Fractal Worlds


Book Description

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 Worlds


Book Description

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


Book Description

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.




The Fractal Geometry of Nature


Book Description

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.




Fractal Growth Phenomena


Book Description

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.




Fractal Shores


Book Description

Carlo Rovelli, Italian physicist, says that "the world is not a collection of things, it is a collection of events." Poet Diane Louie thinks of prose poems as little events. They are happening and happenings. They draw on experience, image, metaphor, and all the properties of language to create little worlds-in-motion: spinning while orbiting, actively shifting our point of view. More genus than hybrid species, prose poems can straddle the obvious limits and less-obvious liberties of perception. This active characteristic of spanning and connecting is especially relevant in a time of cultural polarization. Marrying, even uneasily, the inquiries of science and spiritual longing can illuminate what they—and we—have in common: a desire to understand our presence in a universe that does not yield ultimate answers.




Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot


Book Description

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.




Quick free world maps using GIMP filters and Donjon fractal maps


Book Description

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.




Fractals: A Very Short Introduction


Book Description

Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.




Fractals


Book Description

What are fractals? Why are they such fun? How do you make one? Why is a dripping tap not as random as it seems? What is chaos? Is the Mandelbrot Set really the most complex object in mathematics? In this beautifully illustrated book, fractal-hunter Oliver Linton takes us on a fascinating journey into the mathematics of fractals and chaos, diving into many kinds of self- similar structures to reveal some of the most recently discovered and intriguing patterns in science and nature. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.