ANALYSIS AND DESIGN OF SIERPINSKI CARPET: FRACTAL SHAPES AND CANCEROUS TISSUES

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Published: 2016-09-21

Page: 1-9


AMIR PISHKOO *

Physics and Accelerators Research School, NSTRI, P.O.Box 14395-836, Tehran, Iran

S. NOORI

Physics and Accelerators Research School, NSTRI, P.O.Box 14395-836, Tehran, Iran

F. ARYAMAJD

Physics and Accelerators Research School, NSTRI, P.O.Box 14395-836, Tehran, Iran

*Author to whom correspondence should be addressed.


Abstract

Using construction kit, this paper represents Sierpinski Carpet as the well known fractal shape in terms of Iterated Function System (IFS). IFS as the language of fractals consists of affine linear transformations which may be of type scaling, rotation, shearing, and translation. To clarify subject for pure mathematician one should first give some definitions related to contractions. The fractal structures are defined by notions like contraction, self-similarity, and space filling. By using "IFS construction kit", we show how Sierpinski Carpet fractal can be described and drawn by IFS. Finally, we show that how fractal analysis may be applied to describe tumor vasculature in cancer research.

Keywords: Fractal, self-similar, space- filling, sierpinski carpet, iterated function system, tumor vasculature


How to Cite

PISHKOO, A., NOORI, S., & ARYAMAJD, F. (2016). ANALYSIS AND DESIGN OF SIERPINSKI CARPET: FRACTAL SHAPES AND CANCEROUS TISSUES. Asian Journal of Mathematics and Computer Research, 14(1), 1–9. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/665

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