Sprott-A Attractor

Searching for (algebraically speaking) the most simple systems that would behave chaotic around an attractor in 1994, Julien Clinton Sprott1 found 19 distinct cases from A through S which have at most 6 terms across three dimensions2. They are occasionally called Sprott-Linz attractors because of the contributions by the German physicist Stefan Linz3,4. Case A contains just 5 terms and requires two of them to be nonlinear – meaning the scaling factor of their variable is not constant.


Differential system:

\[\dot{x} = y\] \[\dot{y} = - x + y\, z\] \[\dot{z} = 1 - y^2\]



Stereographic Animation

Here you can find case D which I also rendered in this series. Case G can be found here.

You can now get a print of the Sprott attractors in my shop! Read more about it here.

  1. You can find his awesome suff in Sprott’s Gateway 

  2. J.C. Sprott, 1994. "Some simple chaotic flows". Phys. Rev. E. 50(2). doi:10.1103/PhysRevE.50.R647

  3. S.J. Linz, 1997. "Nonlinear dynamical models and jerky motion". Am. J. Phys. 65(6). doi:10.1119/1.18594

  4. S.J. Linz and J.C. Sprott, 1999. "Elementary chaotic flow". Phys. Let. A. 259(3–4). doi:10.1016/S0375-9601(99)00450-8