Fractals have been one of the tools used in Euclidean geometry to explain the abnormal shapes in nature. Fractals are able to explain the irregular shapes that are a far cry from the normal circle or square. It is an object of symmetry that uses components to create the picture of a self-similar entity. Fractals first appeared on the scene in 1918 due to the mathematician, Felix Hausdroff. A Poland mathematician by the name of Beniot B. Mandelbrot began the term fractals. Fractals originated from the Latin term fractus meaning broken or fractured. It is a series of self-similar images repeated; The Koch snowflake, the Mandelbrot set, the Julia set and the Box fractal are many examples. The idea of a fractal is a pattern of repetitive images of the entire picture. When magnified upon, the image continues to look the same and builds upon the whole picture. “A key characteristic of fractals is fractal dimension.” [http://www.reference.com/browse/wiki/Fractal] This is the parameter of the fractal that uses fractions or nonintergers. “The table below shows the complexity of a figure as it increases its dimension.” [http://library.thinkquest.org/26242/full/index.html.] FA finite number greater than 0

IAn infinite number
DimensionNum of PointsLengthAreaVolume
D = 0F000
0 < D < 1I000
D = 1IF00
1 < D < 2II00
D = 2IIF0
2 < D < 3III0
D = 3IIIF
[http://library.thinkquest.org/26242/full/index.html.]
Fractals are most often found in nature where the patterns aren’t exactly self-similar. These fractals are known as stochastic. This can be seen in tree bark, leaves, and snowflakes. All fractals aren’t exactly self-similar, such as the Julia set, or stochastic but are random or statistical. These fractals involve a numerical measure that is “preserved across the scale.” [http://www.reference.com/browse/wiki/Fractal] Fractals are used in an assortment of fields such as computer programming, art, nature, astronomy, molecules, and the...

...Fractals
Introduction
Fractals are geometric patterns that when repeated at increasingly smaller scales they produce irregular shapes and surfaces. All fractals have a feature of ‘self-similarity’. A set is self-similar if it can be broken into arbitrary small pieces, each of which is a small copy of the entire set, for fractals the pattern reproduced must be detailed (Nuhfer 2006). Self-similarity may be demonstrated as exact...

...Fractal Geometry
"Fractal Geometry is not just a chapter of mathematics, but one that helps
Everyman to see the same old world differently". - Benoit Mandelbrot
The world of mathematics usually tends to be thought of as abstract. Complex and
imaginary numbers, real numbers, logarithms, functions, some tangible and others
imperceivable. But these abstract numbers, simply symbols that conjure an image,
a quantity, in our mind, and complex equations, take on a new...

...is also no doubt that patterns are just as mysterious as they are beautiful. In fact, there are some patterns that are so perfect that they self-replicate. To be technical, some patterns are fractal in nature. Fractal or not, patterns give us something more to admire and wonder about.
Introduction
Fractals never fail to fascinate. If you aren't just gazing at their unearthly beauty, you ponder the mathematics behind them... and then you can't help...

...Introduction
The birth of every technology is the result of the quest for automation of some form of human work. This has led to many inventions that have made life easier for us. Fractal Robot is a science that promises to revolutionize technology in a way that has never been witnessed before.
The principle behind Fractal Robots is very simple. You take some cubic bricks made of metals and plastics, motorize them, put some electronics inside them and...

...Fractal Geometry
How would you like to take a class called geometry of chaos? Probably doesn’t sound too thrilling. A man named Benoit Mandelbrot is responsible for creating the geometry of chaos. The geometry of chaos is considered to be the fourth-dimension. It is considered to be the world in which we live in, a world where there is constant change based on feedback, an open system where everything is related to everything else. It is now recognized as the true geometry of...

...Fractal Antenna Engineering: The Theory and
Design of Fractal Antenna Arrays
Douglas H. Werner', Randy L. Haup?,
and Pingjuan L. WerneJ
'Communications and Space Sciences Laboratory
The Pennsylvania State University
Department of Electrical Engineering
21 1A Electrical Engineering East
University Park, PA 16802
E-mail: dhw@psu.edu
2Department of Electrical Engineering
Utah State University
Logan, UT 84322-4 120
Tel: (435) 797-2840
Fax: (435) 797-3054...

...with fractal architecture as one of the defining solutions for the contemporary complex urban fabric.
SUBMITTED BY: Lily Tandon
SEMESTER:VIII
CHAPTERS
1. The End Of The Modern World
2. What abstraction does
3. From the modern to the complex
4. From complexity to form generation
5. Form generation and...

...The Application of Fractal Geometry to Ecology
Principles of Ecology 310L
Victoria Levin
7 December 1995
Abstract
New insights into the natural world are just a few of the results from the use
of fractal geometry. Examples from population and landscape ecology are used to
illustrate the usefulness of fractal geometry to the field of ecology. The
advent of the computer age played an important role in the development and
acceptance of...