Fractal Deformation Using Displacement Vectors Based on Extended Iterated Shuffle Transformation

Abstract

In this paper, we propose a framework of "fractal deformation" using displacement vectors based on "extended Iterated Shuffle Transformation (ext-IST)". An ext-unit-IST is a one-to-one and onto mapping that is extended from a unit-IST, which we have proposed, and is basically defined on a code space. When the mapping is applied on a geometric space, a fractal-like repeated structure, which is referred to as "local resemblance in space/scale directions", is constructed on the relationship between points on the domain and those on the range. By applying the mapping to displacement vectors given on a geometric shape, the shape can be deformed in the fractal-like repeated manner. This fractal deformation is easy to control by changing the displacement vectors intuitively. In addition, a continuous transition between a continuous deformation and a fractal deformation can be realized. We demonstrate how the fractal deformation technique produces attractive results by showing various examples.