SprottA Attractor
Searching for (algebraically speaking) the most simple systems that would behave chaotic around an attractor in 1994, Julien Clinton Sprott^{1} found 19 distinct cases from A through S which have at most 6 terms across three dimensions^{2}. They are occasionally called SprottLinz 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 find his awesome suff in Sprott’s Gateway ↩

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

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

S.J. Linz and J.C. Sprott, 1999. "Elementary chaotic flow". Phys. Let. A. 259(3–4). doi:10.1016/S03759601(99)004508. ↩