Generative systems with chaotic behavior.
A new 3D autonomous dynamical system proposed by Dequan Li (Physics
Letters A, 372, 387, 2008.) produces a chaotic attractor whose global topological
properties are unusual. The attractor has a rotation symmetry and only a single real
fixed point for the parameters used in his study. The symmetric, complex pair of fixed
points cannot be ignored: they play a major role in organizing the motion on a surface
of peculiar toroidal type. #1
The algorithm
javascript·dequan-li.js
const a = 40.0;
const b = 1.833;
const c = 0.16;
const d = 0.65;
const e = 55.0;
const f = 20.0;
const next = (x,y,z) => {
const dx = a * (y - x) + c * x * z;;
const dy = e * x + f * y - x * z;
const dz = b * z + x * y - d * x * x;
return {dx,dy,dz};
};
References
