Polygonal Surface Visualization of Strange Attractors

Strange attractors are stable sets of vector field flows that have a fractal geometric structure in one dimension, and smooth surface behaviour in the other two. Previous visualization methods show the flow dynamics well, but not the fractal structure. Here we approximate the attractor by polygonal surfaces, which reveal the fractal geometry. We start with a polygonal approximation which neglects the fractal dimension, and then deform it by the flow to create multiple sheets of the fractal structure. We use adaptive subdivision and retiling methods to preserve the quality of the polygonal surface in the face of extreme stretching, bending, and creasing caused by the flow.