Fractalize That!

Fractalize That! PDF

Author: John Shier

Publisher: World Scientific Publishing

Published: 2018-11-29

Total Pages: 124

ISBN-13: 9813275189

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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. /remove Sample Chapter(s)Chapter 1: Introduction: Space-Filling Patterns /remove

The Fractal Geometry of Nature

The Fractal Geometry of Nature PDF

Author: Benoit Mandelbrot

Publisher: Echo Point Books & Media, LLC

Published: 2021-07-16

Total Pages: 0

ISBN-13: 9781648370410

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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 Creations

Fractal Creations PDF

Author: Timothy I. Wegner

Publisher:

Published: 1993

Total Pages: 524

ISBN-13: 9781878739346

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A new, more powerful version of FRACTINT--an ingenious program that works like a combination fractal microscope, paint program, and lab bench. Enables users to create any of 95 built-in fractals or type in their own fractal formulas to create completely original patterns. With two companion disks and red/blue 3D glasses. color insert.

The Fractal Self

The Fractal Self PDF

Author: John L. Culliney

Publisher: University of Hawaii Press

Published: 2017-07-31

Total Pages: 257

ISBN-13: 0824866649

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Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an unprecedented arena of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice.

The Fractal Brain Theory

The Fractal Brain Theory PDF

Author: Wai Tsang

Publisher: Lulu.com

Published: 2016-08-02

Total Pages: 532

ISBN-13: 1326753223

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The Fractal Brain Theory, or the Symmetry, Self Similarity and Recursivity Theory of Brain and Mind, is a Revolutionary new way of looking at the nature of intelligence and also genomics. It is the key to a powerful and new kind of Recursively Self Modifying Artificial Intelligence. Wai H. Tsang presents an exciting new synthesis of all things psychological, linguistic, neuroscientific, genomic, evolutionary, informatic, computational, complex and fractal. Dealing with the most central puzzles of mind science and AI, and weaving in some of the most fundamental concepts in mathematics such as symmetry, geometry, functions, discrete maths and formal axiomatic systems. This book presents nothing less than a seamless unified theory of Brain, Mind, Artificial Intelligence, Functional Genomics, Ontogenesis and Evolution. Also covering topics such as the quest for the Perfect & Universal Language, Recursively Self Modifying Algorithms, Super Intelligence & Technological Singularity.

Fractal Shores

Fractal Shores PDF

Author: Diane Louie

Publisher: University of Georgia Press

Published: 2020-10-15

Total Pages: 75

ISBN-13: 082035791X

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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 Cities

Fractal Cities PDF

Author: Michael Batty

Publisher:

Published: 1994-01-01

Total Pages: 394

ISBN-13: 9780124555709

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Fractal Cities is the pioneering study of the development and use of fractal geometry for understanding and planning the physical form of cities, showing how this geometry enables cities to be simulated throughcomputer graphics. The book explains how the structure of cities evolve in ways which at first sight may appear irregular, but when understood in terms of fractals reveal a complex and diverse underlying order. The book includes numerous illustrations and 16 pages full-color plates of stunning computer graphics, along with explanations of how to construct them. The authors provide an accessible and thought-provoking introduction to fractal geometry, as well as an exciting visual understanding of the formof cities. This approach, bolstered by new insights into the complexity of social systems, provides one of the best introductions to fractal geometry available for non-mathematicians and social scientists. Fractal Cities is useful as a textbook for courses on geographic information systems, urban geography, regional science, and fractal geometry. Planners and architects will find that many aspects of fractal geometry covered in this book are relevant to their own interests. Those involved in fractals and chaos, computer graphics, and systems theory will also find important methods and examples germane to their work. Michael Batty is Director of the National Center for Geographic Information and analysis in the State University of New York at Buffalo, and has worked in planning theory and urban modeling. Paul Longley is a lecturer in geography at the University of Bristol, and is involved in the development of geographic information systems in urban policy analysis. Richly illustrated, including 16 pages of full-color plates of brilliant computer graphics Provides an introduction to fractal geometry for the non-mathematician and social scientist Explains the influence of fractals on the evolution of the physical form of cities

The Waite Group's Fractal Creations

The Waite Group's Fractal Creations PDF

Author: Timothy Wegner

Publisher:

Published: 1991

Total Pages: 364

ISBN-13:

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The dazzling world of fractals is now at the fingertips of any computer user with a wonderful new program, included with the book, which combines the features of fractal microscope, a paint prgram, and a lab bench. It's called FRACTINT, and it lets users control fractal generation, manipulation, editing, alteration and storage. The program enables users to generate any of 60 built-in fractals or type in their own fractal formulas.

Fractal Geometries Theory and Applications

Fractal Geometries Theory and Applications PDF

Author: Alain Le Mehaute

Publisher: CRC Press

Published: 1991-11-11

Total Pages: 214

ISBN-13: 9780849377228

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Fractal geometry, based on recursive mathematical schemas, provides a means for modeling a great number of natural phenomena. For this reason, it is of increasing interest to physicists, chemists, biologists, and geographers, among others. A major quality of fractality is that it not only unifies phenomena previously thought to be anomalous or disparate in a single theoretical framework, but it also promotes a return to graphical treatment, which had been almost completely banished from scientific thought in favor of analysis. This book casts a new, lively light on scientific territories still not fully explored. It is designed for research workers, engineers, and experimentalists faced with problems of measure and action in heterogenous materials and environments. Several color plates illustrate the implications and consequences of this theory for most of the questions raised by the taking into consideration of time in a fractal space.

Fractal Cuts

Fractal Cuts PDF

Author: Diego Uribe

Publisher:

Published: 1993

Total Pages: 0

ISBN-13: 9780906212882

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Endlessly developing pop-up designs which belong to the class of curious geometrical objects called fractals.