Top Document: Fractal Frequently Asked Questions and Answers Previous Document: Complexity Next Document: Acknowledgements See reader questions & answers on this topic!  Help others by sharing your knowledge Q28a: What are some general references on fractals, chaos, and complexity? A28a: Some references are: M. Barnsley, _Fractals Everywhere_, Academic Press Inc., 1988. ISBN 0120790629. This is an excellent text book on fractals. This is probably the best book for learning about the math underpinning fractals. It is also a good source for new fractal types. M. Barnsley and L. Anson, _The Fractal Transform_, Jones and Bartlett, April, 1993. ISBN 0867202181. This book is a sequel to _Fractals Everywhere_. Without assuming a great deal of technical knowledge, the authors explain the workings of the Fractal Transform (tm). The Fractal Transform is the compression tool for storing highquality images in a minimal amount of space on a computer. Barnsley uses examples and algorithms to explain how to transform a stored pixel image into its fractal representation. R. Devaney and L. Keen, eds., _Chaos and Fractals: The Mathematics Behind the Computer Graphics_, American Mathematical Society, Providence, RI, 1989. This book contains detailed mathematical descriptions of chaos, the Mandelbrot set, etc. R. L. Devaney, _An Introduction to Chaotic Dynamical Systems_, Addison Wesley, 1989. ISBN 0201130467. This book introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas. It goes into great detail on the exact structure of the logistic equation and other 1D maps. The book is fairly mathematical using calculus and topology. R. L. Devaney, _Chaos, Fractals, and Dynamics_, AddisonWesley, 1990. ISBN 020123288X. This is a very readable book. It introduces chaos fractals and dynamics using a combination of handson computer experimentation and precalculus math. Numerous fullcolor and black and white images convey the beauty of these mathematical ideas. R. Devaney, _A First Course in Chaotic Dynamical Systems, Theory and Experiment_, Addison Wesley, 1992. A nice undergraduate introduction to chaos and fractals. A. K. Dewdney, (1989, February). Mathematical Recreations. _Scientific American_, pp. 108111. G. A. Edgar, _Measure Topology and Fractal Geometry_, Springer Verlag Inc., 1990. ISBN 0387972722. This book provides the math necessary for the study of fractal geometry. It includes the background material on metric topology and measure theory and also covers topological and fractal dimension, including the Hausdorff dimension. K. Falconer, _Fractal Geometry: Mathematical Foundations and Applications_, Wiley, New York, 1990. J. Feder, _Fractals_, Plenum Press, New York, 1988. This book is recommended as an introduction. It introduces fractals from geometrical ideas, covers a wide variety of topics, and covers things such as time series and R/S analysis that aren't usually considered. Y. Fisher (Ed), _Fractal Image Compression: Theory and Application_. Springer Verlag, 1995. J. Gleick, _Chaos: Making a New Science_, Penguin, New York, 1987. B. Hao, ed., _Chaos_, World Scientific, Singapore, 1984. This is an excellent collection of papers on chaos containing some of the most significant reports on chaos such as ``Deterministic Nonperiodic Flow'' by E.N.Lorenz. H. Jurgens, H. O Peitgen, & D. Saupe. (1990, August). The Language of Fractals. _Scientific American_, pp. 6067. H. Jurgens, H. O. Peitgen, H.O., & D. Saupe. (1992). _Chaos and Fractals: New Frontiers of Science_. New York: SpringerVerlag. S. Levy, _Artificial life : the quest for a new creation_, Pantheon Books, New York, 1992. This book takes off where Gleick left off. It looks at many of the same people and what they are doing postGleick. B. Mandelbrot, _The Fractal Geometry of Nature_, W. H. FreeMan, New York. ISBN 0716711869. In this book Mandelbrot attempts to show that reality is fractallike. He also has pictures of many different fractals. H. O. Peitgen and P. H. Richter, _The Beauty of Fractals_, Springer Verlag, New York, 1986. ISBN 0387158510. This book has lots of nice pictures. There is also an appendix giving the coordinates and constants for the color plates and many of the other pictures. H. Peitgen and D. Saupe, eds., _The Science of Fractal Images_, SpringerVerlag, New York, 1988. ISBN 0387966080. This book contains many color and black and white photographs, high level math, and several pseudocoded algorithms. H. Peitgen, H. Juergens and D. Saupe, _Fractals for the Classroom_, SpringerVerlag, New York, 1992. These two volumes are aimed at advanced secondary school students (but are appropriate for others too), have lots of examples, explain the math well, and give BASIC programs. H. Peitgen, H. Juergens and D. Saupe, _Chaos and Fractals: New Frontiers of Science_, SpringerVerlag, New York, 1992. C. Pickover, _Computers, Pattern, Chaos, and Beauty: Graphics from an Unseen World_, St. Martin's Press, New York, 1990. This book contains a bunch of interesting explorations of different fractals. J. Pritchard, _The Chaos Cookbook: A Practical Programming Guide_, ButterworthHeinemann, Oxford, 1992. ISBN 0750603046. It contains type inandgo listings in BASIC and Pascal. It also eases you into some of the mathematics of fractals and chaos in the context of graphical experimentation. So it's more than just a typeandseepictures book, but rather a lab tutorial, especially good for those with a weak or rusty (or even nonexistent) calculus background. P. Prusinkiewicz and A. Lindenmayer, _The Algorithmic Beauty of Plants_, SpringerVerlag, NY, 1990. ISBN 0387972978. A very good book on Lsystems, which can be used to model plants in a very realistic fashion. The book contains many pictures. M. Schroeder, _Fractals, Chaos, and Power Laws: Minutes from an Infinite Paradise_, W. H. Freeman, New York, 1991. This book contains a clearly written explanation of fractal geometry with lots of puns and word play. J. Sprott, _Strange Attractors: Creating Patterns in Chaos_, M&T Books (subsidary of Henry Holt and Co.), New York. " ISBN 155851 2985. This book describes a new method for generating beautiful fractal patterns by iterating simple maps and ordinary differential equations. It contains over 350 examples of such patterns, each producing a corresponding piece of fractal music. It also describes methods for visualizing objects in three and higher dimensions and explains how to produce 3D stereoscopic images using the included red/blue glasses. The accompanying 3.5" IBMPC disk contain source code in BASIC, C, C++, Visual BASIC for Windows, and QuickBASIC for Macintosh as well as a readytorun IBMPC executable version of the program. Available for $39.95 + $3.00 shipping from M&T Books (18006289658). D. Stein, ed., _Proceedings of the Santa Fe Institute's Complex Systems Summer School_, AddisonWesley, Redwood City, CA, 1988. See especially the first article by David Campbell: ``Introduction to nonlinear phenomena''. R. Stevens, _Fractal Programming in C_, M&T Publishing, 1989 ISBN 1558510389. This is a good book for a beginner who wants to write a fractal program. Half the book is on fractal curves like the Hilbert curve and the von Koch snow flake. The other half covers the Mandelbrot, Julia, Newton, and IFS fractals. I. Stewart, _Does God Play Dice?: the Mathematics of Chaos_, B. Blackwell, New York, 1989. T. Wegner and M. Peterson, _Fractal Creations_, The Waite Group, 1991. This is the book describing the Fractint program. http:wwwrefs.html Web references to Julia and Mandelbrot sets http://alephwww.cern.ch/~zito/chep94sl/sd.html Dynamical Systems (G. Zito) http://alephwww.cern.ch/~zito/chep94sl/chep94sl.html Scanning huge number of events (G. Zito) http://www.nonlin.tumuenchen.de/chaos/Dokumente/WiW/wiw.html The Who Is Who Handbook of Nonlinear Dynamics Q28b: What are some relevant journals? A28b: Some relevant journals are: "Chaos and Graphics" section in the quarterly journal _Computers and Graphics_. This contains recent work in fractals from the graphics perspective, and usually contains several exciting new ideas. "Mathematical Recreations" section by I. Stewart in _Scientific American_. _Fractal Report_. Reeves Telecommunication Labs. West Towan House, Porthtowan, TRURO, Cornwall TR4 8AX, U.K. _FRAC'Cetera_. This is a gazetteer of the world of fractals and related areas, supplied on IBM PC format HD disk. FRACTCetera is the home of FRUG  the Fractint User Group. For more information, contact: Jon Horner, Editor, FRAC'Cetera Le Mont Ardaine, Rue des Ardains, St. Peters Guernsey GY7 9EU Channel Islands, United Kingdom. Email: 100112,1700@compuserve.com _Fractals, An interdisciplinary Journal On The Complex Geometry of Nature_. This is a new journal published by World Scientific. B.B Mandelbrot is the Honorary Editor and T. Vicsek, M.F. Shlesinger, M.M Matsushita are the Managing Editors). The aim of this first international journal on fractals is to bring together the most recent developments in the research of fractals so that a fruitful interaction of the various approaches and scientific views on the complex spatial and temporal behavior could take place.  Subject: Notices Q29: Are there any special notices? NOTICE (from Michael Peters): HOP  Fractals in Motion opens the door to a completely new world of fractals! Based on almost 30 new Hopalong type formulas and loads of incredible special effects, it produces an unlimited variety of images/animations quite unlike anything you have seen before. HOP features Fractintlike parameter files, GIF read/write, MAP palette editor, a screensaver for DOS, Windows, and OS/2, and more. Math coprocessor (386 and above) and SuperVGA required "HOP was originally based on HOPALONG, the Barry Martin creation which was popularized by A.K. Dewdney in one of his Scientific American articles. The HOP authors have taken Martin's idea well beyond his original concept, and developed it to such a degree that you need to keep reminding yourself of its modest beginnings. This program illustrates compellingly how a fundamentally simple idea can be extended, through the use of various graphics techniques, into something far removed from its humble origins. Don't let the simple name fool you  this is serious, robust, user friendly, IMAGINATIVE software !" (Jon Horner, editor, FRAC'cetera) $30 shareware Written by Michael Peters and Randy Scott HOP is usually contained in a selfextracting HOPZIP.EXE file. Places to download HOPZIP.EXE from: Compuserve GRAPHDEV forum, lib 4 The Well under ibmpc/graphics slopoke.mlb.semi.harris.com ftp.uniheidelberg.de (under /pub/msdos/graphics) spanky.triumf.ca [128.189.128.27] (under pub.fractals.programs.ibmpc) HOP WWW page: http://rever.nmsu.edu/~ras/hop HOP mailing list: write to hoprequest@acca.nmsu.edu To subscribe to the HOP mailing list, simply send a message with the word "subscribe" in the Subject: field. For information, send a message with the word "INFO" in the Subject: field. One thing that I forgot to mention about HOP is that it is contained in the December issue of Jon Horner's FRAC'cetera magazine, and that FRAC'cetera subscribers can register HOP for $20 instead of $30. NOTICE from J. C. (Clint) Sprott (SPROTT@juno.physics.wisc.edu): The program, Chaos Data Analyzer, which I authored is a research and teaching tool containing 14 tests for detecting hidden determinism in a seemingly random time series of up to 16,382 points provided by the user in an ASCII data file. Sample data files are included for model chaotic systems. When chaos is found, calculations such as the probability distribution, power spectrum, Lyapunov exponent, and various measures of the fractal dimension enable you to determine properties of the system Underlying the behavior. The program can be used to make nonlinear predictions based on a novel technique involving singular value decomposition. The program is menudriven, very easy to use, and even Contains an automatic mode in which all the tests are performed in succession and the results are provided on a onepage summary. Chaos Data Analyzer requires an IBM PC or compatible with at least 512K of memory. A math coprocessor is recommended (but not required) to Speed some of the calculations. The program is available on 5.25 or 3.5" disk and includes a 62page User's Manual. Chaos Data Analyzer is peer reviewed software published by Physics Academic Software, a cooperative Project of the American Institute of Physics, the American Physical Society, And the American Association of Physics Teachers. Chaos Data Analyzer and other related programs are available from The Academic Software Library, North Carolina State University, Box 8202, Raleigh, NC 276958202, Tel: (800) 955TASL or (919) 5157447 or Fax: (919) 5152682. The price is $99.95. Add $3.50 for shipping in U.S. or $12.50 for foreign airmail. All TASL programs come with a 30day, moneyback guarantee. NOTICE from Noel Giffin (noel@erich.triumf.ca): Welcome to the Spanky Fractal Database This is a collection of fractal's and fractal related material for free distribution on the net. Most of the software was gathered from various ftp sites on the internet and it is generally freeware or shareware. Please abide by the guidelines set down in the individual packages. I would also like to make a disclaimer here. This page points to an enormous amount of information and no single person has the time to thoroughly check it all. I have tested software when I had the resources, and read through papers when I had the time, but other than certifying that it is related to fractals I can't assume any other responsibility. Enjoy and discover. The correct URL for this site is: http://spanky.triumf.ca/ User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Fractal Frequently Asked Questions and Answers Previous Document: Complexity Next Document: Acknowledgements Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: stepp@marshall.edu
Last Update March 27 2014 @ 02:11 PM
