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L System Fractals

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L System Fractals

L System Fractals Book
Author : Jibitesh Mishra,Sarojananda Mishra
Publisher : Elsevier
Release : 2007-01-08
ISBN : 9780080469386
Language : En, Es, Fr & De

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Book Description :

L-System Fractals covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Fractals generated from L-System including hybrid fractals Dimension calculation for L-system fractals Images and codes for L-system fractals Research directions in the area of L-system fractals Usage of various freely downloadable tools in this area

Lindenmayer Systems Fractals and Plants

Lindenmayer Systems  Fractals  and Plants Book
Author : Przemyslaw Prusinkiewicz,James Hanan
Publisher : Springer Science & Business Media
Release : 2013-11-11
ISBN : 1475714289
Language : En, Es, Fr & De

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Book Description :

1-systems are a mathematical formalism which was proposed by Aristid 1indenmayer in 1968 as a foundation for an axiomatic theory of develop ment. The notion promptly attracted the attention of computer scientists, who investigated 1-systems from the viewpoint of formal language theory. This theoretical line of research was pursued very actively in the seventies, resulting in over one thousand publications. A different research direction was taken in 1984 by Alvy Ray Smith, who proposed 1-systems as a tool for synthesizing realistic images of plants and pointed out the relationship between 1-systems and the concept of fractals introduced by Benoit Mandel brot. The work by Smith inspired our studies of the application of 1-systems to computer graphics. Originally, we were interested in two problems: • Can 1-systems be used as a realistic model of plant species found in nature? • Can 1-systems be applied to generate images of a wide class of fractals? It turned out that both questions had affirmative answers. Subsequently we found that 1-systems could be applied to other areas, such as the generation of tilings, reproduction of a geometric art form from East India, and synthesis of musical scores based on an interpretation of fractals. This book collects our results related to the graphical applications of- systems. It is a corrected version of the notes which we prepared for the ACM SIGGRAPH '88 course on fractals.

The Algorithmic Beauty of Plants

The Algorithmic Beauty of Plants Book
Author : Przemyslaw Prusinkiewicz,Aristid Lindenmayer
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461384761
Language : En, Es, Fr & De

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Book Description :

Now available in an affordable softcover edition, this classic in Springer's acclaimed Virtual Laboratory series is the first comprehensive account of the computer simulation of plant development. 150 illustrations, one third of them in colour, vividly demonstrate the spectacular results of the algorithms used to model plant shapes and developmental processes. The latest in computer-generated images allow us to look at plants growing, self-replicating, responding to external factors and even mutating, without becoming entangled in the underlying mathematical formulae involved. The authors place particular emphasis on Lindenmayer systems - a notion conceived by one of the authors, Aristid Lindenmayer, and internationally recognised for its exceptional elegance in modelling biological phenomena. Nonetheless, the two authors take great care to present a survey of alternative methods for plant modelling.

L Systems

L Systems Book
Author : G. Rozenberg,A. Salomaa
Publisher : Springer
Release : 2014-03-12
ISBN : 9783662209653
Language : En, Es, Fr & De

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Book Description :

Profiles EM Systems, a software house servicing the transport and distribution industries. Features the Transport and Distribution Package (TRUST II), a transport management package written in ORACLE. Includes information on the property management system, ORACLE analysis and programming, and MS-Access analysis and programming. Posts an online inquiry and comments form.

Graph Grammars and Their Application to Computer Science

Graph Grammars and Their Application to Computer Science Book
Author : Hartmut Ehrig,Manfred Nagl,Grzegorz Rozenberg,Azriel Rosenfeld
Publisher : Springer Science & Business Media
Release : 1987-12-17
ISBN : 9783540187714
Language : En, Es, Fr & De

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Book Description :

The generic term "graph-grammars" refers to a variety of methods for specifying (possibly infinite) sets of graphs or sets of maps. The area of graph-grammars originated in the late 60s motivated by considerations concerning pattern recognition - since then the list of areas which have interacted with the development of graph-grammars has grown quite impressively. It includes pattern recognition, software specification and development, VLSI layout schemes, data bases, lambda-calculus, analysis of concurrent systems, massively parallel computer architectures, incremental compilers, computer animation, complexity theory, developmental biology, music composition, representation of physical solids, and many others. This volume is based on the contributions presented at the third international workshop on graph-grammars and their applications, held in Warrenton, Virginia, USA in December 1986. Aiming at the best possible representation of the field not all of the papers presented at the meeting appear in this volume and some of the papers from this volume were not presented at the workshop. The volume consists of two parts: Part I presents tutorial introductions to a number of basic graph and map rewriting mechanisms. Part II contains technical contributions. This collection of papers provides the reader with an up-to-date overview of current trends in graph-grammars.

Chaos and Fractals

Chaos and Fractals Book
Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Publisher : Springer Science & Business Media
Release : 2013-06-29
ISBN : 1475747403
Language : En, Es, Fr & De

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Book Description :

For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.

Chaos Noise and Fractals

Chaos  Noise and Fractals Book
Author : E. Roy Pike,L .A. Lugiato
Publisher : CRC Press
Release : 2020-08-27
ISBN : 1000156915
Language : En, Es, Fr & De

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Book Description :

The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Parallel Problem Solving from Nature PPSN III

Parallel Problem Solving from Nature   PPSN III Book
Author : Yuval Davidor,International Conference on Evolutionary Computation,Hans-Paul Schwefel,Conference on Parallel Problem Solving from Nature,Reinhard Männer
Publisher : Springer Science & Business Media
Release : 1994-09-21
ISBN : 9783540584841
Language : En, Es, Fr & De

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Book Description :

The challenges in ecosystem science encompass a broadening and strengthening of interdisciplinary ties, the transfer of knowledge of the ecosystem across scales, and the inclusion of anthropogenic impacts and human behavior into ecosystem, landscape, and regional models. The volume addresses these points within the context of studies in major ecosystem types viewed as the building blocks of central European landscapes. The research is evaluated to increase the understanding of the processes in order to unite ecosystem science with resource management. The comparison embraces coastal lowland forests, associated wetlands and lakes, agricultural land use, and montane and alpine forests. Techniques for upscaling focus on process modelling at stand and landscape scales and the use of remote sensing for landscape-level model parameterization and testing. The case studies demonstrate ways for ecosystem scientists, managers, and social scientists to cooperate.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics Fractals in pure mathematics

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics  Fractals in pure mathematics Book
Author : David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Release : 2013-10-22
ISBN : 0821891472
Language : En, Es, Fr & De

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Book Description :

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.

Analysis for Computer Scientists

Analysis for Computer Scientists Book
Author : Michael Oberguggenberger,Alexander Ostermann
Publisher : Springer
Release : 2018-11-06
ISBN : 9783319911540
Language : En, Es, Fr & De

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Book Description :

This easy-to-follow textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling. The text describes the mathematical theory alongside the basic concepts and methods of numerical analysis, enriched by computer experiments using MATLAB, Python, Maple, and Java applets. This fully updated and expanded new edition also features an even greater number of programming exercises. Topics and features: describes the fundamental concepts in analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives, integrals, and curves; discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes added material on hyperbolic functions, curves and surfaces in space, second-order differential equations, and the pendulum equation (NEW); contains experiments, exercises, definitions, and propositions throughout the text; supplies programming examples in Python, in addition to MATLAB (NEW); provides supplementary resources at an associated website, including Java applets, code source files, and links to interactive online learning material. Addressing the core needs of computer science students and researchers, this clearly written textbook is an essential resource for undergraduate-level courses on numerical analysis, and an ideal self-study tool for professionals seeking to enhance their analysis skills.

Application of Fractals in Earth Sciences

Application of Fractals in Earth Sciences Book
Author : V.P. Dimri
Publisher : CRC Press
Release : 2000-01-01
ISBN : 9789054102847
Language : En, Es, Fr & De

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Book Description :

This text examines the emerging field of fractals and its applications in earth sciences. Topics covered include: concepts of fractal and multifractal chaos; the application of fractals in geophysics, geology, climate studies, and earthquake seismology.

Chaos and Fractals

Chaos and Fractals Book
Author : C.A. Pickover
Publisher : Elsevier
Release : 1998-08-03
ISBN : 9780080528861
Language : En, Es, Fr & De

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Book Description :

These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art. Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art. Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

Fractal Concepts in Surface Growth

Fractal Concepts in Surface Growth Book
Author : A.- L. Barabási,H. E. Stanley
Publisher : Cambridge University Press
Release : 1995-04-13
ISBN : 9780521483186
Language : En, Es, Fr & De

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Book Description :

This book brings together two of the most exciting and widely studied subjects in modern physics: namely fractals and surfaces. To the community interested in the study of surfaces and interfaces, it brings the concept of fractals. To the community interested in the exciting field of fractals and their application, it demonstrates how these concepts may be used in the study of surfaces. The authors cover, in simple terms, the various methods and theories developed over the past ten years to study surface growth. They describe how one can use fractal concepts successfully to describe and predict the morphology resulting from various growth processes. Consequently, this book will appeal to physicists working in condensed matter physics and statistical mechanics, with an interest in fractals and their application. The first chapter of this important new text is available on the Cambridge Worldwide Web server: http://www.cup.cam.ac.uk/onlinepubs/Textbooks/textbookstop.html

Fractals in Physics

Fractals in Physics Book
Author : L. Pietronero,E. Tosatti
Publisher : Elsevier
Release : 2012-12-02
ISBN : 0444598413
Language : En, Es, Fr & De

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Book Description :

The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of the critical properties of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and their methods have extended to various fields of physics. The purpose of this Symposium was to provide an overview of the physical phenomena that manifest scale invariance and fractal properties with the aim of bringing out the common mathematical features. The emphasis was on theoretical and experimental work related to well defined physical phenomena.

Fractal Geometry in Biological Systems

Fractal Geometry in Biological Systems Book
Author : Philip M. Iannaccone,Mustafa Khokha
Publisher : CRC Press
Release : 1996-07-25
ISBN : 9780849376368
Language : En, Es, Fr & De

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Book Description :

Fractal Geometry in Biological Systems was written by the leading experts in the field of mathematics and the biological sciences together. It is intended to inform researchers in the bringing about the fundamental nature of fractals and their widespread appearance in biological systems. The chapters explain how the presence of fractal geometry can be used in an analytical way to predict outcomes in systems, to generate hypotheses, and to help design experiments. The authors make the mathematics accessible to a wide audience and do not assume prior experience in this area.

Fractal Physiology

Fractal Physiology Book
Author : James B Bassingthwaighte,Larry S Liebovitch,Bruce J West
Publisher : Springer
Release : 2013-05-27
ISBN : 1461475724
Language : En, Es, Fr & De

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Book Description :

I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.

Fractal Surfaces

Fractal Surfaces Book
Author : John C. Russ
Publisher : Springer Science & Business Media
Release : 1994-02-28
ISBN : 9780306447020
Language : En, Es, Fr & De

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Book Description :

The author integrates discussions of fractal geometry, surface modeling techniques, and applications to real world problems to provide a comprehensive, accessible overview of the field. His work will equip researchers with the basic tools for measurement and interpretation of data, stimulating more work on these problems and, perhaps, leading to an understanding of the reasons that Nature has adopted this geometry to shape much of our world.

Illustrating Evolutionary Computation with Mathematica

Illustrating Evolutionary Computation with Mathematica Book
Author : Christian Jacob,Faculty Member Anthropologie Et Histoire Des Mondes Antiques Christian Jacob
Publisher : Morgan Kaufmann
Release : 2001
ISBN : 1558606378
Language : En, Es, Fr & De

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Book Description :

Part 1: Fascinating Evolution -- Part 2: Evolutionary Computation -- Part 3: If Darwin was a Programmer -- Part 4: Evolution of Developmental Programs.

Fractals for the Classroom

Fractals for the Classroom Book
Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461244064
Language : En, Es, Fr & De

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Book Description :

Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled.

The Science of Fractal Images

The Science of Fractal Images Book
Author : Heinz-Otto Peitgen,Dietmar Saupe
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 146123784X
Language : En, Es, Fr & De

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Book Description :

This book is based on notes for the course Fractals:lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, Heinz-Otto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by Heinz-Otto Peitgen and was part of the SIGGRAPH '87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudo-code or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot's fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics.