3da_frac_lorenz.cpp File Reference

Draw lorenz attractors with different initial conditions. More...

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Detailed Description

Draw lorenz attractors with different initial conditions.

Author

Mitch Richling https://www.mitchr.me

Standards

C++20

Copyright

Copyright (c) 1988-2015, Mitchell Jay Richling https://www.mitchr.me All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
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Details

This code generates a fractal-like image from the Lorenz system. The image represents a rectangle in \(\mathbb{R}^3\) parallel to the \(x\)- \(z\) plane, and hitting the \(y\) axis at \(1.51\). We start the IVP problem with initial conditions in this rectangle. The color represents the time required for the \(x\) value to change sign.

For reference the Lorenz system is defined by:

\[ \begin{array}{lcl} \frac{dx}{dt} & = & a(y-x) \\ \frac{dy}{dt} & = & x(b-z)-y \\ \frac{dz}{dt} & = & xy-cz \end{array} \]

Traditional parameter values are:

\[ \begin{array}{lcc} a & = & 10 \\ b & = & 28 \\ c & = & \frac{8}{3} \end{array} \]

Definition in file 3da_frac_lorenz.cpp.