图书简介
The book describes a recently discovered random fractal space-filling algorithm beginning with tessellations and Sierpinski, illustrating the relationship to statistical geometry and bringing together all that is known about it to a wider audience of mathematicians and scientists.
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.
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○ The book brings together information from the few published papers and unpublished material reported here for the first time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 book-length description of the subject
○ Examples of the use of the algorithm for decorative art
○ A visual feast
Introduction; Space-Filling Patterns; Squares and Rectangles; Triangles and Diamonds; Discs and Circular Arcs; Mixed and Irregular Shapes; Mixed and Irregular Shapes; Examples; The Statistical Geometry Algorithm; The Area-Perimeter Algorithm; Statistical Geometry in One Dimension; Do It Yourself
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