SprottD Attractor
Searching for 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}. This is case D.
Renders
Differential system:
\[\dot{x} = y\] \[\dot{y} = x + z\] \[\dot{z} = x\, z + \alpha\, y^2\]Constants:
\[\alpha = 3\]
You can find his awesome suff in Sprott’s Gateway ↩

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