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Author: Przemyslaw Prusinkiewicz
Publisher: Springer Science & Business Media
ISBN: 1475714289
Category : Mathematics
Languages : en
Pages : 127
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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.
Author: Przemyslaw Prusinkiewicz
Publisher: Springer Science & Business Media
ISBN: 1475714289
Category : Mathematics
Languages : en
Pages : 127
Get Book Here
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.
Author: Daniel Shiffman
Publisher: No Starch Press
ISBN: 1718503717
Category : Computers
Languages : en
Pages : 642
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Book Description
All aboard The Coding Train! This beginner-friendly creative coding tutorial is designed to grow your skills in a fun, hands-on way as you build simulations of real-world phenomena with “The Coding Train” YouTube star Daniel Shiffman. What if you could re-create the awe-inspiring flocking patterns of birds or the hypnotic dance of fireflies—with code? For over a decade, The Nature of Code has empowered countless readers to do just that, bridging the gap between creative expression and programming. This innovative guide by Daniel Shiffman, creator of the beloved Coding Train, welcomes budding and seasoned programmers alike into a world where code meets playful creativity. This JavaScript-based edition of Shiffman’s groundbreaking work gently unfolds the mysteries of the natural world, turning complex topics like genetic algorithms, physics-based simulations, and neural networks into accessible and visually stunning creations. Embark on this extraordinary adventure with projects involving: A physics engine: Simulate the push and pull of gravitational attraction. Flocking birds: Choreograph the mesmerizing dance of a flock. Branching trees: Grow lifelike and organic tree structures. Neural networks: Craft intelligent systems that learn and adapt. Cellular automata: Uncover the magic of self-organizing patterns. Evolutionary algorithms: Play witness to natural selection in your code. Shiffman’s work has transformed thousands of curious minds into creators, breaking down barriers between science, art, and technology, and inviting readers to see code not just as a tool for tasks but as a canvas for boundless creativity. Whether you’re deciphering the elegant patterns of natural phenomena or crafting your own digital ecosystems, Shiffman’s guidance is sure to inform and inspire. The Nature of Code is not just about coding; it’s about looking at the natural world in a new way and letting its wonders inspire your next creation. Dive in and discover the joy of turning code into art—all while mastering coding fundamentals along the way. NOTE: All examples are written with p5.js, a JavaScript library for creative coding, and are available on the book's website.
Author: Przemyslaw Prusinkiewicz
Publisher: Springer Science & Business Media
ISBN: 1461384761
Category : Computers
Languages : en
Pages : 235
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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.
Author: Michael Oberguggenberger
Publisher: Springer
ISBN: 3319911554
Category : Computers
Languages : en
Pages : 372
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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.
Author: Jibitesh Mishra
Publisher: Elsevier
ISBN: 0080469388
Category : Computers
Languages : en
Pages : 274
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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
Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
ISBN: 1475721722
Category : Mathematics
Languages : en
Pages : 468
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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.
Author: Hartmut Ehrig
Publisher: Springer Science & Business Media
ISBN: 9783540187714
Category : Computers
Languages : en
Pages : 626
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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.
Author: Jeffrey Ventrella
Publisher: Eyebrain Books
ISBN: 9780983054634
Category : Computers
Languages : en
Pages : 154
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Book Description
This book explains a taxonomy of plane-filling curves (fractal curves with a fractal dimension of 2). it includes the classic fractal curves described in Mandelbrot's original book. Many new fractal curves are introduced. The taxonomy is based upon the Gaussian integers and the Eisenstein integers - each forming a lattice (square and triangular). These lattices have algebraic properties, which allows number theory to be used in describing and classifying these curves. This work has been under development for over 30 years. An earlier version of this taxonomy is described in the book ""Brain-filling Curves"", also by Jeffrey Ventrella. More on plane-filling curves can be found at fractalcurves.com
Author: James B Bassingthwaighte
Publisher: Springer
ISBN: 1461475724
Category : Medical
Languages : en
Pages : 371
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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.
Author: C.A. Pickover
Publisher: Elsevier
ISBN: 0080528864
Category : Mathematics
Languages : en
Pages : 469
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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.
