A SUPERFAT ATTRACTOR WITH A SINGULAR-CONTINUOUS 2-D WEIERSTRASS FUNCTION IN A CROSS-SECTION

A 3-D invertible map generating a 4-loop solenoid attractor is present ed. The attractor of the ''standard'' 4-solenoid turns out to be ''fat '' - that is, fractal dimensionality exceeds topological dimensionalit y by more than unity. If a fourth variable that is weakly damped is ad ded to this 3-variable map, a new type of attractor is generated. In a cross section it is a continuous nowhere-differentiable function over a 2-D domain which is a 2-D Cantor set. Such an object can be called a ''singular-continuous 2-D Weierstrass function''. The latter can be ''superfat'' (dimension gap larger than 2). Realistic systems possessi ng attractors of this new type are possible.