28:null 29:["$","title",null,{"children":"Lorentz Attractor | C. Cossé | Observable"}] 2e:T5b3,ntuple={ var rk4sum; var t0=1000. var txyz=[[t0,0,.1,3],] for(var i=1;ivrange){\n \tvmin=extrema[2][0];\n vmax=extrema[2][1];\n vrange=vmax-vmin;\n }\n if((extrema[2][1]-extrema[2][0])>vrange){\n \tvmin=extrema[3][0];\n vmax=extrema[3][1];\n vrange=vmax-vmin;\n }\n \n var dataline=d3.line()\n\t.x(function(d,i){\n \treturn ( (xfpt(d)[0]-vmin)/vrange*W);\n\t})\n\t.y(function(d){\n \treturn ( (xfpt(d)[1]-2*vmin)/vrange*H);\n\t});\n \n svg.append(\"path\")\n \t\t.attr(\"d\",dataline(ntuple))\n \t\t.style(\"fill\",\"none\")\n\t\t.style(\"stroke\",fg_color)\n\t\t.style(\"stroke-width\",1);\n \n svg.append(\"circle\")\n \t.attr(\"cx\",(xfpt(ntuple[ntuple.length-1])[0]-vmin)/vrange*W)\n .attr(\"cy\",(xfpt(ntuple[ntuple.length-1])[1]-2*vmin)/vrange*H)\n \t.attr(\"r\",5)\n \t.attr(\"fill\",\"#F00\")\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":100,"value":"current_vars={\n var colnames=[\"rotZ\",\"beta\",\"rho\",\"sigma\",\"h\",\"npts\"]\n var table=d3.create(\"table\");\n var thr=table.append(\"tr\")\n var tdr=table.append(\"tr\")\n for(var colname of colnames){\n \tthr.append(\"th\").html(colname)\n switch(colname){\n case \"rotZ\":\n tdr.append(\"td\").html(rotZ.toFixed(4));break;\n case \"beta\":\n tdr.append(\"td\").html(beta.toFixed(4));break;\n case \"rho\":\n tdr.append(\"td\").html(rho.toFixed(4));break;\n case \"sigma\":\n tdr.append(\"td\").html(sigma.toFixed(4));break;\n case \"h\":\n tdr.append(\"td\").html(h.toFixed(4));break;\n case \"npts\":\n tdr.append(\"td\").html(npts.toFixed(0));break; \n default:\n tdr.append(\"td\").html(\"ERR!\")\n }\n }\n \n return table.node();\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":405,"value":"viewof rotZ=html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"viewof beta=html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"viewof rho=html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"viewof sigma=html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"viewof h=html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"viewof npts=html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":307,"value":"desc={\n\tvar _desc=html`\n

\n\nThis implements a classic 4th order Runge-Kutta scheme[1]:\n\ndydx=f(x,y) -> y_(n+1)=y_(n)+[\n\th*f(x_n,y_n)+\n\t2*h*f(x_n+h/2,y_n+(h*f(x_n,y_n))/2)+\n\t2*h*f(x_n+h/2,y_n+(h*f(x_n+h/2,y_n+(h*f(x_n,y_n))/2))/2)+\n\th*f(x_n+h,y_n+(h*f(x_n+h/2,y_n+(h*f(x_n,y_n))/2))\n\t]/6\n\nRK4 Generalized to coupled equations:\n\n\t-> dudx=f1(x,u,v),dvdx=f2(x,u,v)\n\t-> dxdt=f1(t,x,y,z),dydt=f2(t,x,y,z),dzdt=f3(t,x,y,z)\n\nwhere [2]:\n\n\tf1=dxdt=sig(y-x)\n\tf2=dydt=-xz+rx-y\n\tf3=dzdt=xy-bz\n\n

\n\t`\n return _desc;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"f=function(i,t,x,y,z){\n \tswitch(i){\n case 1:\n return sigma*(y-x)\n break;\n case 2:\n return (-x*z+rho*x-y)\n break;\n case 3:\n return (x*y-beta*z)\n break;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"$2e","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":77,"value":"extrema={\n\tvar ext=[[null,null],[null,null],[null,null],[null,null]]\n for(var i=1;iext[idx][1])ext[idx][1]=ntuple[i][idx];\n }\n }\n }\n return ext\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"W=window.innerWidth*.92","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"H=2*W/3","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"d3 = require(\"https://d3js.org/d3.v5.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":180,"value":"viewof fg_color=html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":182,"value":"viewof bg_color=html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":301,"value":"init={\n\tvar event = document.createEvent('Event');\n \tevent.initEvent('input', true, true);\n \td3.selectAll(\"#npts\").node().dispatchEvent(event);\n \treturn \"ok\"\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":349,"value":"md`## References`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":331,"value":"md`\\[0\\] [Wikipedia, Lorentz System](https://en.wikipedia.org/wiki/Lorenz_system)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":345,"value":"md`\\[1\\] [Arfken & Weber, Mathematical Methods for Physicists](\"https://www.amazon.com/Mathematical-Methods-Physicists-George-Arfken/dp/0120598760/ref=sr_1_2?ie=UTF8&qid=1518717297&sr=8-2&keywords=arfken\")`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":467,"value":"md`\\[2\\] [Abarbanel, Analysis of Observed Chaotic Data](https://www.amazon.com/Analysis-Observed-Chaotic-Institute-Nonlinear/dp/0387983724/ref=sr_1_13?ie=UTF8&qid=1518762483&sr=8-13&keywords=nonlinear+chaotic)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":533,"value":"md`\\[3\\] [AIP Article](https://publishing.aip.org/publishing/journal-highlights/taming-chaos-calculating-probability-complex-systems?Track=CHAOStweet)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":391,"value":"quat={\n\tvar transformPrecalc=[];\n\tvar cosB=Math.cos(rotZ);\n\tvar sinB=Math.sin(rotZ);\n\ttransformPrecalc[0]=cosB;\n\ttransformPrecalc[1]=0;\n\ttransformPrecalc[2]=sinB;\n\ttransformPrecalc[3]=0;\n\ttransformPrecalc[4]=1;\n\ttransformPrecalc[5]=0;\n\ttransformPrecalc[6]=-sinB;\n\ttransformPrecalc[7]=0;\n\ttransformPrecalc[8]=cosB;\n \treturn transformPrecalc;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":393,"value":"xfpt=function(point){\n\treturn [\n\t\tquat[0]*point[1]-quat[1]*point[3]+quat[2]*point[2],\n\t\tquat[3]*point[1]-quat[4]*point[3]+quat[5]*point[2],\n\t\tquat[6]*point[1]-quat[7]*point[3]+quat[8]*point[2]\n\t];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2f","stdlib":"1","titling":"auto"}} 2d:"$2c:body"