VCG - Lorenz Attractor

Description

Model of a Lorenz Attractor, a set of chaotic solutions for the Lorenz Equations described by Edward Lorenz in 1963.

Details

The Lorenz Attractor [Lorenz] is one of many solutions to the Lorenz System, first studied by Edward Lorenz in 1963. Most notable, the Lorenz Attractor in particular is a set of chaotic solutions, satisfying the equation:
$v(x,y,z,t)=\begin{pmatrix}\sigma*(y-x)\\x*(\rho-z)-y\\x*y-\beta*z\end{pmatrix}$
Where the variables $x$, $y$, $z$ relate to the rate of convection, horizontal temperature variation and vertical temparature variation of a 2d-fluid layer uniformly warmed from below and cooled from above.

Input

Output

vtkImageData

Parameters

Name
Description
 Values/Default
Sigma Sigma system parameter of the Lorenz System. Proportional to the Prandtl-Number of the system. 10.0
Beta Beta system parameter of the Lorenz System. Proportional to other specific system characteristics. 2.6666666
Rho Rho system parameter of the Lorenz System. Proportional to the Rayleigh-Number. 28.0
OutputSpaceTime Add time dimension to output dimenstions. 0
TimeRange Time range of samples. 0.0 0.0
TimeSteps Number of time steps for the samples. 1
Samples Number of samples in each dimension. 100 100 100
Origin Point of origin for the samples window. -30.0 -30.0 -10.0
Scale Scale of sample distance in each dimension. 70.0 70.0 70.0

Installation Instructions

Authors

Lutz Hofmann

References

E. N. Lorenz:
Deterministic Nonperiodic Flow
Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130-141, 1963.

Acknowledgements