Fractalize That! A Visual Essay on Statistical Geometry brings a new class of geometric fractals to a wider audience of mathematicians and scientists. It describes a recently discovered random fractal space-filling algorithm. Connections with tessellations and known fractals such as Sierpinski are developed. And, the mathematical development is illustrated by a large number of colorful images that will charm the readers.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. Readers can also create these computer-generated art with the advice and examples provided.

In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.

Fractals are intricate geometrical forms that contain miniature copies of themselves on ever smaller scales. This colorful book describes methods for producing an endless variety of fractal art using a computer program that searches through millions of equations looking for those few that can produce images having aesthetic appeal. Over a hundred examples of such images are included with a link to the software that produced these images, and can also produce many more similar fractals. The underlying mathematics of the process is also explained in detail.Other books by the author that could be of interest to the reader are Elegant Chaos: Algebraically Simple Chaotic Flows (J C Sprott, 2010) and Elegant Circuits: Simple Chaotic Oscillators (J C Sprott and W J Thio, 2020).

Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.

Departing from conventional narratives of the United States and the Americas as fundamentally continental spaces, the contributors to Archipelagic American Studies theorize America as constituted by and accountable to an assemblage of interconnected islands, archipelagoes, shorelines, continents, seas, and oceans. They trace these planet-spanning archipelagic connections in essays on topics ranging from Indigenous sovereignty to the work of Édouard Glissant, from Philippine call centers to US militarization in the Caribbean, and from the great Pacific garbage patch to enduring overlaps between US imperialism and a colonial Mexican archipelago. Shaking loose the straitjacket of continental exceptionalism that hinders and permeates Americanist scholarship, Archipelagic American Studies asserts a more relevant and dynamic approach for thinking about the geographic, cultural, and political claims of the United States within broader notions of America. Contributors Birte Blascheck, J. Michael Dash, Paul Giles, Susan Gillman, Matthew Pratt Guterl, Hsinya Huang, Allan Punzalan Isaac, Joseph Keith, Yolanda Martínez-San Miguel, Brandy Nālani McDougall, Ifeoma Kiddoe Nwankwo, Craig Santos Perez, Brian Russell Roberts, John Carlos Rowe, Cherene Sherrard-Johnson, Ramón E. Soto-Crespo, Michelle Ann Stephens, Elaine Stratford, Etsuko Taketani, Alice Te Punga Somerville, Teresia Teaiwa, Lanny Thompson, Nicole A. Waligora-Davis