🚀 go-pugleaf

I'm writing a book that contains several hundred examples of strange attractors
with a simple description of the underlying mathematics.  Perhaps some of you
experts could answer the following questions:

1) I notice that simple attractors like the Mandelbrot set have complicated
basins of attraction, while complicated (strange) attractors like the Henon map
have simple basins.  Is this a general principle, and if so, is there a reason
for it?

2) I've heard that strange attractors arising from systems of ordinary
differential equations must have dimension greater than 2.0.  If this is true,
is there an easy way to see why?

3) Is there a mapping or system of ODE's involving only polynomials whose
solution attracts to:
     a) a 2-torus
     b) a 3-torus
     c) a Moebius strip?

I would also welcome suggestions for classes of equations that produce visually
interesting attractors other than the standard ones, such as those in FRACTINT.
(The book is "Strange Attractors," and it will be published by M&T Books in
June 1993.)