Fractal Deformation Using Displacement Vectors Based on Extended Iterated Shuffle Transformation

• Published in: Journal of the Society for Art and Science Vol. 1; no. 3; pp. 134 - 146
• Main Authors: Ohno, Yoshio, Fujimoto, Tadahiro, Muraoka, Kazunobu, Chiba, Norishige
• Format: Journal Article
• Language: English; Japanese
• Published: The Society for Art and Science 2002
• Subjects: attractor; computer graphics (CG); fractal; geometric model; Iterated Function System (IFS); Iterated Shuffle Transformation (IST); shape deformation
• ISSN: 1347-2267; 1347-2267
• DOI: 10.3756/artsci.1.134

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.