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Lorenz3D

by Massimo Salzano (Submitted: 05/14/2005)

[screen shot]

Download Lorenz3D
If clicking does not initiate a download, try right clicking or control clicking and choosing "Save" or "Download".(The run link is disabled for this model because it requires NetLogo 3-D Preview 1, or later, to run.)

WHAT IS IT?

The Lorenz system is a well known example of a simple system showing chaos. Its dynamics depend on many parameters. Here named a b c mu gamma and deltat and the initial conditions x0 y0 z0.

HOW IT WORKS

We calculate the values of k points x, y, and z (k = 2000) iterating the 3 main equations:
x(n)= x(n - 1) + gamma * y(n - 1) - x(n - 1) * deltat
y(n)= y(n - 1) + ( - (x(n - 1) * z(n - 1)) + mu * x(n - 1) - (y(n - 1)) * deltat)
z(n)= z(n - 1) + ((x(n - 1) * y(n - 1) - b * z(n - 1) * deltat
Initial points are x(0)=x0, y(0)=y0 and z(0)=z0 This give the trajectory.

HOW TO USE IT

deltat slider: sets deltat between 0.0010 and 0.015
SETUP: Clears all the parameter and start again the the 3D graphic window.
GO: Build the trajectory for the choosen values.
BallColor slider: sets foundamental color of the points.
BallSize slider: sets the size of points between 0.03 to 2
SameColor switch: "On" gradually changes the color of points otherways the color is fixed.
Screen slider: virtually sets the edge of 3D.
THINGS TO TRY

Identify the attractor for different values of "deltat".
Try to lok at different representation in the XY, XZ, YZ and Zt (where t is time) spaces. Especially the last one, if compared with the 3D graph, can be interesting for the novice.

CREDITS AND REFERENCES

Program by Massimo Salzano, www.ecople.org, http://www.dise.unisa.it/docenti/salzano.htm
14 May 2005.

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