Lorenz systems simulation as seen on Wikipedia

wikipedia-lorenz.ipynb

sigma = 10;
beta = 8/3;
rho = 28;
f = @(t,a) [-sigma*a(1) + sigma*a(2); rho*a(1) - a(2) - a(1)*a(3); -beta*a(3) + a(1)*a(2)];
[t,a] = ode45(f,[0 100],[1 1 1]); % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3)){
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "sigma = 10;\n",
    "beta = 8/3;\n",
    "rho = 28;\n",
    "f = @(t,a) [-sigma*a(1) + sigma*a(2); rho*a(1) - a(2) - a(1)*a(3); -beta*a(3) + a(1)*a(2)];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "[t,a] = ode45(f,[0 100],[1 1 1]);     % Runge-Kutta 4th/5th order ODE solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bChTHkB0gWvbOgnBvt/+WcM93MECXsZyKvNL8RpIJpSCQALkMx5AHD1XCCbBBRIXDSYWihfkhSEMgAUKlplH4efU2nFSoZ0EfiwuXU+Y1syQW6kQgARJlX/0aiGzsndRrkGXXhtgDzlP7GoCCCCRAnCwdBPo2qXoU6Z8Qfo0hRcLvNW+Xl/l3AtIRSIAs+XYGinwR+d+kHEr9Qakt3cQSSkQgAYKY90sNvo58oQ/KRd5+Un8d0BTWIQGtkdQdl/S83tGQ1MlNVkECAgmQLilUIgkUfll4GilpM4Xsy4zMF5bjNwJiMWQHtEAkPFTcwlV9gZE+Y6R/jnrbKV7trwEYEUiAFOYtUyPP6BNI5oG7fGET6eVLfR4ogkAC5IptT1BacRN+GPvepEZwnV42AbUhkIAWiAzTheeTIlsEhfcKMqycjf388MOkFj6gOjQ1AEIlNS8EImNx4WG02B2DInuwRoqtUxFUKB0VEiBCUgtc7F4MKjmlDAVQpNmBLewgDRUSIFfsIFvSZqmGlbO5m+hSV+kCJaJCAsTRt5KLlEexrx/879yj8LfC43J6YgGiEEhA81JrDr2LIfICw15zhnfpnw80iEACZIn0MpiDKlz0hGebDOuZsvfamS8PKB2BBAgVlDWG3Rb0JjqlZYYhZszrk5goQs0IJECQ2P3lzEVJZFWsnjGRyaekqit7eURQoSIEEtAww5ET6u3dX1+vGi6h9PTS+8hzbNkA1IZAAqRI3VhBXyobGdbLUf3oPeX5fwGgGAIJkChj013sZkL6yyJNevl+OsuPUDUCCRAhaVdvdUp9o2+9qn/X0DKeWh6RSaiUxEA6Ho+e5wUPXdcNPwS6JPYWH3km+zCa+ZVJDXtZuvJoZ0ANxAWS53mz2ez8/Nx/OJ/Pt9vtYrFwHKfZCwOqo8dS9lZsw0bdsVVXbNnEYROQQFwg3d3dnZ2d+SXRbrezLOv29vb+/v7h4aHpSwMqlDEPzGN05s/J0mKXumgJqI6sQNpsNh8+fLAsy6+QXNcdjUZKKcuy9vt901cHlCx1Rx+zpLkf8zZCKpRMGZc6MXWEeggKJNd1XdddLpfhJy3L8r8Yj8f6WwYhdVwiULbYMbSM64Rid1NVBeZ7SB00S1AgbTab9+/f27Z9PB7X6/XxeFRK+f+rlIqtkF5Dar1WoDz56g9zD17ScbHm15R4eUAOggJpuVx++vTp06dP5+fn0+n07OxsNBq9vLwopY7H43A4bPoCgUoYtqeLvCzyhf5eA33pUtLnx74LqIGgQBqNRpPJZDKZnJ2dTSYTP5b2+71t26vVKjKUB7Rd7MBaliVHsRuq6i+O5Fbqa4DGDeQPdjmOY1lWMJmUZDBowe8CBE7dXM4Xef1Jb489ZzbyyUlXCNRAUIWUZDKZpKYR0EY50sjvYog98cj8U3SpaUQUoWYtCCSge/LNzeQrqoJ3mRMo9o1kEupEIAGCpAZAwfNeA5RHEIhAAupm6KnLso1C5O3Fw0m/PNIIjSCQgBaI3ZTBsP2dvgjp1NwillA/AgmoVZZDJSIiG/ykHsGX/ZNjN3Ulh9AUAgmoT47bffhAWJWtZS7jdw1TR8QSGkEgAY1JXegTpFFsp5z5Y7O8jAWzEIVAAmpiCIDUN6rMA3GpA3rmyyON0CACCahVeFgs8i3Dtt/hIbsco3OpP4s0ggQEElCH8L0+Y6mU1P6QdAyS/krD28keCEQgAS1jGMHTm8L1ikp/O+URhCCQgMoVudfna6tLekHskeekEYQgkID6GCaQYhUMiaTyKOmqgGYRSKhK0q42fRO53WdZVGT4VurxfanfilyM+b1Anb5p+gLQZTl2mO4VQ7qcWrXENjiE93cInoy8hf9TIAcVEqoS3FWDf/yaqbdl06njdYZPyLIpuJ43+rtII4hChYT66P3K3BB15vIo+y4M6m2Fyp51kI9AQoWS7q1Z9q7uhhz3/dS3pK6N1QfrDPuCA3IQSGiSPqWhOppMviJJELw3YxqZc6vDf8hoL+aQUK2M+4H6r+zwVFP2Uim1PDI/yWAd2osKCfXJ2NYVGdDj7qnSyqNw9uhH80VeyZ8nxCKQULnwTNJJjeCRnrQ+3EkL/o6R8og0QrsQSKhP5HQflS1sOlAwFUyCk0YvDWmU+wKAehBIqEPqSs8sZVPbC6bUSCjlNzKM6bXuTwx9QyChVpEiKbb/2xxOHSiYYhVceGT4tI79QaHDCCTUxFwkJZ3xY6iHwgWTzLttzXM2sYN1zBuhRQgk1C1cJOm3S3MymWMp9gWNi0ybnfreU18cu7QLaAUCCfWJLZJOOhfVHEuGFwhX1gUzUodWExdIjuMMh8Pz8/PgGdd1LcsKP4O205dtGlbC6huSGm61MgumGsqj2PcK+fWBjAQFkud5i8ViPB6v1+vr6+vpdKqUms/nlmUdDofr6+vJZNL0NaIow+52sc0OSru3RlrGzTsX9Oq+3M/fGl0yeH19bfoa/rDZbJRSy+XyeDyu1+vHx8fdbuc4zu3tbfCM4e2DgaDfBQb6KQzBQ8Omq6kTJKk95fXfoLPsKacSLuzU8og0QgcIqpCWy6X/hT9G538xGo2UUpZl7ff7Ji8O5cl4vEJkKE+PpUiqZRzH6+SdmjRCN4jbXNW27bu7Oz+HlFJ+MimlxuOx/uJBSH2XiJLEjsL5+6uGX6MnU3jCKfJ681xUnTu3Zuy3Ll4ekUboDInDXJ7n/f3vf//ll19s2/7w4cPl5aVS6ttvv/31118N72LIrl30ZugsG4Pqn5NvEE9Vf/uubbyu8/Uf+kNQhbRer3e7nVIqaKgbjUYvLy9KqePxOBwOm7w4VMnQ8B3+J/bF+aol9bZgKuW3KEu+NCKK0AGCqgrXdVer1cXFxeFw+PTpkz+lNJvNxuPxfr9fLpd+310SKqTWMfd5q7j2h/BrYp9M+vD6q6UsFVLB8iicRmQSOkDWTdzzvMPhYFlWMHWklHIcJ/JMLAKpdSJ93rGddeFbbcZYUtq0iv580vWkvia7LLmi/yzSCH3WnZs4gdRG4ftp6r3YEDOxc1GGGDNfUuprssjyS2WZJDO8kTRCxwiaQ0KfGe6q+pSS/l6lDfSFY+mk+35tzXi5U4Q0Qld1p6qgQmopvUjKUi0libScJe3yEH5x6uVlfGXsG1MvNfvrw+9KavEAWq07N3ECqb3Ct9eMw3dm4U/Qy4ikuEq9wux3/+rSiChChzFkBxGC22vSMFQw8nZqfvhf693h4dW4WfLj1JgsPTDCfzKkETqJQELzUguj8IIhc4kQqYQMK5P0b2W8zoyxlD29sv9oJo3Qbd0Z5mLIru1O7TEzvMuwB0TSCF7sh5sv1fDKcpvrGKlDT3TnJk4gtd1JLeC+pG6F4LtJsRR5u/4JGWMp38rWkyqzk+a6gFbrzk2cQOqAUprrzC8rPZP0V+ZeUBX7StII/dGdmziB1AE5iqRTxUZXubFUViCRRuib7tzECaRuMKRRiSmlzyopY06cNIKXMZBIIyCiOzdxAqkz8qVOvrbsSIN4bKmUvbctx3IiwwuIIvQNbd+QKMdqm6Siyvz6IIqCykzvZ4u0m6dedsHXkEbore5UFVRIXVLpJnIR5lLp1OG7HI0V+ndJI/QTFRIkCm/cUO4H6s+E92DVN9N7PXFv1lSkEZCEQIJcJXYxxO7aoH8dm0lKC8ikqyoYJ6QReq47w1wM2XVPFQN3qSNm6m2/nF4eGfrfCjask0boOSokiFb6XqJJO7cG31WhPetiF9Ka27tztwiSRgCBBLmCPCirw82XVPcEX6u3pVLGTMo94EYUAT4CCaKdFDPZP1Z/cRAn4fJInZhJOZBGQIBAQgvUc9cOqrHYmaQqMok0AsIIJEiXu00g9+0+NpOUFjxJLXlVXx7QVQQSWiDfvbvIYFp4QijcWBG79WqOKS7SCNARSOigHLd7cw93lmIo+7dIIyBWd9busA6p86reTyg2UfS5In0/BX1drfmnlHnRQIdQIaFNst/Nc9z3Y/u2w7NHhh6H8IuLXwnQTwQSWuOk3oF8q4IM7zJnUuq24qkvA0AgoU3yHUhx6rvMrw83O2QJm9I3igW6Slwgua57PB4jz3ie19T1oANK3KE18nWWoq3OozSAVhMUSJ7nzWaz7Xa7Xq9t2/afnM/n2+12sVg4jtPs5UGIGuqM7AN32T+T8ghIJSiQnp6exuPx7e3t4+Pj58+flVK73c6yrNvb2/v7+4eHh6YvEFI0kkmxm93VczFATwgKpIuLi++//14pFQzQua47Go2UUpZl7ff7Ji8O/RMpgGLPT8pYJBFaQBaCAsmyLMuyHMdZLBZXV1fBk/4X4/FYf8sgpL4LhQASbvGRXYUMq2JrvSygtQQFklLKtu3tdnt/f395eek/EzQ4xFZIryH1XSV6LLwjeNPXAnSNoEDabrdfvny5v78PqqLRaPTy8qKUOh6Pw+Gw0auDOI1UHpEVSFQ/QIkEbbezXq8Ph8PZ2Zn/8PHxUSk1m83G4/F+v18ul9Pp1PB2tg7qJyGVSlLNRGIB2bXgJu44jj+9ZH4ZgdRPpwZS7qMikvLG/GkEEpBdd27iBFJv5VsPVFZpZd7ku5QfAfSEoDkkIJ989/1T30W6AFUjkNAvubc6Tdq+Id8urgB0BBK6QGAkCLwkQDgCCb1TpEgKPyx9OgroOQIJHVFPRRJ7UCyAUhBI6I7smZRaJBWMN8brgBwIJPSUub5J+i5VEVAdAgmdUsORslQ/QEUIJHRN1YFBkQRUhEBCr5EugBwEEjqoSDN3zT8dQIBAAqiTABEIJHQTZQrQOgQSOotMAtqFQALKRAoCuRFI6DLiAWgRAgkdRyYBbUEgAQBEIJDQfRmLJGopoFkEEvAHViMBzSKQ0AvZq5/Xu7/lLpWosYAiCCT0Rca0GFz/NLj+iWgB6kcgATEYvgPqRyChR+oZuAOQD4EExKBCAupHIKFfstc9ZBJQMwIJiMF4HVA/Agm9kyVsKI+A+okLJM/zjsdj+BnXdT3Pa+p6AAD1EBdIT09PP/74Y/BwPp9vt9vFYuE4ToNXhY5hRA4QSFYgzWazu7u74OFut7Ms6/b29v7+/uHhocELA1IRckBBsgLp+fn5hx9+CB66rjsajZRSlmXt9/vmrgsdRH4A0nzT9AWksCzL/2I8HuvfHQwG9V4OAKAqsiokXdDgEFshvYbUe13oAookQBTRgTQajV5eXpRSx+NxOBw2fTkAgAqJDqTpdLrf723bXq1Wy+Wy6ctBB1EkAXIM5A92OY5jWVYwmZRkMGjB7wKB/MMmiq+EJduAgrpzEyeQkFsp+zIQSEBBoofsgNoQJ0DjCCRAJQ3ZkVJAnQgk4A96/LDFKlAnAglQKlQkURUBTSGQgD8RS0CDCCTgD+GZpMhgHfkE1IBAAt6IzR4mk4AaEEjAnyLtdhRGQJ0IJCDKz6FStm8AkB2BBLwR5BDdDUDNCCQgBkUSUD8CCYiKLZIolYCqEUhAvEiR5G8K3vRFAV3WnR2y2e0b5UodrKMlDygXFRKQyDxYx/QSUK7uVBVUSChdEDnhYijIJ3ZzAMpFhQSYRGKGvjugOgQSkEjvaCCNgOoQSECK2HOSSCagdAQSYKIXScwVARUhkIB0+kxSU1cCdFh3OtPoskN1ktrtWIcElIgKCciEdjugagQSkC52AyFKIqBcBBKQVTiKKI+A0hFIQCZ+CBFFQHUIJOBk4cMpAJSlBYHkuq7neU1fBfBnkRR5sqnrATpGeiDN5/PtdrtYLBzHafpagD8lbbEKIDfRgbTb7SzLur29vb+/f3h4aPpygJiZJCokoCzfNH0BJq7rjkYjpZRlWfv9vunLAd5gu1WgXBIrJMdxgkkjy7KUUq7rfvz4UX/lIKTWS0SP0W4HVERWIHmeN5vNfv7559lsttvtlFLH49GfRvrll1/0aaTIXkEkExrBqB1QClmB9PT0NJ1Ob25uHh8ft9vtaDT6z3/+Y1nW1dXVX//619hppFcNsYSqxRZJFExAQbICablcLpdLpZTrupZlTafT//73v7/99ttqtfrXv/6VcRqJWEKd2L4BKIvEpgbbtj9//nx1daWU+sc//vHu3buLiwvLsrbbbfYP8UfzgkxiI3BUgTVJQIlkVUi+m5ub5+fnu7s7/+HZ2Znf2pCj0Y5xPFSEeggonaxAWq/Xfi/D+fm5/8xoNHp5eVFKHY/H4XCY+5OJJQAQTtaQ3eXl5Wq1cl33cDj4Q3bT6XSz2di2vd/v/emlIsLjeAzioaDYnYQA5CbulFXP8w6Hg2VZ/jCdz3GcyDPFEUsoRdBuRzIBBYkLpJoRSyjOn0wikICCZM0h1Y+5JRRHFAGl6HuFFEa1BAANIpCiWLoEAI0gkBJRMAFAnXo3h+S67vF4DD9MOo6W6SUAqJOsdUiV8jxvsVgMh0N/je3Nzc18Prcs63A4XF9fTyYTw3uplgCgaj0KpKenp/F4fHNzo5T67rvvRqORfxzt8Xhcr9d6IOkhRCwBQHV6FEgXFxf+F/4YXepxtHrwsNEDAFSnR3NI/l4PjuMsFgt/X6Jg64fxeJz9c5hbAoAq9KhCUkrZtv3ly5f7+3vLsmzbDrob8u0jrugRB4Dy9CiQttutn0b+w9Fo5LquKraPeJBDjOMBQEE9CiS/4Xs+n/sPHx8f2UccQEtFpgz8247ruufn5+F9qP3Tt4MDfYTr+8JY9hEH0BbhEIrcYf7yl7+8f//+n//8Z7CsRSmVfWWLEH0PpOoQSwCKM4RQ2Gaz+fr1a7Cs5d///vdut3McJ1jZ8vj4WMPVFtSjIbuaMYgHILdTG6Yiy1pUhpUtAhFI1SKWAGSUsRiK5c87OI5zd3fnL2tReVe2NIhAqgM94gBiFQmhiPCyFv+ZIitbGkEg1YcecQC+0v/zNLKsRZW0sqVmNDU0hlgCeqXEYki3Xq8Ph8PZ2Zn/0G9hmM1m4/HYX9kynU7L/YlVIJBK43ne77//fuoKAGIJ6LDY1UL6vaI6VaxsqQ6BVJpw26VKWwEQKdiJJaBLkkbk/OcfHh7C94qPHz/6Q2rB+qHeYg6pHLPZ7HA4/PDDD/7D3W5nPtsi8teUWALaLsuI3Ovr62w2u7u7C+4V/gRPKxYJ1aBHu31X6vn5OfgbpvKuAGAfcaB1Bv/zGmJ4feRecTwez8/P1+u1bdtJp1f3B4FUldwrAMKxRDIBAg1CsoSQged579+/n06n7969W61W5V5n6zBkV5WCKwDoEQdEqahHbjqd+v1vk8lkt9uV9bEtRYVUidFo9PLyospYAcA4HtCgU0fkTrXZbBzHKfEDW40KqRLT6bTEsy0UXQ9AjSpdMBQxHo9Xq9XFxcXhcLi8vKz0Z8lH23eFKloBQCwBpaszhHTtWi1UHQKprYgloDh9wVDwb1a+pe4ogjmktmJuCcjH3CMXPHx6evrxxx+D5+fz+Xa7XSwWTPlUh0BqN3rEgSxiQ8gwwOAvXw0eBkvd7+/vHx4earnkPiKQuiD4t4tYAsJy98iVstQdp6LLrlNoxgMqak9o3WF3bUSF1Fau6yZtNEK1hB6qesFQ6w67ayMCqZXM86vhKCKW0GElbuFjVuJSdxgwZNc+p24lrhjEQ4c0smCo9KXuiMU6pPaxbfvDhw/+ou5vv/32119/zfhGYgntNRBwhBjLV6tGhdRK+eZXw/8mK5IJ4hmKoeAvs/9FPWfc6aMRKBeB1EpF5lfZRxySnTQi57+AM+46g6aG9ilrfpVmPMhRpEeOM+46g0Bqn+l0ut/vbdterVbF51eJJTSlrB45zrjrDJoa2qqK+VUG8VCDSmcxZ7PZ8/Nz6R+LelAhtdVkMim924dqCRWpdMEQZ9x1Bk0NiGL/IZSitgVDnHHXGQzZwYQecZwqUl5H/uZUd6QQi4Q6gEBCJhRMMDAUQ+G/OfP53LKsw+FwfX3Nmh7oGLJDJozjISLjiFzwrdQtrwCaGqA8zwtW2ir2EYdR7gVDHCmEVAQS3hzVnP2cZmKpP8rqkeNIIZgRSH0XPqo59Zxm/T+NiaWuig2hgqO1HCkEMwKp78JHNacOqui3JGKpY0oPoQBHCiEVTQ14o/g+4rQ8tE49C4Y4UgipCKQ+chzn559/Dg5VCiu+jzhLl9qi/pPunp+fHcf5/vvvWS2EWARSH00mk9im29Fo5LquKjaowvEWkiWFUOT/rOqOF6LbGwYEEv5U7qAK43hCZKmEws9zvBCawk4NiGIf8W7IPXbqOM52uz07Ozs7O7u6uqpimx8gFl12iGIf8fYqZcEQxwuhKVRIqBvVUrnK6k2IbXXheCHUiTkk1I25pVKU3s0YtLpsNpvhcEj3AepHIKEZ9IjnUE+jNscLoSkM2UEECqYk9a8W8nG8EOpHIEEQYimg146RPxzP837//fcgMKo7+A6oDV12qJbruhnPtlC9b8Yz98hFHubbox2QjDkkVMXzvMViMRwO/YWWNzc35gNDIzVBf6qlHBNps9nscDj4u+Jy8B06g0BCVZ6ensbjsb/xzHfffTcajcz3TX0fcdXdWCo4M/T8/Gzbtv81B9+hMwgkVOXi4sL/wh+jy3ff7FIsVdeewMF36AYCCVXx75KO49zd3V1dXb28vOS+b7a6R7yUyzZs0K44+A5dQSChTJH7pm3bX758ub+/tyzLtu2C980W7SNeejGUtEG7KmmPdkACAgllCt83t9utn0b+wxLvmzLH8ZpaMMTBd+gM1iGhKuv1+nA4nJ2d+Q8fHx9ns9l4PPbvm9PptJSf0ngshUfk9NG5yGqh6rCOFR1AIKFWFd03a46l1GLIX0iklNpsNl+/fvVbDas79Q7oBobsUKuKVsnUMIh30oic/4LwaiFOvQNSsVMDuqOKjR70rROyB97z87OfRkqp4/F4fn6+Xq9t2zbsVQH0GYGErgnHUr5kKuWYuwhOvQNSMWSHbsrRI158wZBhtdB0OvX7OCaTyW63y/f5QLcRSOg48/RSub3ahtVCnHoHpCKQ0FaO4wyHw/CBC4YjGCJ7PUSerwGn3gGpaPtG+/j7iI/H48+fP19fX/tDYeatxJWWRuG/+a7rnp+f13C2EKuFAAMCCe2z2WyUUsvl0t84/PHxcbfbOY4TbCWud1cHC4PCzyilvn79etIZGQCqw5Ad2ifYIMcvZVSGrcT1//AKFq6edEYGgOoQSGgr27Y/f/58dXXlP8y3lXgpZ2QAKAXrkNAajuPYtr3dbv2HNzc3z8/Pd3eD9xZuAAABGklEQVR3/sN8W4n7MzqO4ywWCz/bOFsIaAoVElojaKr2B9Om02nQd3DSVuKVnpEBIDcCCe1zeXm5Wq1c1z0cDn5Zc9IRDPWckQHgVHTZoZU8zzscDpEW6hxN1fWckQEgCwIJiGK1ENAIAgkAIAJddgAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQIT/BxTfDdOYBmAyAAAAAElFTkSuQmCC"
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot3(a(:,1),a(:,2),a(:,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}