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Proceedings of CAD'14, 2014, 103-105
Design for Manufacturing of IFS Fractals from the Perspective of Barnsley's Fern-leaf

A. M. M. Sharif Ullah, Yoshimi Sato, Akihiko Kubo, Kitami Institute of Technology

Abstract. Fractal geometry is effective in creating CAD models of complex shapes including the natural ones (tree, leaf, landscape). Here, a (complex) shape modeled by fractal geometry is referred to as fractal. One of the popular fractals is known as Barnsley's fern-leaf that is created using the Iterative Function System (IFS). As defined by the system, four affine maps create a set of points in a recurrent manner and model the fern-leaf. The objective of this article is to elucidating a methodology of design for manufacturing of IFS fractals putting emphasis on the Barnsely's fern-leaf. To achieve the objective the following issues are addressed: (1) What is the basic shape that repeats?, (2) What are the roles of affine maps?, (3) What is the scaling factor and how to control it?, (4) How to control the levels?, (5) How to create non-crossing tool paths?, and (5) How to create facets and control their population?

Keywords. Fractals, design for manufacturing, geometric modeling, physical model

DOI: 10.14733/cadconfP.2014.103-105