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 presented. The attractor of the "standard" 4-solenoid turns out to be "fat" that is, fractal dimensionality exceeds topological dimensionality by more than unity. If a fourth variable that is weakly damped is added to this 3-variable map, a new type of attractor is generated. In a cross section it is a continuous nowheredifTerentiable 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 possessing attractors of this new type are possible.