Fractal Frenzy 2/Fractal_Frenzy_Volume_II_Walnut_Creek_August_1995.iso/mac/Intro.txt

Text File | 1995-06-12 | 20KB | 368 lines

                                INTRODUCTION

                             by Bradley Beacham


    FRACTALS
    --------
    A revolution occurred in 1987, but it never made the papers because
    it happened in my head.  It started when I read "Chaos" by James
    Gleick.  The book is full of stimulating ideas, but what really
    caught my imagination was the discussion of fractal geometry.  As I
    looked at images of that beautiful and mysterious object called the
    Mandelbrot Set, and as I tried to grasp the ideas that lay behind
    it, something changed within me.

    Fractals give us a new way of looking at the world.  After using the
    idealized forms of Euclidian geometry for thousands of years, we
    have a new geometry that describes many of the forms we see in the
    real world; rougher perhaps, far more complex, and yet richer.
    Benoit Mandelbrot opens his book "The Fractal Geometry Of Nature"
    with this challenge to the old paradigm:

        Why is geometry often described as "cold" and "dry?"  One reason
        lies in its inability to describe the shape of a cloud, a
        mountain, a coastline, or a tree.  Clouds are not spheres,
        mountains are not cones, coastlines are not circles, and bark is
        not smooth, nor does lightning travel in a straight line.

    Mandelbrot's work was the spark that ignited the current fascination
    with fractals, but much of the mathematics we now recognize as
    belonging to the realm of fractals is not new -- Julia sets, Cantor
    dusts, Koch snowflakes and Peano curves, for instance, had been
    described many years before Mandelbrot came to the arena.  But where
    other people saw mere curiosities (or worse, monstrosities)
    Mandelbrot saw a deep correspondence with reality.  And when he
    pulled these strange concepts together and formulated his notion of
    a "fractal" geometry with fractional dimension, he changed the way
    we see.  We're still just beginning to understand the implications
    and potential uses of it all.

    Certainly Dr. Mandelbrot's intellectual synthesis was essential to
    our present understanding of fractals, but another development was
    equally important : cheap computer power.

    The mathematical procedures behind fractals can be startlingly
    simple. For example, the Mandelbrot Set is created by squaring the
    number 'Z' adding the number 'C', and then resetting 'Z' to equal
    the result. The incredible complexity of the Mandelbrot set arises
    from the fact that this simple process is repeated millions of times
    for a typical image, with the result from one calculation becoming
    the basis for the next in a feedback loop.  A crude sketch of a
    Julia set (which is closely related to the Mandelbrot set) was
    created as early as 1925 with manually performed calculations, but
    the enormous amount of computation involved made this very
    impractical, even to a determined investigator. Computers changed
    all of that.  And today's computers, with their combination of high
    speed and low cost, have made possible a new era of fractal
    exploration.

    The contributors to this CD are enthusiastic explorers of this new
    graphic terrain, and our images document some of the strange and
    beautiful places we have visited.  The vehicle we have used in our
    explorations is the program FRACTINT, by the Stone Soup Group.


    THE ART OF FRACTAL IMAGES
    -------------------------
    Fractint is, in many ways, a model of good software: It's free.
    It's the product of collaboration between many volunteers.  It's
    very well written.  It's fast.  And best of all, it's very powerful
    - the user of Fractint has many, many options.  There are over a
    hundred built-in fractal types, and most of these can be modified by
    the selection of numeric parameters and functions.  There are
    already thousands of formulas that can be accessed through the
    wonderful formula parser feature, and more formulas are being
    written as time goes on.

    Plus, there's a large array of options that modify the way Fractint
    generates an image:  You can invert an image, in effect turning it
    inside-out. You can use options that modify the way Fractint
    calculates an image or applies its colors.  You can choose from a
    collection of color palettes, or you can have Fractint create one
    randomly.  And there are many other options that I won't attempt to
    describe here.

    The point that I'm trying to make is that the knowledgeable user of
    Fractint is presented with a staggering number of choices.  You can
    create very interesting images simply by accepting Fractint's
    defaults, and that's all that many users do.  But some people go
    much farther.

    I like to compare the process to photography.  Certainly there's
    more than one way to take a picture.  Some people are satisfied by
    the point-and-shoot approach; there's absolutely nothing wrong with
    taking snapshots, of course, and you can get a lot of pleasure out
    of pictures created this way.

    But sometimes a person is driven to do more.  Such a person will
    learn all she can about her camera, so she'll be able to make good
    choices when it's time to select a lens and shutter speed and
    aperture setting. She will study filters and light meters and the
    varieties of film and darkroom techniques.  To put it simply, she'll
    attain a much higher level of mastery over her tools than the
    average user, and that mastery will be evident in the pictures she
    produces.

    In addition, she'll carefully choose her subjects, taking the
    lighting into account, and she will look for the best camera angle
    and placement so her images are effectively framed.  Beyond
    technical mastery, in other words, a fine photographer will also
    have qualities that are important in any of the visual arts: a
    sensitivity to composition, balance, contrast, line, texture, color,
    and so on.  She'll have a "good eye."

    These are the same virtues that distinguish a good fractal artist.

    Some people may balk at the idea of fractal images as art.  One
    might argue that the process is too mechanical, that it can't be art
    because the creator isn't physically manipulating the medium.
    Another might say that it isn't art because it isn't created within
    the context of artistic tradition.  Certainly the early
    photographers had to contend with similar arguments, but nowadays
    most people accept the notion that a photograph can also be a work
    of art.  As more people gain exposure to fine fractal images, and as
    our tools and techniques improve, I expect that a similar conversion
    awaits many of the current naysayers of fractal art.

    But the images on this CD provide a visual argument that far
    surpasses anything I could say in words.  See for yourself.


    THE PEOPLE BEHIND THE IMAGES
    ----------------------------
    Years after I read "Chaos," I found a copy of Fractint, and that's
    when I got seriously hooked.  What really pushed me over the edge
    was discovering the wonders of "par files."  Fractint allows you to
    save all of the details needed to recreate an image (somewhat like a
    recipe for the image) in an ASCII text file.  These parameter files
    have the advantage of being very compact compared to full image
    files (GIF or BMP files, for instance), so they're great for sharing
    images without running up big online expenses.  I thought my images
    were pretty good until I discovered a computer bulletin board system
    that carried fractal-related files and started downloading parameter
    files.  Some of the images they created were amazing.  Time after
    time, I found myself saying "I didn't know Fractint could do that!"
    I spent months collecting the files, generating the images, and then
    trying to understand how they might have been originally created.

    Finally, I couldn't stand working in isolation anymore.  A little
    less than a year ago, I joined CompuServe and met most of my
    Fractint heros. I was a little awe-struck, I'll admit, but I have
    learned a great deal from my contact with them, just as I had hoped.
    My most pleasant discovery is that these are very likable people.
    Far from being the condescending "artistes" that I thought I might
    encounter, I have found them to be very generous with their time and
    resources, full of encouragement and good advice.


    DONALD ARCHER ([e-mail]):  One of the most
    impressive things about Don Archer, in my opinion, is his artistic
    conscience. Fractint makes it very easy to apply dazzling color to
    an otherwise lackluster image, and Don reminds us that the formal
    qualities (or lack of them) in an image should not be so easily
    glossed over.  He has created whole collections of images in two and
    three colors, emphasizing the pure beauty of fractal structures.
    Lest you think he's overly serious, Don has also created images
    suggesting whimsical animals and people.  Many people know Don for
    his pseudo-scriptural "The Fractal Commandments" which mixes gentle
    humor and good advice.

    Don is a resident of Brooklyn, New York, where he is a licensed
    professional massage therapist.  He's a graduate of Cornell
    University, and is the father of eight and the grandfather of one.
    His work has been displayed in several shows (one-man and group) in
    NYC art galleries, and he is the director of the Museum of Computer
    Art.


    RON BARNETT ([e-mail]):  Ron is one of the most
    versatile talents in the computer graphics community.  He makes
    beautiful images with the POV ray-tracing software.  He has written
    a utility program called MAKEMAP, which aids in the creation of
    color palette files (also known as "map" files) for use with
    Fractint and other programs.  He is also the author of many
    excellent formulas that are widely used with the Fractint formula
    parser.  That would be enough to earn my respect, but Ron also
    creates beautiful fractal images.

    Many of his images suggest organic forms to me, and they often
    create an atmosphere of stately, timeless quiet.

    Ron lives in Voorhees, New Jersey.  He is a biochemist/biophysist by
    profession, and is group manager in science and technology at the
    Campbell Soup Company.  His hobbies are music performance, cooking,
    chaos theory and exploring artificial intelligence using computer
    programming.


    BRADLEY BEACHAM ([e-mail]):  I'm still very much a
    student of fractals and Fractint, although I've been using the
    program for a couple of years now.  There's always something new to
    learn.  I especially enjoy inventing new formulas and then exploring
    them, and I have written a tutorial to help other people get started
    with Fractint's formula parser.  I get a deep satisfaction from
    creating fractal images; the process provides a wonderful
    combination of intellectual and aesthetic stimulation.

    I live in Salt Lake City, Utah, with my sweetheart (and incredibly
    patient spouse) Valerie.  We share our house with three cats, two
    birds, and a cowdog named Patsy Cline.  By day I do computer
    support, programming, and supervising for Jetway Systems.  Other
    enthusiasms include music, travel, reading and writing, bad/weird
    movies, and the amazing landscapes of my home state.


    ROBERT W. CARR, M.D. ([e-mail]):  Although a
    relative newcomer to fractal graphics, Bob has become one of the
    most prolific creators around.  He's an enthusiastic supporter of
    WinFract, the Windows version of Fractint.  His enthusiasm for all
    things fractal, in fact, has been very energizing for the
    Fractint-user community on CompuServe.  Bob has already created
    hundreds of formulas, and I think his images demonstrate a real feel
    for composition and color.  Many of Bob's images use Fractint's
    boundary-tracing method to produce unique forms he calls "Carr's
    Crystals."  He certainly gets my vote for Rookie of the Year.

    Bob is a retired M.D. (Emergency and Pediatrics) living in Ocala,
    Florida.  He also devotes some of his seemingly boundless energy to
    his other hobbies, which include Daylily hybridizing, Civil War
    history (emphasis on General Robert E. Lee), breeding show guppies,
    bass fishing, and collecting guns, U.S. stamps, and 0-27 gauge model
    trains.


    DON LEBOW ([e-mail]):  Don LeBow is one of the first
    people I met when I joined CompuServe, and I'm certainly glad I did
    because he's the polar opposite of the self-important snobs I
    imagined I might encounter.  Although he creates beautiful fractal
    images, Don typically receives praise with gentle, self-deprecating
    humor.  He's a genuinely modest guy, and I think his down-to-earth
    perspective makes him all the more likable.  He says his favorite
    fractal images are "the ones that don't look like fractals are
    'supposed' to look.  A little shaking up of preconceptions is a very
    healthy thing."  His work, in my opinion, is characterized by
    elegance, creativity, wit, and style.

    Don lives in Lahaina, Hawaii, and says that after twenty years in
    Hawaii he can't imagine living anywhere else.  I don't know how he
    can tear himself away from the beautiful scenery to work on a
    computer, but I'm glad that he does.


    CAREN K. PARK ([e-mail]):  If I had to choose the
    work of just one person to help me make a case for fractals as art,
    that person would probably be Caren Park.  Nobody is better at
    making me envious; whenever I look at her work I find myself saying
    "I wish I had done that."  Caren's images are so polished, so
    elegant, so beautifully composed and perfectly colored.  As luck
    would have it, Caren is also a delightful person.  She's been very
    generous with me, sharing her files and giving encouragement, and
    despite recent medical problems and a rugged work schedule she has
    kept her sense of humor.

    Caren lives in a huge house in Issaquah, Washington, with her
    partner Janie and two cats, and loves reading and listening to
    music.  She is a computer consultant, a semi-professional bowler,
    and the proud new owner of a book store.


    LEE H. SKINNER ([e-mail]):  I have met many fractal
    enthusiasts in the last year, but none have been as helpful to me as
    Lee Skinner.  Lee never ceases to amaze me; he knows everything
    about fractals and Fractint.  (Well, probably not, but it sure seems
    that way.)  He's the inventor of several of the fractal types and
    formulas (including the Tetrate and Zexpe fractals) that have become
    standard parts of Fractint.  He creates gorgeous fractal images in
    astonishing quantities, and his images are very distinctive.  Lee
    loves to zoom deep into fractals, exploring areas that no one has
    ever seen before. (Fittingly, he also enjoys exploring caves.)  To
    top it all off, Lee's very generous, freely sharing tips and
    techniques, encouragement, and stimulating ideas.

    Lee lives in Albuquerque, New Mexico, where he is a member of the
    Spectra Research Institute.  He is currently programming groundwater
    models for Sandia National Laboratories.  On his home computer,
    currently a 100Mh 486/DX4, Lee has generated over 7000 images using
    Fractint.  In 1970, he authored the HP-35 Math Pac for
    Hewlett-Packard, the first manual of algorithms for a hand-held
    scientific calculator. Besides fractals, his interests include
    mathematical games and diversions, cosmology and the new physics,
    astronomy, topographic maps and photogrammetry, wilderness hiking,
    caving, and classical music.


    CAROL WALSKE ([e-mail]):  After months of
    reverse-engineering Carol's intriguing work, I finally did meet her
    online and found her to be as creative as I had expected.  Carol is
    a versatile artist who has trained at the Pratt Institute of Art and
    is well versed in using traditional media.  In addition to her work
    with Fractint, she is also an active user of other computer graphics
    software, sometimes loading fractal images into "paint" programs and
    manipulating them in interesting ways.  I appreciate Carol for her
    inventiveness, her kind support, and her wicked sense of humor. And,
    of course, those beautiful images.

    Carol lives in New York, New York, where she works as a software
    trainer, troubleshooter, graphics guru and assistant network
    administrator for an insurance broker.  After twenty years in New
    York ("a long enough sentence for anyone") she and her long-term
    flatmate will be moving to San Francisco this year.  She writes
    fiction, and says she has "two cats, too many CDs (the audio kind),
    too many books, and too little time."


    QUOTES
    ------
        Why do I do fractals? I love the combination of math and beauty.
    I was never good at freehand drawing though I loved art.  Now by
    using simple math I need no hand-eye coordination to create
    beautiful images.  The play here is very similar to hybridizing
    tetraploid Daylilys -- working out formulas and seeing what your
    thoughts and ideas can create.  It's a whole new freedom.  For me,
    creating formulas and fractals therefrom is not work but the most
    entertaining hobby I've ever had (and I've had many, including
    breeding ants, worms, Belgium Hares, parakeets, etc.)

                        -- Bob Carr


    I take it for granted that fractals are indeed a high form of art. I
    think of myself as a serious fractal artist, and I labor at it
    compulsively.  I gnaw at the technical possibilities of a formula
    like a dog gnawing a bone, and I will not give up until I have run
    myself and a series of images into exhaustion.  Thus my pars are
    often variations on a theme.  Many of my images are drawn in
    monocolor, often greyscale.  Indeed, even my color images are first
    drawn or tested in black and white, so I can be certain of their
    graphic strength sans color.

    We may be in the Golden Age of fractal art, just enough years having
    gone by since Mandelbrot (A.M.) to weed out the cliches and to
    separate the wheat from the chaff.  If so, we are lucky to be
    working now.

                        -- Don Archer



        I think it's a disease.  A compulsion that you either feel or
    you don't.  That drive separates the fractal artists from the
    dabblers, I think.  Why do I feel driven?  I'm painfully aware of
    the number of hours I've "wasted" on fractals, the 10-hour fractals
    that turn out not to be worth the effort, the hard drives that have
    been eaten by fractals, the boxes upon boxes of disks of images I've
    got stored that few will ever see.  But I still love doing it.  I'm
    in love with, to para a-by-now-hackneyed phrase, "going where no
    artist has gone before."  I'm in love with the mind-boggling
    complexity and delicacy of fractals that usually go way beyond what
    any artist can create by traditional means.  I'm in love with the
    constant interplay between chaos and order among fractals--and, to
    wax philosophical for a moment, the way that interplay so aptly
    mirrors the "real world."  I love the depths of fractals and the
    feeling that, no matter how far you keep exploring, there's always
    more amazing images yet to discover.

                    -- Carol Walske