Strange Attractor [gnuplot]

Lorenz equation

\begin{eqnarray*} \frac{\mathrm{d}x}{\mathrm{d}t}&=&-\sigma(x-y) \\ \frac{\mathrm{d}y}{\mathrm{d}t}&=&Rx-y-xz\\ \frac{\mathrm{d}z}{\mathrm{d}t}&=&xy-bz \end{eqnarray*} \[(R=28,~b=\frac{8}{3},~\sigma=10)\]

PLT files

lorenz.plt

make.plt

lorenz.gif

Rössler equation

\begin{eqnarray*} \frac{\mathrm{d}x}{\mathrm{d}t}&=&-y-z \\ \frac{\mathrm{d}y}{\mathrm{d}t}&=&z+ay\\ \frac{\mathrm{d}z}{\mathrm{d}t}&=&b+xz-cz \end{eqnarray*} \[(a=0.3,~b=0.3,~c=5.7)\]

Langford equation

\begin{eqnarray*} \frac{\mathrm{d}x}{\mathrm{d}t}&=&(z-\beta)x-\omega y \\ \frac{\mathrm{d}y}{\mathrm{d}t}&=&\omega x+(z-\beta)y\\ \frac{\mathrm{d}z}{\mathrm{d}t}&=&\lambda+\alpha z-\frac{z^3}{3}-(x^2+y^2)(1+\rho z)+\varepsilon zx^3 \end{eqnarray*} \[(\alpha=1,~\omega=3.5,~\beta=0.7,~\rho=0.25,~\lambda=0.6,~\varepsilon=0)\]

Other examples

GitHub: https://github.com/hiroloquy/strange-attractor.git