ENGLISH

Exploring Scale Symmetry

By Thomas Lowe

Book information

Publisher
World Scientific Publishing
Year
2021
ISBN
9813278544, 9789813278547
Language
english
Format
PDF
Filesize
61 MB (63926168 bytes)
Series
Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications
Pages
252\253
Time added
2022-08-28 23:29:53

Description

Welcome to the world of scale symmetry, the last elementary symmetry and the least explored! Find out how this long-neglected element transforms the traditional geometry of lines and planes into a rich landscape of trees, craggy mountains and rolling oceans. Enjoy a visual exploration through the intricate and elaborate structures of scale-symmetric geometry. See unique fractals, Mandelboxes, and automata and physical behaviors. Take part in the author's forage into the lesser-trodden regions of this landscape, and discover unusual and attractive specimens! You will also be provided with all the tools needed to recreate the structures yourself. Every example is new and developed by the author, and is chosen because it pushes the field of scale-symmetric geometry into a scarcely explored region. The results are complex and intricate but the method of generation is often simple, which allows it to be presented graphically without depending on too much mathematical syntax. If you are interested in the mathematics, science and art of scale symmetry, then read on! This is also a book for programmers and for hobbyists: those of us who like to dabble with procedural imagery and see where it leads. Contents Preface About the Author Chapter 1 Introduction What is Scale Symmetry? Chapter 2 Fractal Structures Chapter 3 Non-Fractal Structures Chapter 4 Sphere Inversion Chapter 5 Mandelbrot Sets Chapter 6 Cellular Automata Chapter 7 Dynamics and Physics Billiards Sea Trees Planets Chapter 8 Classification Appendix: Table References Chapter 9 Quantification Chapter 10 Conclusion Science Maths Physics Education Programming Art Building the Examples Summary Software Image Attributions Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 8 Chapter 9 Chapter 10 Glossary Glossary of Shapes Glossary of Terms References Index

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