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In this essential primer, mathematician Michael Frame, a close collaborator with Benoit Mandelbrot, the founder of fractal geometry, and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology
Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.
Encompassing a Fractal World presents a groundbreaking, innovative paradigm which opens up new perspectives for understanding and analyzing Hindu life and culture. This book is an interdisciplinary comparative work which attempts to 'connect the dots', moving beyond isolated local village-based studies in order to bridge the gulf between anthropology and Hindu studies.
Quick free world maps using GIMP filters and Donjon fractal maps by Ken N Wickham Pdf
I will show step-by-step instructions how to use two online tools to make several kinds of maps from randomized fractal maps. The value in this book isn't the original maps, which are free. The value is in the techniques used to turn those maps into 3d, contour, and highly detailed maps by using digital techniques in the book. Also I show how to create a better outline map. You don't actually draw the map. You pick which one you like from a random created map. Doing so only takes a few steps - depending on what details you want - and can be done whenever you want. I show how to make highly detailed maps. It's pretty easy. Just a few buttons and setting adjustments to automate results which I show. It's much easier than drawing or using digital brushes although you depend on randomly made maps. Ideal chunks of 100 pixels or less clips. Even better are 3 to 20 pixel clips such as the small island.
Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot by Michel Laurent Lapidus,Machiel Van Frankenhuysen Pdf
This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
A Fractal Epistemology for a Scientific Psychology by Terry Marks-Tarlow,Yakov Shapiro,Katthe P. Wolf,Harris L. Friedman Pdf
Fractal dynamics provide an unparalleled tool for understanding the evolution of natural complexity throughout physical, biological, and psychological realms. This book’s conceptual framework helps to reconcile several persistent dichotomies in the natural sciences, including mind-brain, linear-nonlinear, subjective-objective, and even personal-transpersonal processes. A fractal approach is especially useful when applied to recursive processes of consciousness, both within their ordinary and anomalous manifestations. This novel way to study the interconnection of seemingly divided wholes encompasses multiple dimensions of experience and being. It brings together experts in diverse fields—neuropsychologists, psychiatrists, physicists, physiologists, psychoanalysts, mathematicians, and professors of religion and music composition—to demonstrate the value of fractals as model, method, and metaphor within psychology and related social and physical sciences. The result is a new perspective for understanding what has often been dismissed as too subjective, idiosyncratic, and ineffably beyond the scope of science, bringing these areas back into a natural-scientific framework.
Heaven's Fractal Net by William Joseph Jackson Pdf
Accompanying DVD contains ... "Two hours of Supercomputed frame-by-frame fractal animation. Includes Mandelbrot Zooms, Julia Promenades, Cascade maps and the Lorenz Attractor. Forty six scenes with original music."--[container of 1990 VHS release].
Virtual Reality: Applications and Explorations provides information pertinent to the fundamental aspects of virtual reality and artificial reality. This book discusses the potential applications of virtual reality. Organized into three parts encompassing 10 chapters, this book begins with an overview of the traditional computer science activities ad discusses how hard problems in computer science can be addressed with virtual reality ideas and technology. This text then explores some applications of virtual reality technology that could potentially touch almost every purposeful activity that humans undertake in a technological civilization. Other chapters consider the use of virtual reality to manage and present to users information that cannot otherwise be comprehended. This book discusses as well the use of artificial worlds in both computer art and virtual reality. The final chapter deals with how the ideas of virtual reality and artificial reality can be of use to anyone who has to manage a business or organization. This book is a valuable resource for computer scientists.
Colliding Worlds: How Cutting-Edge Science Is Redefining Contemporary Art by Arthur I. Miller Pdf
A dazzling look at the artists working on the frontiers of science. In recent decades, an exciting new art movement has emerged in which artists utilize and illuminate the latest advances in science. Some of their provocative creations—a live rabbit implanted with the fluorescent gene of a jellyfish, a gigantic glass-and-chrome sculpture of the Big Bang (pictured on the cover)—can be seen in traditional art museums and magazines, while others are being made by leading designers at Pixar, Google’s Creative Lab, and the MIT Media Lab. In Colliding Worlds, Arthur I. Miller takes readers on a wild journey to explore this new frontier. Miller, the author of Einstein, Picasso and other celebrated books on science and creativity, traces the movement from its seeds a century ago—when Einstein’s theory of relativity helped shape the thinking of the Cubists—to its flowering today. Through interviews with innovative thinkers and artists across disciplines, Miller shows with verve and clarity how discoveries in biotechnology, cosmology, quantum physics, and beyond are animating the work of designers like Neri Oxman, musicians like David Toop, and the artists-in-residence at CERN’s Large Hadron Collider. From NanoArt to Big Data, Miller reveals the extraordinary possibilities when art and science collide.
The investigation of phenomena involving fractals has gone through a spectacular development in the last decade. Many physical, technological and biological processes have been shown to be related to and described by objects with non-integer dimensions. The physics of far-from-equilibrium growth phenomena represents one of the most important fields in which fractal geometry is widely applied. During the last couple of years considerable experimental, numerical and theoretical information has accumulated concerning such processes. This book, written by a well-known expert in the field, summarizes the basic concepts born in the studies of fractal growth and also presents some of the most important new results for more specialized readers. It also contains 15 beautiful color plates demonstrating the richness of the geometry of fractal patterns. Accordingly, it may serve as a textbook on the geometrical aspects of fractal growth and it treats this area in sufficient depth to make it useful as a reference book. No specific mathematical knowledge is required for reading this book which is intended to give a balanced account of the field.
The Butterfly in the Quantum World by Indubala I Satija Pdf
Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.
Describing the biology, sociology, and technology of the fictional Latoocarfian civilization of Ganymede, one of Jupiter's moons, this book includes a cornucopia of curiosities--games played on fractal boards, instructions on creating globular star clusters using personal computers, and puzzles to stimulate the imagination.
Our daily universe is rough and infinitely diverse. The fractal approach clarifies and orders these disparities. It helps us to envisage new explanations of geographical phenomena, which are, however, considered as definitely understood. Written for use by geographers and researchers from similar disciplines, such as ecologists, economists, historians and sociologists, this book presents the algorithms best adapted to the phenomena encountered, and proposes case studies illustrating their applications in concrete situations. An appendix is also provided that develops programs written in Mathematica. Contents 1. A Fractal World. 2. Auto-similar and Self-affine Fractals. 3. From the Fractal Dimension to Multifractal Spectrums. 4. Calculation and Interpretation of Fractal Dimensions. 5. The Fractal Dimensions of Rank-size Distributions. 6. Calculation and Interpretation of Multifractal Spectrums. 7. Geographical Explanation of Fractal Forms and Dynamics. 8. Using Complexity Theory to Explain a Fractal World. 9. Land-use Planning and Managing a Fractal Environment.