Fractality of refined triangular grids and space-filling curves

Abstract

In this paper we explain the fractal geometry of refined and derefined triangular and tetrahedral meshes by means of the application of iterated function systems (IFS). These meshes feature a remarkable amplifying invariance under changes of scale. The applications of IFS families are shown equivalent to the use of adaptive strategies that combine the refinement procedure with the derefinement procedure. In addition, space-filling curves (SFC) are used to assign a binary code for any 2D triangular refined mesh. SFC are also shown as useful for the problem of automatic domain decomposition.