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.
Author(s): Thomas Lowe
Series: Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications
Publisher: World Scientific Publishing
Year: 2021
Language: English
Pages: 252
City: New Jersey
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
