A Multicontrol p-ary Subdivision Scheme to Generate Fractal Curves

Hong Chan Zheng; Yi Li; Guo Hua Peng; Ya Ning Tang

doi:10.4028/www.scientific.net/AMM.263-266.1830

Paper Titles

Three Dimensional Visualization Technologies for Water Conservancy Works
p.1809

Time and Cost Management of Project Development Based on Cloud Computing Platform
p.1813

A Media Stream Multicast Model Based on Proxy
p.1818

A Mesh Deformation Method with Multiple Editing Granularities
p.1822

A Multicontrol p-ary Subdivision Scheme to Generate Fractal Curves
p.1830

A Pattern for Partial Software Architecture
p.1838

Algorithms of Data Mining and Knowledge Discovery of Correlativity in Two-Dimensional Time Series
p.1844

Design and Implementation of Landscape System for East and West Huashi Street in Beijing Based on Virtual Reality Technology
p.1849

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 263-266A Multicontrol p-ary Subdivision Scheme to...

A Multicontrol p-ary Subdivision Scheme to Generate Fractal Curves

Abstract:

In this paper, we firstly devise a p-ary subdivision scheme based on normal vectors with multi-parameters to generate fractals. The method is easy to use and effective in generating fractals since the values of the parameters and the directions of normal vectors can be designed freely to control the shape of generated fractals. Secondly, we illustrate the technique with some design results of fractal generation and the corresponding fractal examples from the point of view of visualization. Finally, some fractal properties of the limit of the presented subdivision scheme are described from the point of view of theoretical analysis.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volumes 263-266)

Pages:

1830-1833

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.263-266.1830

Citation:

Cite this paper

Online since:

December 2012

Authors:

Hong Chan Zheng*, Yi Li, Guo Hua Peng, Ya Ning Tang

Keywords:

Fractal, Fractal Generation, Fractal Property, Subdivision Scheme

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] E. Catmull, and J. Clark: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design 10, 6 (1978), 350-355.

DOI: 10.1016/0010-4485(78)90110-0

Google Scholar

[2] B.B. Mandelbrot: The Fractal Geometry of Nature. Freeman, 1982.

Google Scholar

[3] M.F. Barnsley, and S. Demko: Iterated function systems and the global construction of fractals. In Proc. the Royal Society A 399 (1985), pp.243-275.

Google Scholar

[4] P. Prusinkiewicz, and A. Lindenmayer: The algorithmic beauty of plants. Springer-Verlag, 1990.

Google Scholar

[5] Wei Ding, and Dongxu Qi: Recursive refinement algorithm of fractal generation and its application. Journal of Image and Graphics 3, 2 (1998), 123-128 (in Chinese).

Google Scholar

[6] P. Lévy: Plane or space curves and surfaces consisting of parts similar to the whole. In Gerald Edgar, ed. Classics on Fractals. Addison-Wesley, pp.181-239, 1993.

Google Scholar

[7] A. Chang, and Tianrong Zhang: The fractal geometry of the boundary of dragon curves. Journal of Recreational Mathematics 30, 1 (1999-2000), 9-22.

Google Scholar

[8] F. Kenneth: Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons Ltd, 2003.

Google Scholar

[9] C. McMullen: The Hausdorff dimension of general Sierpiński carpets. Nagoya Mathematical Journal Volume 96 (1984), 1-9.

DOI: 10.1017/s0027763000021085

Google Scholar

[10] H. Koch: On a continuous curve without tangents constructible from elementary geometry. In Gerald Edgar, ed. Classics on Fractals. Addison-Wesley, pp.24-45, 1993.

Google Scholar