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 Linz^3,4. Case A contains just 5 terms and requires two of them to be nonlinear – meaning the scaling factor of their variable is not constant.

Renders

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.

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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. ↩