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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.
Preface
About the Author
Introduction
What is Scale Symmetry?
Fractal Structures
Non-Fractal Structures
Sphere Inversion
Mandelbrot Sets
Cellular Automata
Dynamics and Physics
Billiards
Sea
Trees
Planets
Classification
Appendix: Table References
Quantification
Conclusion
Science
Maths
Physics
Education
Programming
Art
Building the Examples
Summary
Software
Image Attributions
Glossary
Glossary of Shapes
Glossary of Terms
References
Index