Lorenz Attractor

Author

Eric W. Weisstein
November 19, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DynamicalSystems/LorenzAttractor.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/LorenzAttractor.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Solution

V5

Timing[soln=NDSolve[{
x'[t]==-3 (x[t]-y[t]),
y'[t]==-x[t]z[t]+26.5 x[t]-y[t],
z'[t]==x[t] y[t]-z[t],
x[0]==z[0]==0,
y[0]==1
},{x,y,z},{t,0,20},MaxSteps->3000]]

plot=ParametricPlot3D[Evaluate[{x[t],y[t],z[t],Red}/.soln],{t,0,20},PlotPoints->1000]

ParametricPlot3D[Evaluate[{x[t],y[t],z[t],Hue[t/100]}/.soln],{t,0,20},PlotPoints->1000]

V6

Timing[soln=NDSolve[{
x'[t]==-3 (x[t]-y[t]),
y'[t]==-x[t]z[t]+26.5 x[t]-y[t],
z'[t]==x[t] y[t]-z[t],
x[0]==z[0]==0,
y[0]==1
},{x,y,z},{t,0,20},MaxSteps->3000]]

plot=ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.soln],{t,0,20},Ticks->None]

LiveGraphics3D

<<Utilities`LiveGraphics3D`

WriteLiveForm["lorenz.m",plot]