A Review of Fractals Properties: Mathematical Approach

Md. Nurujjaman; Ahammad Hossain; Dr. Payer Ahmed

doi:doi:10.11648/j.sjams.20170503.11

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A Review of Fractals Properties: Mathematical Approach

Md. Nurujjaman, Ahammad Hossain, Dr. Payer Ahmed

Published in Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 3)

Received: 16 March 2017 Accepted: 12 April 2017 Published: 17 May 2017

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Abstract

In this article, we will discuss some spectacularly beautiful images known as Fractals such as Sierpiński Triangle, Koch Curve, Dragon Curve, Koch Island, H Fractal, The Levy Curve Fractal, Box Fractal etc. We will investigate and calculate the area, perimeter and self-similar dimension of fractals. Observing the results we see some similarities about the said properties for some fractals those are generated by particular method. Our attention is restricted to find the mathematical behavior of Fractals so that we can establish mathematical formulas concerning the fractals.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 3)
DOI	10.11648/j.sjams.20170503.11
Page(s)	98-105
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Fractals, Iterations, Area, Perimeter, Fractal Dimension

References

[1]	Prof. Emma Carberry, Alan Dunn, 18.091 Introduction to Dynamical Systems, Lecture 11: Fractals and Dimension, Spring 2005.
[2]	Peitgen, H.-O., Jürgens, H., Saupe, D.: Chaos and Fractals, Springer-Velag New York, inc., 1992
[3]	Peitgen, H.-O., Richter, P.: The Beauty of Fractals, Springer-Verlag, Heidelberg, 1986
[4]	Peitgen, H.-O., Saupe, D.: The Science of Fractal Images, Springer-Verlag, New York, 1988
[5]	http://www.math.nus.edu.sg/aslaksen/gem-projects/maa/World_of_Fractal.pdf
[6]	https://en.wiktionary.org/wiki/frangere.
[7]	Robert L. Devaney, Fractal Dimension, Sun Apr 2 14:31:18 EDT 1995.
[8]	wikipedia.org/wiki/Fractal.
[9]	Bahman Zohuri, Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists, Springer International Publishing Switzerland 2015.
[10]	Laxmi Narayan Padhy, Fractal Dimension of Gray Scale & Colour Image, ijarcsse, © 2015.
[11]	The GEOMETRY OF NATURE:FRACTALS,Josefina Dexeus, IES Severo Ochoa.
[12]	Rupleen Kaur, A Review of Various Fractal Geometries for Wireless Applications, Int. Journal of Electrical & Electronics Engg.
[13]	Gabriele A. Losa, From Fractal Geometry to Fractal Analysis, Applied Mathematics, 2016, 7, 346-354 Scientific Research Publishing Inc.
[14]	Ankit Garg, A Review on Natural Phenomenon of Fractal Geometry, International Journal of Computer Applications (0975 – 8887) Volume 86 – No 4, January 2014.
[15]	Dr. Vyomesh Pant, FRACTAL GEOMETRY: AN INTRODUCTION, Journal of Indian Research, vol:1, No:2, 66-70, April-June.
[16]	T Pant, Effect of Noise in Estimation of Fractal Dimension of Digital Images, International Journal of Signal Processing, Image Processing and Pattern Recognition Vol.6, No.5 (2013), pp.101-116.
[17]	Harry A. Schmitz, On the Role of the Fractal Cosmos in the Birth and Origin of Universes, Journal of Theoretics, 5 Marwood Road South, Port Washington, New York 11050.
[18]	GUOQIANG SHEN, Fractal dimension and fractal growth of urbanized areas, int. j. geographical information science, 2002 vol. 16, no. 5, 419± 437.

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APA Style

Md. Nurujjaman, Ahammad Hossain, Dr. Payer Ahmed. (2017). A Review of Fractals Properties: Mathematical Approach. Science Journal of Applied Mathematics and Statistics, 5(3), 98-105. https://doi.org/10.11648/j.sjams.20170503.11

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ACS Style

Md. Nurujjaman; Ahammad Hossain; Dr. Payer Ahmed. A Review of Fractals Properties: Mathematical Approach. Sci. J. Appl. Math. Stat. 2017, 5(3), 98-105. doi: 10.11648/j.sjams.20170503.11

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AMA Style

Md. Nurujjaman, Ahammad Hossain, Dr. Payer Ahmed. A Review of Fractals Properties: Mathematical Approach. Sci J Appl Math Stat. 2017;5(3):98-105. doi: 10.11648/j.sjams.20170503.11

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@article{10.11648/j.sjams.20170503.11,
  author = {Md. Nurujjaman and Ahammad Hossain and Dr. Payer Ahmed},
  title = {A Review of Fractals Properties: Mathematical Approach},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {5},
  number = {3},
  pages = {98-105},
  doi = {10.11648/j.sjams.20170503.11},
  url = {https://doi.org/10.11648/j.sjams.20170503.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20170503.11},
  abstract = {In this article, we will discuss some spectacularly beautiful images known as Fractals such as Sierpiński Triangle, Koch Curve, Dragon Curve, Koch Island, H Fractal, The Levy Curve Fractal, Box Fractal etc. We will investigate and calculate the area, perimeter and self-similar dimension of fractals. Observing the results we see some similarities about the said properties for some fractals those are generated by particular method. Our attention is restricted to find the mathematical behavior of Fractals so that we can establish mathematical formulas concerning the fractals.},
 year = {2017}
}

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TY  - JOUR
T1  - A Review of Fractals Properties: Mathematical Approach
AU  - Md. Nurujjaman
AU  - Ahammad Hossain
AU  - Dr. Payer Ahmed
Y1  - 2017/05/17
PY  - 2017
N1  - https://doi.org/10.11648/j.sjams.20170503.11
DO  - 10.11648/j.sjams.20170503.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 98
EP  - 105
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20170503.11
AB  - In this article, we will discuss some spectacularly beautiful images known as Fractals such as Sierpiński Triangle, Koch Curve, Dragon Curve, Koch Island, H Fractal, The Levy Curve Fractal, Box Fractal etc. We will investigate and calculate the area, perimeter and self-similar dimension of fractals. Observing the results we see some similarities about the said properties for some fractals those are generated by particular method. Our attention is restricted to find the mathematical behavior of Fractals so that we can establish mathematical formulas concerning the fractals.
VL  - 5
IS  - 3
ER  -

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Author Information

Md. Nurujjaman

Department of Mathematics, Sonargaon University, Dhaka, Bangladesh
Ahammad Hossain

Department of Mathematics, Sonargaon University, Dhaka, Bangladesh
Dr. Payer Ahmed

Department of Mathematics, Jagannath University, Dhaka, Bangladesh

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APA Style

Md. Nurujjaman, Ahammad Hossain, Dr. Payer Ahmed. (2017). A Review of Fractals Properties: Mathematical Approach. Science Journal of Applied Mathematics and Statistics, 5(3), 98-105. https://doi.org/10.11648/j.sjams.20170503.11

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ACS Style

Md. Nurujjaman; Ahammad Hossain; Dr. Payer Ahmed. A Review of Fractals Properties: Mathematical Approach. Sci. J. Appl. Math. Stat. 2017, 5(3), 98-105. doi: 10.11648/j.sjams.20170503.11

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AMA Style

Md. Nurujjaman, Ahammad Hossain, Dr. Payer Ahmed. A Review of Fractals Properties: Mathematical Approach. Sci J Appl Math Stat. 2017;5(3):98-105. doi: 10.11648/j.sjams.20170503.11

Copy | Download

@article{10.11648/j.sjams.20170503.11,
  author = {Md. Nurujjaman and Ahammad Hossain and Dr. Payer Ahmed},
  title = {A Review of Fractals Properties: Mathematical Approach},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {5},
  number = {3},
  pages = {98-105},
  doi = {10.11648/j.sjams.20170503.11},
  url = {https://doi.org/10.11648/j.sjams.20170503.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20170503.11},
  abstract = {In this article, we will discuss some spectacularly beautiful images known as Fractals such as Sierpiński Triangle, Koch Curve, Dragon Curve, Koch Island, H Fractal, The Levy Curve Fractal, Box Fractal etc. We will investigate and calculate the area, perimeter and self-similar dimension of fractals. Observing the results we see some similarities about the said properties for some fractals those are generated by particular method. Our attention is restricted to find the mathematical behavior of Fractals so that we can establish mathematical formulas concerning the fractals.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - A Review of Fractals Properties: Mathematical Approach
AU  - Md. Nurujjaman
AU  - Ahammad Hossain
AU  - Dr. Payer Ahmed
Y1  - 2017/05/17
PY  - 2017
N1  - https://doi.org/10.11648/j.sjams.20170503.11
DO  - 10.11648/j.sjams.20170503.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 98
EP  - 105
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20170503.11
AB  - In this article, we will discuss some spectacularly beautiful images known as Fractals such as Sierpiński Triangle, Koch Curve, Dragon Curve, Koch Island, H Fractal, The Levy Curve Fractal, Box Fractal etc. We will investigate and calculate the area, perimeter and self-similar dimension of fractals. Observing the results we see some similarities about the said properties for some fractals those are generated by particular method. Our attention is restricted to find the mathematical behavior of Fractals so that we can establish mathematical formulas concerning the fractals.
VL  - 5
IS  - 3
ER  -

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