"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-symmetricgeometry 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"--
This book presents the author's work in exploring the rich field of scale-symmetric and fractal geometry. It ties together the many examples of new and beautiful geometric structures with novel classification systems in order to clarify and map out this relatively uncharted space. The reader would be inspired to explore this space themselves, and gain a better understanding of this landscape of scale-symmetric geometry. The book demonstrates the power of the hobbyist and online community-based exploration in discovering these mathematical worlds, and the power of play and mathematical beauty in driving new innovations, in contrast to traditional academic pathways. This will be a very visual book, with many images to help the reader to understand the underlying structures. 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 book combines fairly advanced mathematical concepts (such as conformal transforms, and negative dimensions) with beautiful imagery and a narrative that appeals to an educated general audience. It therefore is important to engage general audiences with more advanced mathematical ideas to spark an interest and help make this area of mathematics more popular and well understood. It does not dictate a set of rules or axioms, but instead, encourages the reader to explore and provides them tools and ideas to do so.
