How-to-SSA-BinDecModel.ipynb

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  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# SSA for Binary Decision Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cd3951f",
   "metadata": {},
   "source": [
    "In this document we show the user how to create trajectories with the SSA for the binary decision model under fully connected and mean field assumptions. We first import the package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "520c6991",
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"SSABinaryDecision.jl\");\n",
    "using .BinaryDecSSA;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c329d727",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots, LaTeXStrings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "009f41d2",
   "metadata": {},
   "source": [
    "We now need to create a BinDecMod `struct` defining the model that we later wish to simulate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b6a90939",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BinDecMod\n",
       "  N: Int64 100\n",
       "  F: Float64 0.01\n",
       "  J: Float64 2.0\n",
       "  α: Float64 0.0\n",
       "  β: Float64 1.0\n",
       "  γ: Float64 1.0\n",
       "  fixedIC: Bool true\n",
       "  p₀: Float64 0.5\n"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BD1 = BinDecMod(F = 0.01, J = 2.0, β = 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7372de8",
   "metadata": {},
   "source": [
    "Let's now create an ensemble of 100 simulations for `BD1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6a79e55e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ensemble\n",
       "  BD: BinDecMod\n",
       "  e_size: Int64 1000\n",
       "  τₘ: Int64 1000\n",
       "  Δτ: Int64 1\n",
       "  sims: Tuple{Vector{Float64}, Vector{Array{Real, N} where N}}\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ens1 = Ensemble(BD = BD1, e_size = 1000, τₘ = 10^3, Δτ = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a80b929",
   "metadata": {},
   "source": [
    "We can easily then plot the output simulations returned from this ensemble."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7ea8d529",
   "metadata": {
    "scrolled": false
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   "outputs": [
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       "  1456.64,128.708 1458.68,142.286 1460.72,115.131 1462.75,115.131 1464.79,128.708 1466.83,142.286 1468.86,142.286 1470.9,142.286 1472.93,155.863 1474.97,155.863 \n",
       "  1477.01,142.286 1479.04,101.554 1481.08,128.708 1483.12,115.131 1485.15,115.131 1487.19,115.131 1489.23,128.708 1491.26,101.554 1493.3,155.863 1495.34,142.286 \n",
       "  1497.37,128.708 1499.41,115.131 1501.45,128.708 1503.48,101.554 1505.52,155.863 1507.56,101.554 1509.59,115.131 1511.63,155.863 1513.67,115.131 1515.7,87.9763 \n",
       "  1517.74,115.131 1519.78,142.286 1521.81,128.708 1523.85,128.708 1525.89,101.554 1527.92,101.554 1529.96,142.286 1532,183.018 1534.03,155.863 1536.07,196.595 \n",
       "  1538.11,155.863 1540.14,115.131 1542.18,101.554 1544.22,101.554 1546.25,87.9763 1548.29,101.554 1550.33,142.286 1552.36,155.863 1554.4,115.131 1556.44,101.554 \n",
       "  1558.47,142.286 1560.51,128.708 1562.55,128.708 1564.58,101.554 1566.62,115.131 1568.66,142.286 1570.69,115.131 1572.73,101.554 1574.77,101.554 1576.8,87.9763 \n",
       "  1578.84,101.554 1580.88,101.554 1582.91,142.286 1584.95,142.286 1586.99,142.286 1589.02,115.131 1591.06,115.131 1593.1,101.554 1595.13,115.131 1597.17,101.554 \n",
       "  1599.21,101.554 1601.24,115.131 1603.28,87.9763 1605.32,115.131 1607.35,101.554 1609.39,101.554 1611.43,87.9763 1613.46,101.554 1615.5,115.131 1617.54,115.131 \n",
       "  1619.57,128.708 1621.61,115.131 1623.65,115.131 1625.68,142.286 1627.72,101.554 1629.75,128.708 1631.79,115.131 1633.83,101.554 1635.86,128.708 1637.9,101.554 \n",
       "  1639.94,87.9763 1641.97,101.554 1644.01,115.131 1646.05,142.286 1648.08,115.131 1650.12,101.554 1652.16,87.9763 1654.19,101.554 1656.23,87.9763 1658.27,142.286 \n",
       "  1660.3,128.708 1662.34,142.286 1664.38,169.441 1666.41,142.286 1668.45,142.286 1670.49,142.286 1672.52,115.131 1674.56,87.9763 1676.6,87.9763 1678.63,115.131 \n",
       "  1680.67,101.554 1682.71,115.131 1684.74,87.9763 1686.78,169.441 1688.82,169.441 1690.85,128.708 1692.89,128.708 1694.93,101.554 1696.96,101.554 1699,87.9763 \n",
       "  1701.04,101.554 1703.07,87.9763 1705.11,101.554 1707.15,101.554 1709.18,115.131 1711.22,101.554 1713.26,142.286 1715.29,142.286 1717.33,128.708 1719.37,87.9763 \n",
       "  1721.4,87.9763 1723.44,87.9763 1725.48,142.286 1727.51,115.131 1729.55,101.554 1731.59,101.554 1733.62,115.131 1735.66,101.554 1737.7,87.9763 1739.73,101.554 \n",
       "  1741.77,115.131 1743.81,101.554 1745.84,87.9763 1747.88,128.708 1749.92,115.131 1751.95,115.131 1753.99,87.9763 1756.03,101.554 1758.06,128.708 1760.1,87.9763 \n",
       "  1762.14,101.554 1764.17,142.286 1766.21,155.863 1768.25,142.286 1770.28,128.708 1772.32,128.708 1774.36,101.554 1776.39,155.863 1778.43,128.708 1780.46,115.131 \n",
       "  1782.5,115.131 1784.54,101.554 1786.57,101.554 1788.61,87.9763 1790.65,101.554 1792.68,115.131 1794.72,155.863 1796.76,155.863 1798.79,115.131 1800.83,115.131 \n",
       "  1802.87,142.286 1804.9,155.863 1806.94,142.286 1808.98,155.863 1811.01,128.708 1813.05,128.708 1815.09,155.863 1817.12,101.554 1819.16,142.286 1821.2,115.131 \n",
       "  1823.23,115.131 1825.27,101.554 1827.31,87.9763 1829.34,101.554 1831.38,101.554 1833.42,128.708 1835.45,101.554 1837.49,115.131 1839.53,101.554 1841.56,101.554 \n",
       "  1843.6,101.554 1845.64,115.131 1847.67,128.708 1849.71,155.863 1851.75,142.286 1853.78,142.286 1855.82,101.554 1857.86,101.554 1859.89,128.708 1861.93,101.554 \n",
       "  1863.97,87.9763 1866,87.9763 1868.04,128.708 1870.08,115.131 1872.11,87.9763 1874.15,87.9763 1876.19,87.9763 1878.22,87.9763 1880.26,115.131 1882.3,155.863 \n",
       "  1884.33,128.708 1886.37,115.131 1888.41,101.554 1890.44,142.286 1892.48,169.441 1894.52,128.708 1896.55,142.286 1898.59,142.286 1900.63,115.131 1902.66,115.131 \n",
       "  1904.7,115.131 1906.74,101.554 1908.77,142.286 1910.81,128.708 1912.85,115.131 1914.88,115.131 1916.92,101.554 1918.96,101.554 1920.99,155.863 1923.03,115.131 \n",
       "  1925.07,101.554 1927.1,87.9763 1929.14,115.131 1931.18,155.863 1933.21,128.708 1935.25,101.554 1937.28,115.131 1939.32,101.554 1941.36,101.554 1943.39,87.9763 \n",
       "  1945.43,128.708 1947.47,87.9763 1949.5,87.9763 1951.54,101.554 1953.58,101.554 1955.61,142.286 1957.65,128.708 1959.69,101.554 1961.72,87.9763 1963.76,87.9763 \n",
       "  1965.8,115.131 1967.83,115.131 1969.87,101.554 1971.91,87.9763 1973.94,115.131 1975.98,115.131 1978.02,101.554 1980.05,115.131 1982.09,142.286 1984.13,128.708 \n",
       "  1986.16,128.708 1988.2,115.131 1990.24,142.286 1992.27,128.708 1994.31,128.708 1996.35,142.286 1998.38,155.863 2000.42,142.286 2002.46,128.708 2004.49,128.708 \n",
       "  2006.53,128.708 2008.57,87.9763 2010.6,101.554 2012.64,128.708 2014.68,155.863 2016.71,128.708 2018.75,115.131 2020.79,128.708 2022.82,115.131 2024.86,155.863 \n",
       "  2026.9,115.131 2028.93,142.286 2030.97,128.708 2033.01,142.286 2035.04,128.708 2037.08,115.131 2039.12,115.131 2041.15,115.131 2043.19,101.554 2045.23,115.131 \n",
       "  2047.26,87.9763 2049.3,87.9763 2051.34,115.131 2053.37,128.708 2055.41,87.9763 2057.45,101.554 2059.48,142.286 2061.52,115.131 2063.56,115.131 2065.59,155.863 \n",
       "  2067.63,101.554 2069.67,142.286 2071.7,128.708 2073.74,115.131 2075.78,115.131 2077.81,101.554 2079.85,101.554 2081.89,87.9763 2083.92,101.554 2085.96,128.708 \n",
       "  2087.99,128.708 2090.03,115.131 2092.07,142.286 2094.1,128.708 2096.14,155.863 2098.18,128.708 2100.21,115.131 2102.25,128.708 2104.29,101.554 2106.32,128.708 \n",
       "  2108.36,142.286 2110.4,155.863 2112.43,101.554 2114.47,128.708 2116.51,115.131 2118.54,128.708 2120.58,101.554 2122.62,101.554 2124.65,87.9763 2126.69,115.131 \n",
       "  2128.73,169.441 2130.76,128.708 2132.8,155.863 2134.84,128.708 2136.87,128.708 2138.91,87.9763 2140.95,128.708 2142.98,101.554 2145.02,128.708 2147.06,87.9763 \n",
       "  2149.09,142.286 2151.13,115.131 2153.17,115.131 2155.2,115.131 2157.24,87.9763 2159.28,101.554 2161.31,128.708 2163.35,142.286 2165.39,142.286 2167.42,142.286 \n",
       "  2169.46,128.708 2171.5,101.554 2173.53,101.554 2175.57,115.131 2177.61,115.131 2179.64,87.9763 2181.68,101.554 2183.72,87.9763 2185.75,101.554 2187.79,128.708 \n",
       "  2189.83,115.131 2191.86,87.9763 2193.9,87.9763 2195.94,101.554 2197.97,101.554 2200.01,128.708 2202.05,128.708 2204.08,101.554 2206.12,87.9763 2208.16,101.554 \n",
       "  2210.19,115.131 2212.23,128.708 2214.27,115.131 2216.3,142.286 2218.34,128.708 2220.38,142.286 2222.41,115.131 2224.45,101.554 2226.49,101.554 2228.52,128.708 \n",
       "  2230.56,128.708 2232.6,128.708 2234.63,128.708 2236.67,169.441 2238.71,142.286 2240.74,101.554 2242.78,101.554 2244.81,115.131 2246.85,87.9763 2248.89,128.708 \n",
       "  2250.92,101.554 2252.96,115.131 2255,101.554 2257.03,142.286 2259.07,115.131 2261.11,115.131 2263.14,128.708 2265.18,115.131 2267.22,115.131 2269.25,101.554 \n",
       "  2271.29,128.708 2273.33,142.286 2275.36,101.554 2277.4,128.708 2279.44,115.131 2281.47,142.286 2283.51,128.708 2285.55,155.863 2287.58,169.441 2289.62,169.441 \n",
       "  2291.66,155.863 \n",
       "  \"/>\n",
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       "  1212.25,155.863 1214.28,142.286 1216.32,169.441 1218.36,155.863 1220.39,128.708 1222.43,115.131 1224.47,128.708 1226.5,142.286 1228.54,128.708 1230.58,101.554 \n",
       "  1232.61,87.9763 1234.65,128.708 1236.69,115.131 1238.72,115.131 1240.76,115.131 1242.8,155.863 1244.83,142.286 1246.87,128.708 1248.91,115.131 1250.94,115.131 \n",
       "  1252.98,115.131 1255.02,115.131 1257.05,101.554 1259.09,128.708 1261.13,115.131 1263.16,87.9763 1265.2,87.9763 1267.24,128.708 1269.27,128.708 1271.31,128.708 \n",
       "  1273.35,115.131 1275.38,115.131 1277.42,101.554 1279.46,101.554 1281.49,101.554 1283.53,87.9763 1285.57,87.9763 1287.6,101.554 1289.64,101.554 1291.68,87.9763 \n",
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       "  1314.08,115.131 1316.12,128.708 1318.15,128.708 1320.19,183.018 1322.22,183.018 1324.26,115.131 1326.3,87.9763 1328.33,101.554 1330.37,101.554 1332.41,101.554 \n",
       "  1334.44,87.9763 1336.48,115.131 1338.52,101.554 1340.55,115.131 1342.59,87.9763 1344.63,101.554 1346.66,101.554 1348.7,142.286 1350.74,128.708 1352.77,142.286 \n",
       "  1354.81,142.286 1356.85,142.286 1358.88,155.863 1360.92,115.131 1362.96,115.131 1364.99,115.131 1367.03,128.708 1369.07,155.863 1371.1,101.554 1373.14,101.554 \n",
       "  1375.18,87.9763 1377.21,115.131 1379.25,115.131 1381.29,87.9763 1383.32,142.286 1385.36,155.863 1387.4,101.554 1389.43,142.286 1391.47,155.863 1393.51,101.554 \n",
       "  1395.54,87.9763 1397.58,101.554 1399.62,101.554 1401.65,142.286 1403.69,142.286 1405.73,128.708 1407.76,155.863 1409.8,128.708 1411.84,128.708 1413.87,128.708 \n",
       "  1415.91,142.286 1417.95,169.441 1419.98,169.441 1422.02,128.708 1424.06,115.131 1426.09,142.286 1428.13,101.554 1430.17,87.9763 1432.2,87.9763 1434.24,115.131 \n",
       "  1436.28,87.9763 1438.31,101.554 1440.35,115.131 1442.39,115.131 1444.42,101.554 1446.46,101.554 1448.5,128.708 1450.53,142.286 1452.57,101.554 1454.61,115.131 \n",
       "  1456.64,115.131 1458.68,183.018 1460.72,128.708 1462.75,115.131 1464.79,115.131 1466.83,142.286 1468.86,142.286 1470.9,115.131 1472.93,101.554 1474.97,155.863 \n",
       "  1477.01,155.863 1479.04,142.286 1481.08,115.131 1483.12,142.286 1485.15,128.708 1487.19,87.9763 1489.23,87.9763 1491.26,101.554 1493.3,101.554 1495.34,115.131 \n",
       "  1497.37,142.286 1499.41,115.131 1501.45,101.554 1503.48,115.131 1505.52,115.131 1507.56,128.708 1509.59,87.9763 1511.63,101.554 1513.67,87.9763 1515.7,101.554 \n",
       "  1517.74,115.131 1519.78,128.708 1521.81,87.9763 1523.85,101.554 1525.89,142.286 1527.92,87.9763 1529.96,115.131 1532,115.131 1534.03,101.554 1536.07,128.708 \n",
       "  1538.11,128.708 1540.14,101.554 1542.18,115.131 1544.22,128.708 1546.25,115.131 1548.29,87.9763 1550.33,101.554 1552.36,115.131 1554.4,115.131 1556.44,128.708 \n",
       "  1558.47,115.131 1560.51,101.554 1562.55,115.131 1564.58,115.131 1566.62,142.286 1568.66,115.131 1570.69,128.708 1572.73,101.554 1574.77,115.131 1576.8,115.131 \n",
       "  1578.84,115.131 1580.88,169.441 1582.91,128.708 1584.95,169.441 1586.99,169.441 1589.02,155.863 1591.06,155.863 1593.1,128.708 1595.13,115.131 1597.17,128.708 \n",
       "  1599.21,101.554 1601.24,128.708 1603.28,128.708 1605.32,142.286 1607.35,128.708 1609.39,142.286 1611.43,169.441 1613.46,155.863 1615.5,115.131 1617.54,142.286 \n",
       "  1619.57,142.286 1621.61,115.131 1623.65,115.131 1625.68,115.131 1627.72,128.708 1629.75,115.131 1631.79,169.441 1633.83,183.018 1635.86,115.131 1637.9,115.131 \n",
       "  1639.94,101.554 1641.97,101.554 1644.01,87.9763 1646.05,87.9763 1648.08,101.554 1650.12,101.554 1652.16,115.131 1654.19,101.554 1656.23,115.131 1658.27,128.708 \n",
       "  1660.3,128.708 1662.34,115.131 1664.38,128.708 1666.41,115.131 1668.45,142.286 1670.49,101.554 1672.52,87.9763 1674.56,128.708 1676.6,101.554 1678.63,87.9763 \n",
       "  1680.67,87.9763 1682.71,115.131 1684.74,142.286 1686.78,115.131 1688.82,115.131 1690.85,87.9763 1692.89,115.131 1694.93,183.018 1696.96,128.708 1699,155.863 \n",
       "  1701.04,155.863 1703.07,142.286 1705.11,183.018 1707.15,115.131 1709.18,128.708 1711.22,115.131 1713.26,115.131 1715.29,101.554 1717.33,87.9763 1719.37,115.131 \n",
       "  1721.4,101.554 1723.44,115.131 1725.48,87.9763 1727.51,101.554 1729.55,115.131 1731.59,87.9763 1733.62,101.554 1735.66,101.554 1737.7,87.9763 1739.73,115.131 \n",
       "  1741.77,128.708 1743.81,101.554 1745.84,128.708 1747.88,128.708 1749.92,128.708 1751.95,142.286 1753.99,128.708 1756.03,128.708 1758.06,142.286 1760.1,101.554 \n",
       "  1762.14,115.131 1764.17,101.554 1766.21,128.708 1768.25,101.554 1770.28,101.554 1772.32,115.131 1774.36,155.863 1776.39,142.286 1778.43,142.286 1780.46,155.863 \n",
       "  1782.5,155.863 1784.54,101.554 1786.57,142.286 1788.61,142.286 1790.65,128.708 1792.68,128.708 1794.72,142.286 1796.76,155.863 1798.79,183.018 1800.83,155.863 \n",
       "  1802.87,115.131 1804.9,87.9763 1806.94,87.9763 1808.98,87.9763 1811.01,101.554 1813.05,101.554 1815.09,101.554 1817.12,115.131 1819.16,128.708 1821.2,142.286 \n",
       "  1823.23,128.708 1825.27,115.131 1827.31,101.554 1829.34,87.9763 1831.38,128.708 1833.42,101.554 1835.45,87.9763 1837.49,101.554 1839.53,128.708 1841.56,128.708 \n",
       "  1843.6,142.286 1845.64,101.554 1847.67,142.286 1849.71,128.708 1851.75,87.9763 1853.78,87.9763 1855.82,101.554 1857.86,115.131 1859.89,87.9763 1861.93,115.131 \n",
       "  1863.97,101.554 1866,101.554 1868.04,115.131 1870.08,142.286 1872.11,142.286 1874.15,169.441 1876.19,128.708 1878.22,115.131 1880.26,142.286 1882.3,128.708 \n",
       "  1884.33,115.131 1886.37,142.286 1888.41,115.131 1890.44,101.554 1892.48,101.554 1894.52,128.708 1896.55,155.863 1898.59,142.286 1900.63,115.131 1902.66,142.286 \n",
       "  1904.7,155.863 1906.74,101.554 1908.77,101.554 1910.81,101.554 1912.85,87.9763 1914.88,115.131 1916.92,87.9763 1918.96,101.554 1920.99,115.131 1923.03,142.286 \n",
       "  1925.07,115.131 1927.1,101.554 1929.14,142.286 1931.18,101.554 1933.21,115.131 1935.25,101.554 1937.28,169.441 1939.32,183.018 1941.36,210.173 1943.39,210.173 \n",
       "  1945.43,115.131 1947.47,115.131 1949.5,115.131 1951.54,128.708 1953.58,142.286 1955.61,101.554 1957.65,115.131 1959.69,142.286 1961.72,101.554 1963.76,101.554 \n",
       "  1965.8,115.131 1967.83,128.708 1969.87,115.131 1971.91,115.131 1973.94,87.9763 1975.98,101.554 1978.02,128.708 1980.05,169.441 1982.09,155.863 1984.13,128.708 \n",
       "  1986.16,101.554 1988.2,128.708 1990.24,87.9763 1992.27,101.554 1994.31,101.554 1996.35,87.9763 1998.38,101.554 2000.42,142.286 2002.46,128.708 2004.49,128.708 \n",
       "  2006.53,87.9763 2008.57,87.9763 2010.6,87.9763 2012.64,115.131 2014.68,101.554 2016.71,142.286 2018.75,115.131 2020.79,142.286 2022.82,101.554 2024.86,101.554 \n",
       "  2026.9,115.131 2028.93,101.554 2030.97,101.554 2033.01,142.286 2035.04,115.131 2037.08,101.554 2039.12,87.9763 2041.15,128.708 2043.19,155.863 2045.23,155.863 \n",
       "  2047.26,115.131 2049.3,128.708 2051.34,128.708 2053.37,128.708 2055.41,128.708 2057.45,128.708 2059.48,87.9763 2061.52,101.554 2063.56,155.863 2065.59,115.131 \n",
       "  2067.63,128.708 2069.67,155.863 2071.7,142.286 2073.74,142.286 2075.78,169.441 2077.81,155.863 2079.85,142.286 2081.89,87.9763 2083.92,101.554 2085.96,128.708 \n",
       "  2087.99,128.708 2090.03,210.173 2092.07,142.286 2094.1,128.708 2096.14,128.708 2098.18,169.441 2100.21,128.708 2102.25,128.708 2104.29,101.554 2106.32,101.554 \n",
       "  2108.36,128.708 2110.4,142.286 2112.43,87.9763 2114.47,101.554 2116.51,115.131 2118.54,101.554 2120.58,101.554 2122.62,142.286 2124.65,115.131 2126.69,115.131 \n",
       "  2128.73,142.286 2130.76,142.286 2132.8,115.131 2134.84,101.554 2136.87,128.708 2138.91,142.286 2140.95,183.018 2142.98,169.441 2145.02,169.441 2147.06,169.441 \n",
       "  2149.09,115.131 2151.13,87.9763 2153.17,169.441 2155.2,115.131 2157.24,87.9763 2159.28,87.9763 2161.31,115.131 2163.35,87.9763 2165.39,101.554 2167.42,101.554 \n",
       "  2169.46,87.9763 2171.5,101.554 2173.53,101.554 2175.57,87.9763 2177.61,101.554 2179.64,101.554 2181.68,87.9763 2183.72,142.286 2185.75,183.018 2187.79,128.708 \n",
       "  2189.83,115.131 2191.86,142.286 2193.9,115.131 2195.94,115.131 2197.97,115.131 2200.01,115.131 2202.05,142.286 2204.08,142.286 2206.12,142.286 2208.16,142.286 \n",
       "  2210.19,101.554 2212.23,115.131 2214.27,101.554 2216.3,169.441 2218.34,155.863 2220.38,142.286 2222.41,142.286 2224.45,169.441 2226.49,128.708 2228.52,142.286 \n",
       "  2230.56,142.286 2232.6,142.286 2234.63,155.863 2236.67,101.554 2238.71,87.9763 2240.74,115.131 2242.78,155.863 2244.81,142.286 2246.85,115.131 2248.89,101.554 \n",
       "  2250.92,142.286 2252.96,115.131 2255,128.708 2257.03,87.9763 2259.07,101.554 2261.11,101.554 2263.14,115.131 2265.18,115.131 2267.22,87.9763 2269.25,128.708 \n",
       "  2271.29,128.708 2273.33,128.708 2275.36,101.554 2277.4,115.131 2279.44,128.708 2281.47,155.863 2283.51,196.595 2285.55,115.131 2287.58,128.708 2289.62,101.554 \n",
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       "  947.486,1418.56 949.523,1418.56 951.56,1445.72 953.596,1432.14 955.633,1377.83 957.669,1391.41 959.706,1445.72 961.743,1445.72 963.779,1432.14 965.816,1418.56 \n",
       "  967.853,1418.56 969.889,1445.72 971.926,1404.98 973.962,1404.98 975.999,1404.98 978.036,1391.41 980.072,1404.98 982.109,1391.41 984.146,1377.83 986.182,1391.41 \n",
       "  988.219,1418.56 990.255,1391.41 992.292,1418.56 994.329,1432.14 996.365,1432.14 998.402,1404.98 1000.44,1377.83 1002.48,1445.72 1004.51,1418.56 1006.55,1445.72 \n",
       "  1008.59,1404.98 1010.62,1432.14 1012.66,1432.14 1014.69,1432.14 1016.73,1445.72 1018.77,1445.72 1020.8,1418.56 1022.84,1418.56 1024.88,1377.83 1026.91,1391.41 \n",
       "  1028.95,1364.25 1030.99,1418.56 1033.02,1432.14 1035.06,1432.14 1037.1,1432.14 1039.13,1432.14 1041.17,1432.14 1043.21,1404.98 1045.24,1418.56 1047.28,1445.72 \n",
       "  1049.32,1432.14 1051.35,1432.14 1053.39,1445.72 1055.43,1418.56 1057.46,1404.98 1059.5,1404.98 1061.54,1404.98 1063.57,1418.56 1065.61,1418.56 1067.65,1418.56 \n",
       "  1069.68,1445.72 1071.72,1418.56 1073.76,1404.98 1075.79,1432.14 1077.83,1418.56 1079.87,1418.56 1081.9,1391.41 1083.94,1404.98 1085.98,1404.98 1088.01,1377.83 \n",
       "  1090.05,1418.56 1092.09,1391.41 1094.12,1404.98 1096.16,1418.56 1098.2,1418.56 1100.23,1404.98 1102.27,1418.56 1104.31,1445.72 1106.34,1404.98 1108.38,1391.41 \n",
       "  1110.42,1391.41 1112.45,1432.14 1114.49,1432.14 1116.53,1418.56 1118.56,1418.56 1120.6,1445.72 1122.64,1418.56 1124.67,1432.14 1126.71,1445.72 1128.75,1404.98 \n",
       "  1130.78,1391.41 1132.82,1337.1 1134.86,1391.41 1136.89,1404.98 1138.93,1404.98 1140.97,1445.72 1143,1404.98 1145.04,1432.14 1147.08,1418.56 1149.11,1364.25 \n",
       "  1151.15,1391.41 1153.19,1418.56 1155.22,1418.56 1157.26,1391.41 1159.3,1377.83 1161.33,1364.25 1163.37,1404.98 1165.4,1432.14 1167.44,1432.14 1169.48,1445.72 \n",
       "  1171.51,1432.14 1173.55,1404.98 1175.59,1391.41 1177.62,1418.56 1179.66,1404.98 1181.7,1404.98 1183.73,1445.72 1185.77,1445.72 1187.81,1391.41 1189.84,1418.56 \n",
       "  1191.88,1445.72 1193.92,1418.56 1195.95,1404.98 1197.99,1432.14 1200.03,1432.14 1202.06,1404.98 1204.1,1404.98 1206.14,1418.56 1208.17,1432.14 1210.21,1445.72 \n",
       "  1212.25,1418.56 1214.28,1404.98 1216.32,1404.98 1218.36,1418.56 1220.39,1404.98 1222.43,1391.41 1224.47,1391.41 1226.5,1418.56 1228.54,1404.98 1230.58,1432.14 \n",
       "  1232.61,1445.72 1234.65,1445.72 1236.69,1445.72 1238.72,1432.14 1240.76,1432.14 1242.8,1432.14 1244.83,1404.98 1246.87,1377.83 1248.91,1364.25 1250.94,1350.67 \n",
       "  1252.98,1337.1 1255.02,1350.67 1257.05,1391.41 1259.09,1364.25 1261.13,1391.41 1263.16,1377.83 1265.2,1377.83 1267.24,1364.25 1269.27,1350.67 1271.31,1364.25 \n",
       "  1273.35,1364.25 1275.38,1418.56 1277.42,1391.41 1279.46,1418.56 1281.49,1432.14 1283.53,1445.72 1285.57,1445.72 1287.6,1432.14 1289.64,1377.83 1291.68,1391.41 \n",
       "  1293.71,1432.14 1295.75,1432.14 1297.79,1432.14 1299.82,1404.98 1301.86,1432.14 1303.9,1377.83 1305.93,1377.83 1307.97,1391.41 1310.01,1404.98 1312.04,1432.14 \n",
       "  1314.08,1418.56 1316.12,1445.72 1318.15,1432.14 1320.19,1418.56 1322.22,1391.41 1324.26,1418.56 1326.3,1404.98 1328.33,1404.98 1330.37,1391.41 1332.41,1432.14 \n",
       "  1334.44,1418.56 1336.48,1418.56 1338.52,1432.14 1340.55,1432.14 1342.59,1404.98 1344.63,1391.41 1346.66,1432.14 1348.7,1418.56 1350.74,1432.14 1352.77,1445.72 \n",
       "  1354.81,1445.72 1356.85,1418.56 1358.88,1418.56 1360.92,1445.72 1362.96,1445.72 1364.99,1418.56 1367.03,1432.14 1369.07,1377.83 1371.1,1323.52 1373.14,1377.83 \n",
       "  1375.18,1391.41 1377.21,1432.14 1379.25,1404.98 1381.29,1377.83 1383.32,1377.83 1385.36,1404.98 1387.4,1432.14 1389.43,1432.14 1391.47,1432.14 1393.51,1445.72 \n",
       "  1395.54,1432.14 1397.58,1418.56 1399.62,1377.83 1401.65,1432.14 1403.69,1432.14 1405.73,1377.83 1407.76,1418.56 1409.8,1418.56 1411.84,1418.56 1413.87,1432.14 \n",
       "  1415.91,1432.14 1417.95,1391.41 1419.98,1391.41 1422.02,1418.56 1424.06,1432.14 1426.09,1418.56 1428.13,1445.72 1430.17,1432.14 1432.2,1445.72 1434.24,1432.14 \n",
       "  1436.28,1418.56 1438.31,1432.14 1440.35,1445.72 1442.39,1445.72 1444.42,1445.72 1446.46,1445.72 1448.5,1404.98 1450.53,1418.56 1452.57,1432.14 1454.61,1404.98 \n",
       "  1456.64,1432.14 1458.68,1432.14 1460.72,1432.14 1462.75,1432.14 1464.79,1418.56 1466.83,1418.56 1468.86,1391.41 1470.9,1418.56 1472.93,1432.14 1474.97,1377.83 \n",
       "  1477.01,1377.83 1479.04,1432.14 1481.08,1445.72 1483.12,1445.72 1485.15,1418.56 1487.19,1445.72 1489.23,1418.56 1491.26,1418.56 1493.3,1445.72 1495.34,1445.72 \n",
       "  1497.37,1432.14 1499.41,1418.56 1501.45,1391.41 1503.48,1418.56 1505.52,1391.41 1507.56,1391.41 1509.59,1404.98 1511.63,1418.56 1513.67,1418.56 1515.7,1418.56 \n",
       "  1517.74,1418.56 1519.78,1445.72 1521.81,1445.72 1523.85,1445.72 1525.89,1432.14 1527.92,1445.72 1529.96,1432.14 1532,1377.83 1534.03,1337.1 1536.07,1391.41 \n",
       "  1538.11,1391.41 1540.14,1418.56 1542.18,1418.56 1544.22,1418.56 1546.25,1391.41 1548.29,1418.56 1550.33,1418.56 1552.36,1404.98 1554.4,1404.98 1556.44,1404.98 \n",
       "  1558.47,1432.14 1560.51,1445.72 1562.55,1445.72 1564.58,1432.14 1566.62,1432.14 1568.66,1418.56 1570.69,1404.98 1572.73,1418.56 1574.77,1404.98 1576.8,1391.41 \n",
       "  1578.84,1418.56 1580.88,1445.72 1582.91,1432.14 1584.95,1432.14 1586.99,1418.56 1589.02,1391.41 1591.06,1404.98 1593.1,1377.83 1595.13,1391.41 1597.17,1418.56 \n",
       "  1599.21,1445.72 1601.24,1445.72 1603.28,1445.72 1605.32,1445.72 1607.35,1432.14 1609.39,1418.56 1611.43,1445.72 1613.46,1445.72 1615.5,1391.41 1617.54,1350.67 \n",
       "  1619.57,1364.25 1621.61,1377.83 1623.65,1377.83 1625.68,1377.83 1627.72,1404.98 1629.75,1404.98 1631.79,1432.14 1633.83,1445.72 1635.86,1377.83 1637.9,1404.98 \n",
       "  1639.94,1445.72 1641.97,1391.41 1644.01,1418.56 1646.05,1418.56 1648.08,1418.56 1650.12,1377.83 1652.16,1391.41 1654.19,1418.56 1656.23,1391.41 1658.27,1377.83 \n",
       "  1660.3,1432.14 1662.34,1418.56 1664.38,1404.98 1666.41,1418.56 1668.45,1391.41 1670.49,1432.14 1672.52,1445.72 1674.56,1404.98 1676.6,1404.98 1678.63,1432.14 \n",
       "  1680.67,1391.41 1682.71,1418.56 1684.74,1377.83 1686.78,1418.56 1688.82,1404.98 1690.85,1377.83 1692.89,1391.41 1694.93,1404.98 1696.96,1432.14 1699,1445.72 \n",
       "  1701.04,1418.56 1703.07,1391.41 1705.11,1377.83 1707.15,1391.41 1709.18,1432.14 1711.22,1404.98 1713.26,1377.83 1715.29,1391.41 1717.33,1445.72 1719.37,1445.72 \n",
       "  1721.4,1445.72 1723.44,1445.72 1725.48,1432.14 1727.51,1445.72 1729.55,1404.98 1731.59,1418.56 1733.62,1445.72 1735.66,1404.98 1737.7,1445.72 1739.73,1445.72 \n",
       "  1741.77,1445.72 1743.81,1432.14 1745.84,1350.67 1747.88,1350.67 1749.92,1418.56 1751.95,1418.56 1753.99,1391.41 1756.03,1391.41 1758.06,1404.98 1760.1,1391.41 \n",
       "  1762.14,1432.14 1764.17,1418.56 1766.21,1404.98 1768.25,1377.83 1770.28,1432.14 1772.32,1432.14 1774.36,1432.14 1776.39,1418.56 1778.43,1418.56 1780.46,1377.83 \n",
       "  1782.5,1445.72 1784.54,1445.72 1786.57,1445.72 1788.61,1445.72 1790.65,1432.14 1792.68,1418.56 1794.72,1404.98 1796.76,1418.56 1798.79,1364.25 1800.83,1418.56 \n",
       "  1802.87,1418.56 1804.9,1418.56 1806.94,1418.56 1808.98,1404.98 1811.01,1418.56 1813.05,1418.56 1815.09,1418.56 1817.12,1445.72 1819.16,1445.72 1821.2,1432.14 \n",
       "  1823.23,1432.14 1825.27,1445.72 1827.31,1432.14 1829.34,1432.14 1831.38,1391.41 1833.42,1391.41 1835.45,1391.41 1837.49,1391.41 1839.53,1432.14 1841.56,1404.98 \n",
       "  1843.6,1404.98 1845.64,1391.41 1847.67,1418.56 1849.71,1391.41 1851.75,1391.41 1853.78,1432.14 1855.82,1391.41 1857.86,1323.52 1859.89,1337.1 1861.93,1309.94 \n",
       "  1863.97,1391.41 1866,1432.14 1868.04,1445.72 1870.08,1391.41 1872.11,1377.83 1874.15,1418.56 1876.19,1445.72 1878.22,1418.56 1880.26,1432.14 1882.3,1432.14 \n",
       "  1884.33,1418.56 1886.37,1418.56 1888.41,1391.41 1890.44,1432.14 1892.48,1404.98 1894.52,1418.56 1896.55,1418.56 1898.59,1404.98 1900.63,1432.14 1902.66,1432.14 \n",
       "  1904.7,1418.56 1906.74,1404.98 1908.77,1418.56 1910.81,1432.14 1912.85,1445.72 1914.88,1432.14 1916.92,1445.72 1918.96,1391.41 1920.99,1391.41 1923.03,1418.56 \n",
       "  1925.07,1445.72 1927.1,1432.14 1929.14,1404.98 1931.18,1418.56 1933.21,1377.83 1935.25,1432.14 1937.28,1404.98 1939.32,1404.98 1941.36,1432.14 1943.39,1404.98 \n",
       "  1945.43,1404.98 1947.47,1404.98 1949.5,1404.98 1951.54,1418.56 1953.58,1432.14 1955.61,1432.14 1957.65,1432.14 1959.69,1432.14 1961.72,1418.56 1963.76,1391.41 \n",
       "  1965.8,1391.41 1967.83,1445.72 1969.87,1445.72 1971.91,1432.14 1973.94,1418.56 1975.98,1364.25 1978.02,1391.41 1980.05,1418.56 1982.09,1418.56 1984.13,1404.98 \n",
       "  1986.16,1377.83 1988.2,1377.83 1990.24,1391.41 1992.27,1377.83 1994.31,1377.83 1996.35,1377.83 1998.38,1377.83 2000.42,1364.25 2002.46,1377.83 2004.49,1377.83 \n",
       "  2006.53,1377.83 2008.57,1391.41 2010.6,1432.14 2012.64,1418.56 2014.68,1445.72 2016.71,1432.14 2018.75,1445.72 2020.79,1432.14 2022.82,1445.72 2024.86,1432.14 \n",
       "  2026.9,1418.56 2028.93,1404.98 2030.97,1404.98 2033.01,1391.41 2035.04,1391.41 2037.08,1418.56 2039.12,1418.56 2041.15,1432.14 2043.19,1404.98 2045.23,1432.14 \n",
       "  2047.26,1445.72 2049.3,1418.56 2051.34,1432.14 2053.37,1404.98 2055.41,1432.14 2057.45,1418.56 2059.48,1418.56 2061.52,1418.56 2063.56,1350.67 2065.59,1364.25 \n",
       "  2067.63,1432.14 2069.67,1432.14 2071.7,1445.72 2073.74,1445.72 2075.78,1445.72 2077.81,1418.56 2079.85,1432.14 2081.89,1445.72 2083.92,1445.72 2085.96,1432.14 \n",
       "  2087.99,1391.41 2090.03,1404.98 2092.07,1432.14 2094.1,1432.14 2096.14,1418.56 2098.18,1418.56 2100.21,1418.56 2102.25,1445.72 2104.29,1418.56 2106.32,1432.14 \n",
       "  2108.36,1432.14 2110.4,1418.56 2112.43,1418.56 2114.47,1364.25 2116.51,1404.98 2118.54,1418.56 2120.58,1418.56 2122.62,1391.41 2124.65,1404.98 2126.69,1418.56 \n",
       "  2128.73,1432.14 2130.76,1432.14 2132.8,1432.14 2134.84,1404.98 2136.87,1432.14 2138.91,1432.14 2140.95,1432.14 2142.98,1418.56 2145.02,1391.41 2147.06,1391.41 \n",
       "  2149.09,1377.83 2151.13,1391.41 2153.17,1377.83 2155.2,1377.83 2157.24,1418.56 2159.28,1432.14 2161.31,1432.14 2163.35,1418.56 2165.39,1418.56 2167.42,1404.98 \n",
       "  2169.46,1391.41 2171.5,1364.25 2173.53,1377.83 2175.57,1350.67 2177.61,1418.56 2179.64,1432.14 2181.68,1445.72 2183.72,1445.72 2185.75,1432.14 2187.79,1404.98 \n",
       "  2189.83,1391.41 2191.86,1391.41 2193.9,1418.56 2195.94,1418.56 2197.97,1432.14 2200.01,1432.14 2202.05,1432.14 2204.08,1432.14 2206.12,1432.14 2208.16,1432.14 \n",
       "  2210.19,1418.56 2212.23,1418.56 2214.27,1445.72 2216.3,1418.56 2218.34,1404.98 2220.38,1418.56 2222.41,1418.56 2224.45,1391.41 2226.49,1377.83 2228.52,1418.56 \n",
       "  2230.56,1404.98 2232.6,1432.14 2234.63,1432.14 2236.67,1391.41 2238.71,1432.14 2240.74,1432.14 2242.78,1432.14 2244.81,1418.56 2246.85,1445.72 2248.89,1418.56 \n",
       "  2250.92,1404.98 2252.96,1404.98 2255,1350.67 2257.03,1364.25 2259.07,1377.83 2261.11,1404.98 2263.14,1418.56 2265.18,1418.56 2267.22,1432.14 2269.25,1432.14 \n",
       "  2271.29,1445.72 2273.33,1418.56 2275.36,1445.72 2277.4,1377.83 2279.44,1418.56 2281.47,1364.25 2283.51,1404.98 2285.55,1432.14 2287.58,1432.14 2289.62,1432.14 \n",
       "  2291.66,1445.72 \n",
       "  \"/>\n",
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       "  275.401,1418.56 277.438,1404.98 279.474,1432.14 281.511,1391.41 283.547,1404.98 285.584,1404.98 287.621,1391.41 289.657,1377.83 291.694,1418.56 293.731,1432.14 \n",
       "  295.767,1432.14 297.804,1432.14 299.84,1418.56 301.877,1404.98 303.914,1364.25 305.95,1391.41 307.987,1404.98 310.023,1418.56 312.06,1404.98 314.097,1418.56 \n",
       "  316.133,1404.98 318.17,1445.72 320.207,1445.72 322.243,1445.72 324.28,1432.14 326.316,1418.56 328.353,1404.98 330.39,1418.56 332.426,1404.98 334.463,1404.98 \n",
       "  336.5,1404.98 338.536,1418.56 340.573,1432.14 342.609,1418.56 344.646,1432.14 346.683,1404.98 348.719,1418.56 350.756,1432.14 352.793,1432.14 354.829,1404.98 \n",
       "  356.866,1391.41 358.902,1404.98 360.939,1432.14 362.976,1432.14 365.012,1418.56 367.049,1404.98 369.086,1418.56 371.122,1432.14 373.159,1432.14 375.195,1418.56 \n",
       "  377.232,1391.41 379.269,1404.98 381.305,1391.41 383.342,1391.41 385.379,1445.72 387.415,1404.98 389.452,1418.56 391.488,1418.56 393.525,1432.14 395.562,1404.98 \n",
       "  397.598,1418.56 399.635,1418.56 401.671,1404.98 403.708,1432.14 405.745,1432.14 407.781,1445.72 409.818,1391.41 411.855,1404.98 413.891,1404.98 415.928,1404.98 \n",
       "  417.964,1432.14 420.001,1418.56 422.038,1391.41 424.074,1418.56 426.111,1404.98 428.148,1404.98 430.184,1418.56 432.221,1377.83 434.257,1404.98 436.294,1391.41 \n",
       "  438.331,1432.14 440.367,1418.56 442.404,1404.98 444.441,1418.56 446.477,1404.98 448.514,1418.56 450.55,1418.56 452.587,1418.56 454.624,1418.56 456.66,1404.98 \n",
       "  458.697,1432.14 460.734,1377.83 462.77,1364.25 464.807,1418.56 466.843,1404.98 468.88,1404.98 470.917,1404.98 472.953,1432.14 474.99,1404.98 477.027,1404.98 \n",
       "  479.063,1432.14 481.1,1404.98 483.136,1418.56 485.173,1391.41 487.21,1364.25 489.246,1364.25 491.283,1391.41 493.32,1377.83 495.356,1377.83 497.393,1391.41 \n",
       "  499.429,1391.41 501.466,1418.56 503.503,1404.98 505.539,1418.56 507.576,1418.56 509.612,1377.83 511.649,1350.67 513.686,1364.25 515.722,1364.25 517.759,1323.52 \n",
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       "  540.162,1445.72 542.198,1432.14 544.235,1391.41 546.272,1364.25 548.308,1391.41 550.345,1404.98 552.382,1391.41 554.418,1391.41 556.455,1404.98 558.491,1391.41 \n",
       "  560.528,1391.41 562.565,1404.98 564.601,1445.72 566.638,1432.14 568.675,1432.14 570.711,1432.14 572.748,1445.72 574.784,1432.14 576.821,1418.56 578.858,1432.14 \n",
       "  580.894,1445.72 582.931,1445.72 584.968,1432.14 587.004,1418.56 589.041,1418.56 591.077,1432.14 593.114,1418.56 595.151,1404.98 597.187,1432.14 599.224,1418.56 \n",
       "  601.261,1432.14 603.297,1418.56 605.334,1432.14 607.37,1445.72 609.407,1432.14 611.444,1418.56 613.48,1432.14 615.517,1404.98 617.553,1418.56 619.59,1391.41 \n",
       "  621.627,1391.41 623.663,1445.72 625.7,1404.98 627.737,1445.72 629.773,1418.56 631.81,1391.41 633.846,1418.56 635.883,1432.14 637.92,1432.14 639.956,1445.72 \n",
       "  641.993,1404.98 644.03,1404.98 646.066,1404.98 648.103,1445.72 650.139,1445.72 652.176,1432.14 654.213,1432.14 656.249,1445.72 658.286,1432.14 660.323,1418.56 \n",
       "  662.359,1445.72 664.396,1445.72 666.432,1391.41 668.469,1404.98 670.506,1432.14 672.542,1445.72 674.579,1404.98 676.616,1404.98 678.652,1404.98 680.689,1432.14 \n",
       "  682.725,1445.72 684.762,1418.56 686.799,1445.72 688.835,1418.56 690.872,1404.98 692.909,1418.56 694.945,1418.56 696.982,1432.14 699.018,1432.14 701.055,1432.14 \n",
       "  703.092,1404.98 705.128,1445.72 707.165,1445.72 709.202,1445.72 711.238,1445.72 713.275,1445.72 715.311,1418.56 717.348,1432.14 719.385,1418.56 721.421,1418.56 \n",
       "  723.458,1432.14 725.494,1418.56 727.531,1418.56 729.568,1432.14 731.604,1377.83 733.641,1418.56 735.678,1418.56 737.714,1432.14 739.751,1432.14 741.787,1391.41 \n",
       "  743.824,1391.41 745.861,1432.14 747.897,1432.14 749.934,1418.56 751.971,1418.56 754.007,1432.14 756.044,1418.56 758.08,1391.41 760.117,1404.98 762.154,1391.41 \n",
       "  764.19,1377.83 766.227,1391.41 768.264,1364.25 770.3,1337.1 772.337,1377.83 774.373,1432.14 776.41,1445.72 778.447,1432.14 780.483,1432.14 782.52,1418.56 \n",
       "  784.557,1377.83 786.593,1404.98 788.63,1404.98 790.666,1418.56 792.703,1432.14 794.74,1445.72 796.776,1432.14 798.813,1432.14 800.85,1418.56 802.886,1432.14 \n",
       "  804.923,1418.56 806.959,1391.41 808.996,1418.56 811.033,1432.14 813.069,1432.14 815.106,1445.72 817.142,1445.72 819.179,1432.14 821.216,1418.56 823.252,1432.14 \n",
       "  825.289,1418.56 827.326,1404.98 829.362,1432.14 831.399,1404.98 833.435,1432.14 835.472,1432.14 837.509,1432.14 839.545,1404.98 841.582,1432.14 843.619,1432.14 \n",
       "  845.655,1445.72 847.692,1418.56 849.728,1432.14 851.765,1404.98 853.802,1445.72 855.838,1404.98 857.875,1445.72 859.912,1432.14 861.948,1404.98 863.985,1432.14 \n",
       "  866.021,1391.41 868.058,1418.56 870.095,1432.14 872.131,1445.72 874.168,1445.72 876.205,1432.14 878.241,1445.72 880.278,1418.56 882.314,1418.56 884.351,1418.56 \n",
       "  886.388,1391.41 888.424,1445.72 890.461,1445.72 892.498,1432.14 894.534,1432.14 896.571,1432.14 898.607,1404.98 900.644,1404.98 902.681,1391.41 904.717,1404.98 \n",
       "  906.754,1404.98 908.791,1391.41 910.827,1377.83 912.864,1391.41 914.9,1418.56 916.937,1391.41 918.974,1432.14 921.01,1418.56 923.047,1418.56 925.083,1418.56 \n",
       "  927.12,1404.98 929.157,1404.98 931.193,1404.98 933.23,1418.56 935.267,1404.98 937.303,1404.98 939.34,1418.56 941.376,1418.56 943.413,1445.72 945.45,1445.72 \n",
       "  947.486,1445.72 949.523,1404.98 951.56,1391.41 953.596,1404.98 955.633,1391.41 957.669,1404.98 959.706,1418.56 961.743,1391.41 963.779,1404.98 965.816,1418.56 \n",
       "  967.853,1445.72 969.889,1432.14 971.926,1418.56 973.962,1432.14 975.999,1432.14 978.036,1445.72 980.072,1432.14 982.109,1432.14 984.146,1404.98 986.182,1404.98 \n",
       "  988.219,1432.14 990.255,1404.98 992.292,1391.41 994.329,1404.98 996.365,1418.56 998.402,1377.83 1000.44,1404.98 1002.48,1445.72 1004.51,1432.14 1006.55,1432.14 \n",
       "  1008.59,1432.14 1010.62,1418.56 1012.66,1377.83 1014.69,1377.83 1016.73,1418.56 1018.77,1445.72 1020.8,1418.56 1022.84,1404.98 1024.88,1445.72 1026.91,1418.56 \n",
       "  1028.95,1404.98 1030.99,1404.98 1033.02,1391.41 1035.06,1391.41 1037.1,1404.98 1039.13,1432.14 1041.17,1404.98 1043.21,1432.14 1045.24,1418.56 1047.28,1432.14 \n",
       "  1049.32,1391.41 1051.35,1418.56 1053.39,1404.98 1055.43,1432.14 1057.46,1432.14 1059.5,1418.56 1061.54,1391.41 1063.57,1418.56 1065.61,1404.98 1067.65,1391.41 \n",
       "  1069.68,1391.41 1071.72,1391.41 1073.76,1377.83 1075.79,1377.83 1077.83,1418.56 1079.87,1418.56 1081.9,1391.41 1083.94,1418.56 1085.98,1418.56 1088.01,1377.83 \n",
       "  1090.05,1432.14 1092.09,1432.14 1094.12,1418.56 1096.16,1418.56 1098.2,1391.41 1100.23,1391.41 1102.27,1350.67 1104.31,1377.83 1106.34,1432.14 1108.38,1445.72 \n",
       "  1110.42,1432.14 1112.45,1418.56 1114.49,1404.98 1116.53,1445.72 1118.56,1432.14 1120.6,1432.14 1122.64,1432.14 1124.67,1432.14 1126.71,1418.56 1128.75,1418.56 \n",
       "  1130.78,1404.98 1132.82,1418.56 1134.86,1432.14 1136.89,1432.14 1138.93,1404.98 1140.97,1404.98 1143,1432.14 1145.04,1404.98 1147.08,1377.83 1149.11,1364.25 \n",
       "  1151.15,1377.83 1153.19,1418.56 1155.22,1445.72 1157.26,1418.56 1159.3,1404.98 1161.33,1404.98 1163.37,1418.56 1165.4,1445.72 1167.44,1432.14 1169.48,1432.14 \n",
       "  1171.51,1432.14 1173.55,1418.56 1175.59,1404.98 1177.62,1404.98 1179.66,1418.56 1181.7,1391.41 1183.73,1391.41 1185.77,1418.56 1187.81,1432.14 1189.84,1418.56 \n",
       "  1191.88,1418.56 1193.92,1418.56 1195.95,1432.14 1197.99,1432.14 1200.03,1432.14 1202.06,1391.41 1204.1,1391.41 1206.14,1404.98 1208.17,1418.56 1210.21,1377.83 \n",
       "  1212.25,1404.98 1214.28,1432.14 1216.32,1418.56 1218.36,1418.56 1220.39,1432.14 1222.43,1418.56 1224.47,1391.41 1226.5,1432.14 1228.54,1404.98 1230.58,1404.98 \n",
       "  1232.61,1432.14 1234.65,1432.14 1236.69,1418.56 1238.72,1404.98 1240.76,1432.14 1242.8,1418.56 1244.83,1432.14 1246.87,1432.14 1248.91,1432.14 1250.94,1432.14 \n",
       "  1252.98,1432.14 1255.02,1377.83 1257.05,1418.56 1259.09,1404.98 1261.13,1418.56 1263.16,1418.56 1265.2,1432.14 1267.24,1445.72 1269.27,1432.14 1271.31,1432.14 \n",
       "  1273.35,1404.98 1275.38,1432.14 1277.42,1404.98 1279.46,1404.98 1281.49,1391.41 1283.53,1418.56 1285.57,1404.98 1287.6,1445.72 1289.64,1432.14 1291.68,1418.56 \n",
       "  1293.71,1404.98 1295.75,1404.98 1297.79,1404.98 1299.82,1377.83 1301.86,1364.25 1303.9,1418.56 1305.93,1391.41 1307.97,1391.41 1310.01,1432.14 1312.04,1445.72 \n",
       "  1314.08,1418.56 1316.12,1445.72 1318.15,1418.56 1320.19,1432.14 1322.22,1445.72 1324.26,1432.14 1326.3,1418.56 1328.33,1404.98 1330.37,1418.56 1332.41,1432.14 \n",
       "  1334.44,1432.14 1336.48,1432.14 1338.52,1445.72 1340.55,1445.72 1342.59,1432.14 1344.63,1418.56 1346.66,1404.98 1348.7,1445.72 1350.74,1445.72 1352.77,1418.56 \n",
       "  1354.81,1418.56 1356.85,1404.98 1358.88,1404.98 1360.92,1404.98 1362.96,1432.14 1364.99,1404.98 1367.03,1364.25 1369.07,1391.41 1371.1,1404.98 1373.14,1432.14 \n",
       "  1375.18,1418.56 1377.21,1391.41 1379.25,1404.98 1381.29,1404.98 1383.32,1418.56 1385.36,1404.98 1387.4,1404.98 1389.43,1445.72 1391.47,1445.72 1393.51,1404.98 \n",
       "  1395.54,1364.25 1397.58,1364.25 1399.62,1404.98 1401.65,1432.14 1403.69,1404.98 1405.73,1391.41 1407.76,1404.98 1409.8,1432.14 1411.84,1404.98 1413.87,1404.98 \n",
       "  1415.91,1377.83 1417.95,1391.41 1419.98,1404.98 1422.02,1404.98 1424.06,1404.98 1426.09,1432.14 1428.13,1445.72 1430.17,1432.14 1432.2,1418.56 1434.24,1404.98 \n",
       "  1436.28,1404.98 1438.31,1418.56 1440.35,1432.14 1442.39,1445.72 1444.42,1445.72 1446.46,1445.72 1448.5,1404.98 1450.53,1404.98 1452.57,1445.72 1454.61,1432.14 \n",
       "  1456.64,1432.14 1458.68,1445.72 1460.72,1445.72 1462.75,1445.72 1464.79,1445.72 1466.83,1418.56 1468.86,1445.72 1470.9,1391.41 1472.93,1418.56 1474.97,1432.14 \n",
       "  1477.01,1418.56 1479.04,1432.14 1481.08,1432.14 1483.12,1445.72 1485.15,1418.56 1487.19,1445.72 1489.23,1404.98 1491.26,1432.14 1493.3,1391.41 1495.34,1432.14 \n",
       "  1497.37,1445.72 1499.41,1418.56 1501.45,1432.14 1503.48,1432.14 1505.52,1445.72 1507.56,1404.98 1509.59,1418.56 1511.63,1418.56 1513.67,1404.98 1515.7,1418.56 \n",
       "  1517.74,1418.56 1519.78,1404.98 1521.81,1432.14 1523.85,1432.14 1525.89,1432.14 1527.92,1418.56 1529.96,1432.14 1532,1432.14 1534.03,1418.56 1536.07,1418.56 \n",
       "  1538.11,1377.83 1540.14,1404.98 1542.18,1391.41 1544.22,1323.52 1546.25,1404.98 1548.29,1404.98 1550.33,1418.56 1552.36,1418.56 1554.4,1404.98 1556.44,1391.41 \n",
       "  1558.47,1404.98 1560.51,1350.67 1562.55,1391.41 1564.58,1391.41 1566.62,1418.56 1568.66,1391.41 1570.69,1432.14 1572.73,1404.98 1574.77,1404.98 1576.8,1445.72 \n",
       "  1578.84,1432.14 1580.88,1432.14 1582.91,1432.14 1584.95,1432.14 1586.99,1404.98 1589.02,1418.56 1591.06,1418.56 1593.1,1432.14 1595.13,1445.72 1597.17,1432.14 \n",
       "  1599.21,1432.14 1601.24,1377.83 1603.28,1364.25 1605.32,1391.41 1607.35,1404.98 1609.39,1432.14 1611.43,1404.98 1613.46,1432.14 1615.5,1445.72 1617.54,1432.14 \n",
       "  1619.57,1445.72 1621.61,1404.98 1623.65,1404.98 1625.68,1418.56 1627.72,1432.14 1629.75,1432.14 1631.79,1404.98 1633.83,1377.83 1635.86,1391.41 1637.9,1404.98 \n",
       "  1639.94,1391.41 1641.97,1445.72 1644.01,1432.14 1646.05,1404.98 1648.08,1404.98 1650.12,1391.41 1652.16,1391.41 1654.19,1377.83 1656.23,1404.98 1658.27,1418.56 \n",
       "  1660.3,1418.56 1662.34,1391.41 1664.38,1404.98 1666.41,1432.14 1668.45,1432.14 1670.49,1445.72 1672.52,1445.72 1674.56,1418.56 1676.6,1418.56 1678.63,1432.14 \n",
       "  1680.67,1432.14 1682.71,1445.72 1684.74,1432.14 1686.78,1404.98 1688.82,1432.14 1690.85,1418.56 1692.89,1377.83 1694.93,1418.56 1696.96,1418.56 1699,1404.98 \n",
       "  1701.04,1404.98 1703.07,1404.98 1705.11,1418.56 1707.15,1404.98 1709.18,1391.41 1711.22,1432.14 1713.26,1391.41 1715.29,1391.41 1717.33,1418.56 1719.37,1432.14 \n",
       "  1721.4,1418.56 1723.44,1432.14 1725.48,1445.72 1727.51,1432.14 1729.55,1404.98 1731.59,1337.1 1733.62,1418.56 1735.66,1418.56 1737.7,1432.14 1739.73,1432.14 \n",
       "  1741.77,1432.14 1743.81,1418.56 1745.84,1418.56 1747.88,1404.98 1749.92,1418.56 1751.95,1404.98 1753.99,1418.56 1756.03,1404.98 1758.06,1404.98 1760.1,1404.98 \n",
       "  1762.14,1445.72 1764.17,1432.14 1766.21,1445.72 1768.25,1445.72 1770.28,1418.56 1772.32,1432.14 1774.36,1404.98 1776.39,1432.14 1778.43,1432.14 1780.46,1391.41 \n",
       "  1782.5,1404.98 1784.54,1418.56 1786.57,1418.56 1788.61,1418.56 1790.65,1432.14 1792.68,1432.14 1794.72,1432.14 1796.76,1445.72 1798.79,1418.56 1800.83,1445.72 \n",
       "  1802.87,1432.14 1804.9,1418.56 1806.94,1377.83 1808.98,1418.56 1811.01,1445.72 1813.05,1432.14 1815.09,1432.14 1817.12,1404.98 1819.16,1418.56 1821.2,1432.14 \n",
       "  1823.23,1404.98 1825.27,1432.14 1827.31,1445.72 1829.34,1445.72 1831.38,1377.83 1833.42,1391.41 1835.45,1364.25 1837.49,1377.83 1839.53,1404.98 1841.56,1404.98 \n",
       "  1843.6,1337.1 1845.64,1377.83 1847.67,1432.14 1849.71,1432.14 1851.75,1445.72 1853.78,1432.14 1855.82,1418.56 1857.86,1445.72 1859.89,1418.56 1861.93,1432.14 \n",
       "  1863.97,1432.14 1866,1418.56 1868.04,1418.56 1870.08,1445.72 1872.11,1432.14 1874.15,1445.72 1876.19,1418.56 1878.22,1391.41 1880.26,1418.56 1882.3,1418.56 \n",
       "  1884.33,1432.14 1886.37,1377.83 1888.41,1377.83 1890.44,1404.98 1892.48,1418.56 1894.52,1418.56 1896.55,1432.14 1898.59,1432.14 1900.63,1418.56 1902.66,1377.83 \n",
       "  1904.7,1377.83 1906.74,1364.25 1908.77,1404.98 1910.81,1418.56 1912.85,1404.98 1914.88,1391.41 1916.92,1418.56 1918.96,1418.56 1920.99,1445.72 1923.03,1432.14 \n",
       "  1925.07,1432.14 1927.1,1377.83 1929.14,1377.83 1931.18,1377.83 1933.21,1391.41 1935.25,1404.98 1937.28,1418.56 1939.32,1418.56 1941.36,1432.14 1943.39,1418.56 \n",
       "  1945.43,1445.72 1947.47,1418.56 1949.5,1418.56 1951.54,1445.72 1953.58,1418.56 1955.61,1445.72 1957.65,1404.98 1959.69,1432.14 1961.72,1445.72 1963.76,1418.56 \n",
       "  1965.8,1445.72 1967.83,1418.56 1969.87,1418.56 1971.91,1404.98 1973.94,1404.98 1975.98,1418.56 1978.02,1432.14 1980.05,1418.56 1982.09,1391.41 1984.13,1418.56 \n",
       "  1986.16,1432.14 1988.2,1432.14 1990.24,1404.98 1992.27,1404.98 1994.31,1391.41 1996.35,1404.98 1998.38,1418.56 2000.42,1445.72 2002.46,1445.72 2004.49,1432.14 \n",
       "  2006.53,1432.14 2008.57,1432.14 2010.6,1404.98 2012.64,1432.14 2014.68,1418.56 2016.71,1404.98 2018.75,1418.56 2020.79,1364.25 2022.82,1391.41 2024.86,1391.41 \n",
       "  2026.9,1418.56 2028.93,1445.72 2030.97,1418.56 2033.01,1418.56 2035.04,1404.98 2037.08,1404.98 2039.12,1432.14 2041.15,1391.41 2043.19,1364.25 2045.23,1377.83 \n",
       "  2047.26,1404.98 2049.3,1391.41 2051.34,1445.72 2053.37,1445.72 2055.41,1418.56 2057.45,1418.56 2059.48,1418.56 2061.52,1418.56 2063.56,1418.56 2065.59,1432.14 \n",
       "  2067.63,1418.56 2069.67,1432.14 2071.7,1418.56 2073.74,1418.56 2075.78,1432.14 2077.81,1432.14 2079.85,1404.98 2081.89,1404.98 2083.92,1404.98 2085.96,1432.14 \n",
       "  2087.99,1432.14 2090.03,1404.98 2092.07,1418.56 2094.1,1418.56 2096.14,1377.83 2098.18,1404.98 2100.21,1404.98 2102.25,1418.56 2104.29,1418.56 2106.32,1418.56 \n",
       "  2108.36,1432.14 2110.4,1377.83 2112.43,1418.56 2114.47,1391.41 2116.51,1404.98 2118.54,1418.56 2120.58,1432.14 2122.62,1418.56 2124.65,1418.56 2126.69,1418.56 \n",
       "  2128.73,1418.56 2130.76,1364.25 2132.8,1404.98 2134.84,1404.98 2136.87,1418.56 2138.91,1445.72 2140.95,1404.98 2142.98,1364.25 2145.02,1391.41 2147.06,1418.56 \n",
       "  2149.09,1418.56 2151.13,1418.56 2153.17,1404.98 2155.2,1391.41 2157.24,1391.41 2159.28,1391.41 2161.31,1445.72 2163.35,1445.72 2165.39,1445.72 2167.42,1350.67 \n",
       "  2169.46,1364.25 2171.5,1404.98 2173.53,1391.41 2175.57,1404.98 2177.61,1418.56 2179.64,1432.14 2181.68,1418.56 2183.72,1404.98 2185.75,1391.41 2187.79,1418.56 \n",
       "  2189.83,1418.56 2191.86,1418.56 2193.9,1418.56 2195.94,1418.56 2197.97,1391.41 2200.01,1404.98 2202.05,1418.56 2204.08,1432.14 2206.12,1445.72 2208.16,1445.72 \n",
       "  2210.19,1432.14 2212.23,1432.14 2214.27,1418.56 2216.3,1445.72 2218.34,1445.72 2220.38,1445.72 2222.41,1404.98 2224.45,1391.41 2226.49,1418.56 2228.52,1391.41 \n",
       "  2230.56,1391.41 2232.6,1418.56 2234.63,1432.14 2236.67,1404.98 2238.71,1432.14 2240.74,1432.14 2242.78,1418.56 2244.81,1404.98 2246.85,1350.67 2248.89,1404.98 \n",
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       "  1721.4,1432.14 1723.44,1404.98 1725.48,1391.41 1727.51,1404.98 1729.55,1391.41 1731.59,1377.83 1733.62,1418.56 1735.66,1432.14 1737.7,1418.56 1739.73,1391.41 \n",
       "  1741.77,1391.41 1743.81,1377.83 1745.84,1377.83 1747.88,1404.98 1749.92,1418.56 1751.95,1404.98 1753.99,1364.25 1756.03,1404.98 1758.06,1391.41 1760.1,1418.56 \n",
       "  1762.14,1391.41 1764.17,1391.41 1766.21,1391.41 1768.25,1391.41 1770.28,1445.72 1772.32,1445.72 1774.36,1432.14 1776.39,1432.14 1778.43,1404.98 1780.46,1364.25 \n",
       "  1782.5,1432.14 1784.54,1432.14 1786.57,1418.56 1788.61,1418.56 1790.65,1445.72 1792.68,1445.72 1794.72,1445.72 1796.76,1418.56 1798.79,1404.98 1800.83,1377.83 \n",
       "  1802.87,1377.83 1804.9,1404.98 1806.94,1432.14 1808.98,1418.56 1811.01,1418.56 1813.05,1404.98 1815.09,1418.56 1817.12,1418.56 1819.16,1418.56 1821.2,1418.56 \n",
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     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Ens1.sims[1], Ens1.sims[2][1:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c9b5bb8",
   "metadata": {},
   "source": [
    "We can also plot the probability distribution for each number of spins up at each time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "103ee3f3",
   "metadata": {},
   "outputs": [
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "T = 100; # time step 100\n",
    "pFC = EnsProb(Ens1,T);\n",
    "bar(pFC, label = join([\"P(n,\" T \")\"]))\n",
    "xlabel!(L\"m(n)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0a04fda3",
   "metadata": {},
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       "  942.815,174.42 944.859,175.737 946.902,192.857 948.945,152.032 950.989,138.424 953.032,148.52 955.076,141.058 957.119,136.668 959.162,130.522 961.206,166.079 \n",
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       "  983.683,133.156 985.726,118.67 987.77,150.715 989.813,191.54 991.857,161.69 993.9,150.715 995.943,185.394 997.987,146.325 1000.03,123.938 1002.07,152.91 \n",
       "  1004.12,137.985 1006.16,179.249 1008.2,149.398 1010.25,144.131 1012.29,132.278 1014.33,137.985 1016.38,139.741 1018.42,137.546 1020.46,123.938 1022.51,88.3806 \n",
       "  1024.55,157.739 1026.59,162.568 1028.64,138.863 1030.68,159.495 1032.72,185.394 1034.77,133.156 1036.81,102.867 1038.85,137.985 1040.9,167.396 1042.94,147.203 \n",
       "  1044.98,147.203 1047.03,137.107 1049.07,146.325 1051.12,152.91 1053.16,112.085 1055.2,108.573 1057.25,93.6483 1059.29,133.156 1061.33,145.447 1063.38,165.201 \n",
       "  1065.42,160.812 1067.46,141.058 1069.51,130.522 1071.55,135.79 1073.59,149.837 1075.64,145.886 1077.68,154.666 1079.72,156.861 1081.77,191.54 1083.81,160.812 \n",
       "  1085.85,114.28 1087.9,91.0144 1089.94,143.253 1091.98,162.568 1094.03,164.323 1096.07,154.666 1098.11,152.032 1100.16,163.007 1102.2,112.524 1104.24,125.255 \n",
       "  1106.29,145.008 1108.33,141.058 1110.37,143.692 1112.42,120.865 1114.46,109.451 1116.5,96.2821 1118.55,104.184 1120.59,116.475 1122.63,112.963 1124.68,129.205 \n",
       "  1126.72,148.52 1128.76,130.522 1130.81,120.865 1132.85,148.959 1134.89,138.424 1136.94,138.424 1138.98,135.351 1141.02,145.886 1143.07,157.739 1145.11,157.739 \n",
       "  1147.15,141.058 1149.2,160.812 1151.24,124.816 1153.28,97.1601 1155.33,89.2585 1157.37,119.109 1159.41,132.717 1161.46,117.792 1163.5,141.936 1165.55,168.274 \n",
       "  1167.59,132.717 1169.63,147.642 1171.68,134.912 1173.72,147.203 1175.76,139.741 1177.81,113.402 1179.85,152.91 1181.89,146.325 1183.94,153.349 1185.98,161.69 \n",
       "  1188.02,159.934 1190.07,151.154 1192.11,178.371 1194.15,138.424 1196.2,150.276 1198.24,139.741 1200.28,125.255 1202.33,143.253 1204.37,118.231 1206.41,141.058 \n",
       "  1208.46,145.886 1210.5,129.644 1212.54,171.347 1214.59,166.079 1216.63,136.229 1218.67,168.274 1220.72,144.131 1222.76,116.914 1224.8,139.302 1226.85,153.349 \n",
       "  1228.89,140.18 1230.93,147.203 1232.98,114.28 1235.02,132.278 1237.06,136.229 1239.11,164.323 1241.15,148.52 1243.19,115.597 1245.24,130.961 1247.28,170.469 \n",
       "  1249.32,157.739 1251.37,174.859 1253.41,148.081 1255.45,163.884 1257.5,176.176 1259.54,143.692 1261.58,114.719 1263.63,150.276 1265.67,158.178 1267.71,140.619 \n",
       "  1269.76,163.007 1271.8,173.981 1273.84,148.52 1275.89,192.418 1277.93,179.249 1279.97,206.904 1282.02,177.493 1284.06,119.987 1286.11,144.131 1288.15,136.229 \n",
       "  1290.19,164.762 1292.24,164.762 1294.28,127.888 1296.32,118.231 1298.37,124.377 1300.41,160.812 1302.45,171.347 1304.5,135.79 1306.54,118.231 1308.58,86.1857 \n",
       "  1310.63,132.717 1312.67,141.058 1314.71,163.445 1316.76,187.589 1318.8,166.957 1320.84,123.06 1322.89,122.621 1324.93,152.91 1326.97,141.058 1329.02,158.178 \n",
       "  1331.06,170.908 1333.1,155.544 1335.15,171.786 1337.19,177.932 1339.23,202.953 1341.28,173.103 1343.32,176.176 1345.36,156.422 1347.41,159.495 1349.45,169.591 \n",
       "  1351.49,162.568 1353.54,144.57 1355.58,164.762 1357.62,166.518 1359.67,147.642 1361.71,132.278 1363.75,135.79 1365.8,107.257 1367.84,112.963 1369.88,152.032 \n",
       "  1371.93,140.18 1373.97,132.278 1376.01,163.884 1378.06,167.396 1380.1,127.449 1382.14,163.884 1384.19,150.715 1386.23,155.544 1388.27,159.495 1390.32,166.518 \n",
       "  1392.36,175.298 1394.4,156.861 1396.45,161.69 1398.49,172.664 1400.54,155.983 1402.58,141.497 1404.62,151.593 1406.67,141.497 1408.71,134.034 1410.75,151.593 \n",
       "  1412.8,136.668 1414.84,137.985 1416.88,119.987 1418.93,157.3 1420.97,163.445 1423.01,181.444 1425.06,174.42 1427.1,129.205 1429.14,107.257 1431.19,113.402 \n",
       "  1433.23,148.959 1435.27,179.249 1437.32,163.007 1439.36,173.981 1441.4,170.908 1443.45,191.979 1445.49,170.908 1447.53,148.081 1449.58,147.642 1451.62,145.886 \n",
       "  1453.66,154.227 1455.71,132.717 1457.75,166.079 1459.79,150.715 1461.84,166.518 1463.88,182.76 1465.92,129.644 1467.97,127.01 1470.01,167.396 1472.05,155.544 \n",
       "  1474.1,184.516 1476.14,126.571 1478.18,130.961 1480.23,190.662 1482.27,181.444 1484.31,200.758 1486.36,159.056 1488.4,155.544 1490.44,175.298 1492.49,191.979 \n",
       "  1494.53,172.225 1496.57,170.03 1498.62,173.981 1500.66,163.884 1502.7,149.837 1504.75,145.008 1506.79,125.694 1508.83,160.812 1510.88,120.426 1512.92,110.768 \n",
       "  1514.97,154.227 1517.01,154.227 1519.05,108.573 1521.1,136.668 1523.14,132.717 1525.18,113.841 1527.23,129.205 1529.27,145.886 1531.31,142.375 1533.36,153.349 \n",
       "  1535.4,145.008 1537.44,116.475 1539.49,99.7939 1541.53,119.548 1543.57,119.548 1545.62,94.0872 1547.66,154.666 1549.7,160.373 1551.75,119.548 1553.79,141.058 \n",
       "  1555.83,121.304 1557.88,148.52 1559.92,143.253 1561.96,148.959 1564.01,98.038 1566.05,101.989 1568.09,109.89 1570.14,98.038 1572.18,113.841 1574.22,174.42 \n",
       "  1576.27,164.323 1578.31,148.081 1580.35,150.715 1582.4,162.568 1584.44,151.593 1586.48,151.154 1588.53,121.743 1590.57,128.327 1592.61,158.178 1594.66,147.203 \n",
       "  1596.7,137.546 1598.74,155.544 1600.79,119.987 1602.83,137.985 1604.87,151.154 1606.92,138.424 1608.96,144.57 1611,122.621 1613.05,105.94 1615.09,150.276 \n",
       "  1617.13,156.422 1619.18,165.201 1621.22,148.52 1623.26,157.3 1625.31,161.69 1627.35,151.593 1629.4,122.182 1631.44,138.424 1633.48,147.642 1635.53,138.863 \n",
       "  1637.57,106.818 1639.61,126.571 1641.66,116.914 1643.7,142.375 1645.74,161.69 1647.79,149.398 1649.83,116.475 1651.87,177.054 1653.92,153.349 1655.96,158.617 \n",
       "  1658,141.058 1660.05,124.377 1662.09,139.741 1664.13,139.302 1666.18,165.64 1668.22,148.52 1670.26,111.646 1672.31,133.156 1674.35,172.225 1676.39,184.516 \n",
       "  1678.44,188.467 1680.48,145.447 1682.52,159.495 1684.57,119.109 1686.61,104.184 1688.65,155.105 1690.7,140.18 1692.74,150.715 1694.78,121.743 1696.83,162.568 \n",
       "  1698.87,150.276 1700.91,147.203 1702.96,137.546 1705,105.501 1707.04,106.379 1709.09,150.276 1711.13,157.739 1713.17,167.396 1715.22,173.103 1717.26,202.953 \n",
       "  1719.3,181.005 1721.35,188.467 1723.39,186.711 1725.43,170.03 1727.48,193.735 1729.52,175.298 1731.56,184.077 1733.61,143.692 1735.65,126.133 1737.69,103.745 \n",
       "  1739.74,141.058 1741.78,144.57 1743.83,139.302 1745.87,112.524 1747.91,105.501 1749.96,123.938 1752,147.642 1754.04,145.008 1756.09,149.837 1758.13,151.593 \n",
       "  1760.17,135.351 1762.22,127.449 1764.26,140.18 1766.3,148.52 1768.35,148.081 1770.39,171.347 1772.43,158.617 1774.48,138.863 1776.52,137.546 1778.56,136.668 \n",
       "  1780.61,163.007 1782.65,143.253 1784.69,119.987 1786.74,111.207 1788.78,130.961 1790.82,105.062 1792.87,115.597 1794.91,129.644 1796.95,158.178 1799,141.497 \n",
       "  1801.04,112.963 1803.08,177.493 1805.13,189.345 1807.17,171.347 1809.21,175.298 1811.26,155.544 1813.3,130.961 1815.34,120.865 1817.39,140.619 1819.43,177.493 \n",
       "  1821.47,146.764 1823.52,145.008 1825.56,140.18 1827.6,155.544 1829.65,131.4 1831.69,154.666 1833.73,160.373 1835.78,181.882 1837.82,166.079 1839.86,121.743 \n",
       "  1841.91,145.447 1843.95,141.058 1845.99,193.296 1848.04,170.03 1850.08,195.93 1852.12,165.64 1854.17,163.884 1856.21,130.961 1858.25,120.865 1860.3,154.227 \n",
       "  1862.34,169.591 1864.39,161.251 1866.43,162.129 1868.47,126.571 1870.52,130.961 1872.56,109.012 1874.6,96.2821 1876.65,113.841 1878.69,125.694 1880.73,139.302 \n",
       "  1882.78,145.447 1884.82,148.959 1886.86,138.424 1888.91,134.034 1890.95,149.398 1892.99,181.882 1895.04,154.666 1897.08,142.375 1899.12,149.837 1901.17,127.01 \n",
       "  1903.21,133.156 1905.25,155.983 1907.3,140.619 1909.34,145.886 1911.38,106.818 1913.43,95.8431 1915.47,96.2821 1917.51,118.231 1919.56,107.257 1921.6,173.103 \n",
       "  1923.64,165.64 1925.69,166.079 1927.73,165.64 1929.77,109.451 1931.82,126.571 1933.86,160.812 1935.9,146.764 1937.95,169.591 1939.99,161.251 1942.03,156.861 \n",
       "  1944.08,143.692 1946.12,157.3 1948.16,170.469 1950.21,125.255 1952.25,103.306 1954.29,124.816 1956.34,161.69 1958.38,178.371 1960.42,162.129 1962.47,135.79 \n",
       "  1964.51,127.449 1966.55,112.963 1968.6,116.475 1970.64,128.766 1972.68,99.355 1974.73,110.768 1976.77,138.424 1978.82,148.959 1980.86,151.593 1982.9,123.938 \n",
       "  1984.95,125.694 1986.99,139.741 1989.03,122.182 1991.08,122.182 1993.12,92.3313 1995.16,122.621 1997.21,137.546 1999.25,130.522 2001.29,145.008 2003.34,141.936 \n",
       "  2005.38,154.227 2007.42,165.201 2009.47,129.205 2011.51,152.032 2013.55,156.861 2015.6,151.593 2017.64,139.741 2019.68,163.884 2021.73,137.546 2023.77,126.133 \n",
       "  2025.81,159.495 2027.86,151.593 2029.9,179.249 2031.94,177.932 2033.99,154.666 2036.03,146.325 2038.07,164.323 2040.12,170.469 2042.16,176.176 2044.2,145.008 \n",
       "  2046.25,157.739 2048.29,134.473 2050.33,160.373 2052.38,117.792 2054.42,147.203 2056.46,148.081 2058.51,136.668 2060.55,146.325 2062.59,175.298 2064.64,172.664 \n",
       "  2066.68,205.148 2068.72,155.105 2070.77,170.908 2072.81,156.861 2074.85,166.957 2076.9,166.079 2078.94,152.471 2080.98,153.349 2083.03,157.739 2085.07,130.522 \n",
       "  2087.11,148.52 2089.16,150.715 2091.2,141.497 2093.25,130.522 2095.29,123.499 2097.33,144.131 2099.38,149.837 2101.42,117.792 2103.46,115.597 2105.51,155.105 \n",
       "  2107.55,142.375 2109.59,145.886 2111.64,146.764 2113.68,169.152 2115.72,165.64 2117.77,180.127 2119.81,148.959 2121.85,162.568 2123.9,166.957 2125.94,150.276 \n",
       "  2127.98,178.81 2130.03,126.133 2132.07,163.007 2134.11,173.542 2136.16,166.957 2138.2,163.007 2140.24,115.597 2142.29,126.133 2144.33,149.398 2146.37,120.865 \n",
       "  2148.42,151.593 2150.46,148.52 2152.5,123.938 2154.55,153.349 2156.59,169.591 2158.63,152.471 2160.68,154.227 2162.72,134.473 2164.76,108.134 2166.81,101.111 \n",
       "  2168.85,113.402 2170.89,154.227 2172.94,145.447 2174.98,145.008 2177.02,126.133 2179.07,134.473 2181.11,110.329 2183.15,136.229 2185.2,150.715 2187.24,152.032 \n",
       "  2189.28,120.426 2191.33,156.422 2193.37,156.422 2195.41,171.347 2197.46,127.449 2199.5,130.522 2201.54,136.668 2203.59,153.788 2205.63,163.445 2207.68,127.449 \n",
       "  2209.72,150.715 2211.76,103.745 2213.81,136.668 2215.85,99.355 2217.89,102.428 2219.94,134.912 2221.98,136.229 2224.02,166.518 2226.07,136.229 2228.11,131.839 \n",
       "  2230.15,144.57 2232.2,152.471 2234.24,151.154 2236.28,142.375 2238.33,140.619 2240.37,148.081 2242.41,146.325 2244.46,127.888 2246.5,125.255 2248.54,136.229 \n",
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      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(CentralMoments(Ens1,1), label = join([\"Central moment \", 2]), lw = 3)\n",
    "xlabel!(\"Time/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f55969ee",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3776dff1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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