Narrow Results

To construct symmetrical patterns on the unit sphere from the planar iterative function systems (IFSs), we present a method of constructing IFSs with $D_3$ symmetry which is composed of three-fold rotational symmetries together with reflections. An algorithm is developed to generate strange attractors with $D_3$ symmetry on a triangular face and then project it onto the surface of the unit sphere to form aesthetics patterns with spherical symmetry. As an illustrative example, we consider the regular inscribed icosahedron in the unit sphere which contains 20 triangular faces. This method is valid to randomly generate aesthetic spherical patterns using planar IFSs.