# Fractals in Math and Nature Analytical Essay by Nicky

Fractals in Math and Nature
An in-depth look at fractals in concept and reality.
# 146785 | 1,300 words | 6 sources | MLA | 2011 | Published on Jan 17, 2011 in Engineering (General) , Mathematics (General)

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## Description:

This paper explores fractals, which are often referred to as the geometry of nature. First, fractals are defined as resembling a fracture or a series of complicated and uncoordinated breaks. The paper further considers the complexity of a fractal and its design despite it starting off as a simple figure. Various types of fractals are elaborated upon, which include the Sierpiski triangle, the Sierpiski carpet and the dragon curve among others. The paper traces the development of each fractal, showing its mathematical formula. The paper concludes by stating that there are many fractals in nature for which precise mathematical formalisms have been developed. It also addresses the application of fractals in modern life. The paper contains several illustrations.

Outline:

Sierpi ski Triangle
Sierpi ski Carpet and Menger Sponge
Dragon Curve
Mandelbrot Set
Koch Snowflake (Star)
Conclusion

## From the Paper:

"The end product of these endeavors is often a fascinating figure. While it is possible to create a fractal that appears complex, though it might have started from a very simple figure, the end product cannot be described in terms of a simple figure. One can explain this mathematically using the concept of Hausdorff dimension. Typically, a point can be described as having zero dimension, a line has one dimension and a plane has two dimensions etc., however consider a mountain, which can be reduced to a cone with dimension three, can be considered as a fractal because its dimensionality is non-integral. The dimensions of fractals are non-integral."

## Sample of Sources Used:

• Alfeld, P. The Mandelbrot Set. . 1998. Available: http://www.math.utah.edu/~alfeld/math/mandelbrot/mandelbrot.html. March 30 2009.
• Barnsley, M. F., and Hawley Rising. Fractals Everywhere. 2nd ed. Boston: Academic Press Professional, 1993.
• Mandelbrot, Benoit B. The Fractal Geometry of Nature. Updated and augm. ed. New York: W.H. Freeman, 1983.
• Weisstein, Eric W. Dragon Curve. 2009. Available: http://mathworld.wolfram.com/SierpinskiSieve.html. March 30 2009.
• ---. Menger Sponge. 2009. Available: http://mathworld.wolfram.com/SierpinskiSieve.html. March 30 2009.

## Cite this Analytical Essay:

### APA Format

Fractals in Math and Nature (2011, January 17) Retrieved December 12, 2019, from https://www.academon.com/analytical-essay/fractals-in-math-and-nature-146785/

### MLA Format

"Fractals in Math and Nature" 17 January 2011. Web. 12 December. 2019. <https://www.academon.com/analytical-essay/fractals-in-math-and-nature-146785/>