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Elegant Fractals: Automated Generation Of Computer Art

Author : Julien Clinton Sprott

Publisher : World Scientific Publishing

Page : 266 pages

File Size : 16,19 MB

Release : 2018-10-04

Category : Computers

ISBN : 9813237155

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Book Description

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).



Kitchen Science Fractals: A Lab Manual For Fractal Geometry

Author : Michael Frame

Publisher : World Scientific

Page : 468 pages

File Size : 16,17 MB

Release : 2021-10-04

Category : Young Adult Nonfiction

ISBN : 9811218471

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Book Description

This book provides a collection of 44 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking fractals, videofeedback, and fractal networks of resistors and oscillators.



Elegant Automation: Robotic Analysis Of Chaotic Systems

Author : Julien Clinton Sprott

Publisher : World Scientific

Page : 348 pages

File Size : 37,61 MB

Release : 2023-04-14

Category : Science

ISBN : 9811277532

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Book Description

This book was mostly written by a machine that was programmed to search a system of equations for chaotic solutions, simplify the equations to the extent possible, analyze the behavior, produce figures, and write the accompanying text. The equations are coupled autonomous ordinary differential equations with three variables and at least one nonlinearity. Fifty simple systems are included. Some are old and familiar; others are relatively new and unknown. They are chosen to illustrate by simple example most of dynamical behaviors that can occur in low-dimensional chaotic systems.There is no substitute for the thrill and insight of seeing the solution of a simple equation unfold as the trajectory wanders in real time across your computer screen using a program of your own making. A goal of this book is to inspire and delight as well as to teach. It provides a wealth of examples ripe for further study and extension, and it offers a glimpse of a future when artificial intelligence supplants many of the mundane tasks that accompany dynamical systems research and becomes a true and tireless collaborator.



Elegant Simulations: From Simple Oscillators To Many-body Systems

Author : Julien Clinton Sprott

Publisher : World Scientific

Page : 325 pages

File Size : 17,7 MB

Release : 2022-12-20

Category : Science

ISBN : 9811263582

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Book Description

A recent development is the discovery that simple systems of equations can have chaotic solutions in which small changes in initial conditions have a large effect on the outcome, rendering the corresponding experiments effectively irreproducible and unpredictable. An earlier book in this sequence, Elegant Chaos: Algebraically Simple Chaotic Flows provided several hundred examples of such systems, nearly all of which are purely mathematical without any obvious connection with actual physical processes and with very limited discussion and analysis.In this book, we focus on a much smaller subset of such models, chosen because they simulate some common or important physical phenomenon, usually involving the motion of a limited number of point-like particles, and we discuss these models in much greater detail. As with the earlier book, the chosen models are the mathematically simplest formulations that exhibit the phenomena of interest, and thus they are what we consider 'elegant.'Elegant models, stripped of unnecessary detail while maximizing clarity, beauty, and simplicity, occupy common ground bordering both real-world modeling and aesthetic mathematical analyses. A computational search led one of us (JCS) to the same set of differential equations previously used by the other (WGH) to connect the classical dynamics of Newton and Hamilton to macroscopic thermodynamics. This joint book displays and explores dozens of such relatively simple models meeting the criteria of elegance, taste, and beauty in structure, style, and consequence.This book should be of interest to students and researchers who enjoy simulating and studying complex particle motions with unusual dynamical behaviors. The book assumes only an elementary knowledge of calculus. The systems are initial-value iterated maps and ordinary differential equations but they must be solved numerically. Thus for readers a formal differential equations course is not at all necessary, of little value and limited use.



Elegant Circuits: Simple Chaotic Oscillators

Author : Julien Clinton Sprott

Publisher : World Scientific

Page : 357 pages

File Size : 46,48 MB

Release : 2021-12-17

Category : Science

ISBN : 9811240019

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Book Description

Chaos is the study of the underlying determinism in the seemingly random phenomena that occur all around us. One of the best experimental demonstrations of chaos occurs in electrical circuits when the parameters are chosen carefully. We will show you how to construct such chaotic circuits for use in your own studies and demonstrations while teaching you the basics of chaos.This book should be of interest to researchers and hobbyists looking for a simple way to produce a chaotic signal. It should also be useful to students and their instructors as an engaging way to learn about chaotic dynamics and electronic circuits. The book assumes only an elementary knowledge of calculus and the ability to understand a schematic diagram and the components that it contains.You will get the most out of this book if you can construct the circuits for yourself. There is no substitute for the thrill and insight of seeing the output of a circuit you built unfold as the trajectory wanders in real time across your oscilloscope screen. A goal of this book is to inspire and delight as well as to teach.



Fractals

Author : John Briggs

Publisher : Simon and Schuster

Page : 196 pages

File Size : 37,65 MB

Release : 1992

Category : Art

ISBN : 0671742175

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Book Description

Explains the significance and beauty of fractals using over 170 illustrations.



In Pursuit of Elegance

Author : Matthew E. May

Publisher : Crown Currency

Page : 226 pages

File Size : 21,26 MB

Release : 2010-09-07

Category : Business & Economics

ISBN : 0385526504

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Book Description

What made the Sopranos finale one of the most-talked-about events in television history? Why is sudoku so addictive and the iPhone so darn irresistible? What do Jackson Pollock and Lance Armstrong have in common with theoretical physicists and Buddhist monks? Elegance. In this thought-provoking exploration of why certain events, products, and people capture our attention and imaginations, Matthew E. May examines the elusive element behind so many innovative breakthroughs in fields ranging from physics and marketing to design and popular culture. Combining unusual simplicity and surprising power, elegance is characterized by four key elements—seduction, subtraction, symmetry, and sustainability. In a compelling, story-driven narrative that sheds light on the need for elegance in design, engineering, art, urban planning, sports, and work, May offers surprising evidence that what’s “not there” often trumps what is. In the bestselling tradition of The Tipping Point, Made to Stick, and The Black Swan, In Pursuit of Elegance will change the way you think about the world.



A Random Walk Through Fractal Dimensions

Author : Brian H. Kaye

Publisher : John Wiley & Sons

Page : 452 pages

File Size : 24,62 MB

Release : 2008-07-11

Category : Technology & Engineering

ISBN : 3527615989

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Book Description

Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin



Introduction To Chaos, Fractals And Dynamical Systems

Author : Phillip A Laplante

Publisher : World Scientific

Page : 217 pages

File Size : 12,30 MB

Release : 2023-07-26

Category : Mathematics

ISBN : 981127326X

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Book Description

This book offers a fun and enriching introduction to chaos theory, fractals and dynamical systems, and on the applications of fractals to computer generated graphics and image compression. Introduction to Chaos, Fractals and Dynamical Systems particularly focuses on natural and human phenomenon that can be modeled as fractals, using simple examples to explain the theory of chaos and how it affects all of us. Then, using straightforward mathematic and intuitive descriptions, computer generated graphics and photographs of natural scenes are used to illustrate the beauty of fractals and their importance in our world. Finally, the concept of Dynamical Systems, that is, time-dependent systems, the foundation of Chaos and Fractal, is introduced. Everyday examples are again used to illustrate concepts, and the importance of understanding how these vital systems affect our lives. Throughout the fascinating history of the evolution of chaos theory, fractals and dynamical systems is presented, along with brief introductions to the scientists, mathematicians and engineers who created this knowledge.Introduction to Chaos, Fractals and Dynamical Systems contains ample mathematical definitions, representations, discussions and exercises, so that this book can be used as primary or secondary source in home schooling environments.The book is suitable for homeschooling as a focused course on the subject matter or as a classroom supplement for a variety of courses at the late junior high or early high-school level. For example, in addition to a standalone course on Chaos, Fractals and Dynamical Systems (or similar title), this book could be used with the following courses:The text can also be used in conjunction with mathematics courses for undergraduates for non-science majors. The book can also be used for informal and lively family study and discussion.For each chapter, exercises and things to do are included. These activities range from simple computational tasks to more elaborate computer projects, related activities, biographical research and writing assignments.



Fractals, Chaos, Power Laws

Author : Manfred Schroeder

Publisher : Courier Corporation

Page : 450 pages

File Size : 46,34 MB

Release : 2009-08-21

Category : Science

ISBN : 0486472043

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Book Description

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.