3D Fractals From Periodic Surfaces

Fractals are ubiquitous as in natural objects and have been applied in designing porous structures such as micro antenna and porous silicon. The seemingly complex and irregular structures can be generated based on simple principles. In this paper, we present three approaches to construct 3D fractal geometries using a recently proposed periodic surface model. By applying iterated function systems to the implicit surface model in the Euclidean or parameter space, 3D fractals can be constructed efficiently. Porosity is also proposed as a metric in fractal design.Copyright © 2010 by ASME

[1]  Laurie Hodges,et al.  Construction of fractal objects with iterated function systems , 1985, SIGGRAPH.

[2]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[3]  John C. Hart Implicit Representations of Rough Surfaces , 1997, Comput. Graph. Forum.

[4]  Yan Wang,et al.  Loci Periodic Surface Reconstruction from Crystals , 2007 .

[5]  Javier Alda,et al.  Optical antennas for nano-photonic applications , 2005 .

[6]  D. Werner,et al.  An overview of fractal antenna engineering research , 2003 .

[7]  M. Barnsley,et al.  Iterated function systems and the global construction of fractals , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  Dietmar Saupe,et al.  Rendering Methods for Iterated Function Systems , 1991 .

[9]  Yan Wang,et al.  Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm , 2022 .

[10]  Eric Tosan,et al.  Fractal modeling using free form techniques , 1996, Comput. Graph. Forum.

[11]  Atilla Baskurt,et al.  Fractal approximation of surfaces based on projected IFS attractors , 2001, Eurographics.

[12]  F. Zhou,et al.  Correlation of excitation-wavelength dependent photoluminescence with the fractal microstructures of porous silicon , 2008 .