THOMAS ATTRACTOR

In the dynamical systems theory, Thomas' cyclically symmetric attractor is a 3D strange attractor originally proposed by René Thomas. It has a simple form which is cyclically symmetric in the x,y, and z variables and can be viewed as the trajectory of a frictionally dampened particle moving in a 3D lattice of forces. The simple form has made it a popular example.

and a system of three ordinary differential equations describing the structure as-

$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&\sin y -bx\\ \frac{dy}{dt}&=&\sin z -by\\ \frac{dz}{dt}&=&\sin x-bz \end{eqnarray*}\right. $

When b=0.20, a solution curve of this system has the shape of beautiful curve and the position of particles will follow a similar path.

---