Fractalize That! (eBook)
by john shier (Author)

 25,177 Words
 124 Pages
Fractalize That! A Visual Essay on Statistical Geometry brings a new class of geometric fractals to a wider audience of mathematicians and scientists. It describes a recently discovered random fractal spacefilling algorithm. Connections with tessellations and known fractals such as Sierpinski are developed. And, the mathematical development is illustrated by a large number of colorful images that will charm the readers.
The algorithm claims to be universal in scope, in that it can fill any spatial region with smaller and smaller fill regions of any shape. The filling is complete in the limit of an infinite number of fill regions. This book presents a descriptive development of the subject using the traditional shapes of geometry such as discs, squares, and triangles. It contains a detailed mathematical treatment of all that is currently known about the algorithm, as well as a chapter on software implementation of the algorithm.
The mathematician will find a wealth of interesting conjectures supported by numerical computation. Physicists are offered a model looking for an application. The patterns generated are often quite interesting as abstract art. Readers can also create these computergenerated art with the advice and examples provided.
Contents:
 Introduction: SpaceFilling Patterns
 Squares and Rectangles
 Triangles and Diamonds
 Discs and Circular Arcs
 Mixed and Irregular Shapes
 Examples
 The Statistical Geometry Algorithm
 The Areaâ€“Perimeter Algorithm
 Statistical Geometry in One Dimension
 Do It Yourself
Readership: Students, mathematicians, physicists, professionals, and the general public who are interested in the fractal art of statistical geometry.
Key Features:
 The book brings together information from the few published papers and unpublished material reported here for the first time
 This is the first booklength description of the subject
 Examples of the use of the algorithm for decorative art
 A visual feast
 Released: November 21, 2018
 Categories: Computers & Internet, Education
 Language: English
 Publisher: World Scientific Publishing Company
 ISBN10: 9813275189
 ISBN13: 9789813275188