,\n",
    "                           'partial_sum': partial_sum,\n",
    "                           'resistance': resistance,\n",
    "                           'convergence_array': convergence_array})\n",
    "graph_data['Runs'] = 'Runs'\n",
    "graph_data = graph_data[['iteration', 'resistance', 'Runs']].copy()\n",
    "#if graph_data.shape[0] > 1000:\n",
    "#    graph_data = graph_data.iloc[range(0, \n",
    "#                                      graph_data.shape[0],\n",
    "#                                      graph_data.shape[0] // 1000)].copy()\n",
    "    \n",
    "graph_data = pd.concat([graph_data, \n",
    "                       pd.DataFrame({'iteration': [0, iteration[-1]],\n",
    "                                    'resistance': [resistance[-1] for i in range(2)],\n",
    "                                    'Runs': [\"Convergence\" for i in range(2)]})])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
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0.12717415058947804, \"Runs\": \"Runs\"}, {\"iteration\": 992, \"resistance\": 0.12715785719655134, \"Runs\": \"Runs\"}, {\"iteration\": 993, \"resistance\": 0.12714158437176093, \"Runs\": \"Runs\"}, {\"iteration\": 994, \"resistance\": 0.1271253320679571, \"Runs\": \"Runs\"}, {\"iteration\": 995, \"resistance\": 0.1271091002381463, \"Runs\": \"Runs\"}, {\"iteration\": 996, \"resistance\": 0.12709288883549047, \"Runs\": \"Runs\"}, {\"iteration\": 997, \"resistance\": 0.12707669781330624, \"Runs\": \"Runs\"}, {\"iteration\": 998, \"resistance\": 0.1270605271250644, \"Runs\": \"Runs\"}, {\"iteration\": 999, \"resistance\": 0.1270443767243892, \"Runs\": \"Runs\"}, {\"iteration\": 1000, \"resistance\": 0.1270282465650576, \"Runs\": \"Runs\"}, {\"iteration\": 1001, \"resistance\": 0.12701213660099878, \"Runs\": \"Runs\"}, {\"iteration\": 1002, \"resistance\": 0.12699604678629334, \"Runs\": \"Runs\"}, {\"iteration\": 1003, \"resistance\": 0.1269799770751727, \"Runs\": \"Runs\"}, {\"iteration\": 1004, \"resistance\": 0.12696392742201848, \"Runs\": \"Runs\"}, {\"iteration\": 0, \"resistance\": 0.12696392742201848, \"Runs\": \"Convergence\"}, {\"iteration\": 1004, \"resistance\": 0.12696392742201848, \"Runs\": \"Convergence\"}]}};\n",
       "var opt = {};\n",
       "var type = \"vega-lite\";\n",
       "var id = \"8a6f40d6-400e-475b-9200-b548cb8972f6\";\n",
       "\n",
       "var output_area = this;\n",
       "\n",
       "require([\"nbextensions/jupyter-vega/index\"], function(vega) {\n",
       "  var target = document.createElement(\"div\");\n",
       "  target.id = id;\n",
       "  target.className = \"vega-embed\";\n",
       "\n",
       "  var style = document.createElement(\"style\");\n",
       "  style.textContent = [\n",
       "    \".vega-embed .error p {\",\n",
       "    \"  color: firebrick;\",\n",
       "    \"  font-size: 14px;\",\n",
       "    \"}\",\n",
       "  ].join(\"\\\\n\");\n",
       "\n",
       "  // element is a jQuery wrapped DOM element inside the output area\n",
       "  // see http://ipython.readthedocs.io/en/stable/api/generated/\\\n",
       "  // IPython.display.html#IPython.display.Javascript.__init__\n",
       "  element[0].appendChild(target);\n",
       "  element[0].appendChild(style);\n",
       "\n",
       "  vega.render(\"#\" + id, spec, type, opt, output_area);\n",
       "}, function (err) {\n",
       "  if (err.requireType !== \"scripterror\") {\n",
       "    throw(err);\n",
       "  }\n",
       "});\n"
      ],
      "text/plain": [
       "<vega.vegalite.VegaLite at 0x1915be3bc18>"
      ]
     },
     "metadata": {
      "jupyter-vega": "#8a6f40d6-400e-475b-9200-b548cb8972f6"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": []
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "jupyter-vega": "#8a6f40d6-400e-475b-9200-b548cb8972f6"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alt.Chart(graph_data).mark_line().encode(\n",
    "    x='iteration',\n",
    "    y='resistance',\n",
    "    color = 'Runs'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}