The Landscape Within and Without: Similarities between landscapephotography and fractals

Discussion in 'Photography' started by Wayne J. Cosshall, Apr 29, 2007.

  1. Wayne J. Cosshall, Apr 29, 2007
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  2. It is indeed intriguing. I think it also goes deeper. We have a
    "landscape" of possible fractals once we fix the algorithm, and we
    move around by changing some parameters. if we have n parameters, it
    is an n-dimensional landscape. So our aim is to find the set of
    parameters which produces the fractal we wish (eg which looks like a
    tree, or which expresses "pain" in some sense, or whatever). We do
    this either by aimlessly wandering about the landscape until we find
    what we want, or by "walking around" by looking near to where we are,
    or other techniques.

    But generalise this a bit: any problem we try to solve (in a general
    sense; it could be an attempt to write a poem) will be solved in the
    same way, ie by wandering around some space of possibilities
    (analogous to changing the parameters of the fractal algorithm) until
    we get what we want. Doing science (eg trying to explain something) is
    done this way: I know some facts, and have various ways of putting
    them together; so I try various things (the "wandering around the
    landscape") until I get what I want (an explanation). So is writing
    poetry, in some sense: I try to express something (say); I have words,
    phrases etc which carry meaning, emotions, and which rhyme, don't
    rhyme, and so on, and I want to put them together in some way to
    achieve my goal. It's all the same, for sufficiently general
    definitions of "landscape" and "walk".

    The main difference between different people, it seems to me, is how
    they search around this space. Sometimes, looking just near you isn't
    enough (because you have to go in a nonobvious direction to get to the
    "solution"), and people who have the ability to find these nonobvious
    directions do things others can't (think of Einstein, Bach etc).

    Of course it is possible to generalise these definitions ("space",
    "search") so much that what one says is true but useless; this is a
    constant danger to all philosophers, I guess ;)
    achilleaslazarides, Apr 30, 2007
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  3. Maybe Beethoven fits better there. Bach is more like Newton. But never
    achilleaslazarides, Apr 30, 2007
  4. Wayne J. Cosshall

    Toby Guest

    Interesting Wayne--I've been doing fractal exploration for a number of years
    and my feelings are quite similar. I've written a number of formulae and
    coloring algorithms for Ultra Fractal and a few other proggies, and as I go
    exploring Mandelbrot or Julia sets I feel much like I do when I am out with
    my camera looking for juicy frames.

    Of course with the classic Mandelbrot there are repeating self-similarities
    which are not present in nature, but as soon as that is modified by applying
    various functions things change quite a bit. Finding pleasing symmetries
    amidst the chaos is quite pleasing, isn't it? And, of course, there is
    something weirdly satisfying about realizing that there is no end to the
    detail, no matter what magnification one uses. This certainly mimics the
    natural world.

    I'm not trolling for views, but if you are interested in my fractals (and
    some photos) have a look at:

    More to the point, browse the fractal galleries there in general...

    Toby, Apr 30, 2007
  5. Actually, I disagree. There are many self-similarities in nature.
    Look at e.g. streams that become rivers that become creeks that become a
    brook that becomes a streamlet.

    Same with valleys which have offsprings which in turn have even smaller side
    valleys which in turn ....

    Or coast lines. A statement like "country x has y miles of cost line" is
    meaningless. Did they really measure around each headland and cape into each
    tiny bay? Did they measure around each rocky outcrop? Did they measure
    around each rock laying on the beach? Did they measure around each grain of
    sand? I think this is typical fractal nature.

    And of course the prime example snow flakes, although that probably doesn't
    qualify as landscape photography ;-)

    Jürgen Exner, Apr 30, 2007
  6. Wayne J. Cosshall

    acl Guest

    In fact, turbulent flows (ie most flows in nature, streams etc) are
    self-similar (eddies of various sizes coexist), frustrating our
    attempts to understand it in a deep way (for some definition of
    "deep"). Other examples of this type of self-similarity abound.
    Someone even got a Nobel prize in 1982 for exploiting this self-
    similarity in a particular field of physics.
    Well coastlines are a prototypical example. Mandelbrot goes on about
    this in his book.
    However those are usually symmetrical, not self-similar on different
    scales. Still very nice, of course :)
    acl, Apr 30, 2007
  7. Wayne J. Cosshall, Apr 30, 2007
  8. Toby, you have some wonderful fractal work there. Most impressive.

    As I see others have pointed out, I also disagree with you only on the
    lack of self-similarity in the landscape. I see much that is
    self-similar, from mountain ranges to the edge of rocks to the mentioned
    by others water flows, etc.



    Wayne J. Cosshall
    Publisher, The Digital ImageMaker,
    Publisher, Experimental Digital Photography
    Personal art site
    Wayne J. Cosshall, Apr 30, 2007
  9. So do I, because it allows Photoshop clone tool retouching of parts of
    landscapes with related parts, and the eye can never spot it (image
    analysis can!). The fractal nature of trees, grass, rocks etc means you
    can even change scales of image parts, copy, and retouch.

    We have just ordered Bryce, for my wife to mess around with creating
    some imaginary landscapes. We had it years ago but it was painfully slow
    on a Mac IIcx. I found the software recently, and tried it on a modern
    Mac with Classic running - it was still slow, but also, the image size
    was limited to something like XVGA! We are hoping that modern Bryce is
    capable of big, big output files.

    David Kilpatrick, Apr 30, 2007
  10. Wayne J. Cosshall

    C J Campbell Guest

    The interesting thing is unpredictability. One might generate a
    fractal, for example, that models the exact behavior of the stock
    market for all of its history, but the model will still be unable to
    predict the future. The same goes for the weather. It is possible to
    create a fractal algorithm that predicts the past, but not one that
    predicts the future. A fractal may describe the current appearance of a
    range of mountains but it will be incapable of predicting what the
    mountains will look like in 10,000 years.

    The problem is resolution, of course. Very tiny differences accumulate
    and amount to huge variations, often in a very short time. You reach a
    point where the very act of observing can change the future.

    Thus, a fractal can mimic reality, but it can never duplicate it. There
    are fractal generators that allow a photographer to upsize an image and
    maintain an appearance of reality, but it is not the same image that
    would be obtained by a higher resolution photograph. The effect of
    higher resolution is unpredictable.

    A brush stroke on a painting can be seen as a part of a fractal image.
    The single brush stroke does not seem to resemble any part of the
    subject of the painting, but the combined brush strokes may create a
    realist masterwork.

    A photograph can never look exactly like reality because of its fractal
    limitations. It can never capture enough information to exactly
    duplicate the subject. If it did, it would be the subject, one in
    identity with it.
    C J Campbell, Apr 30, 2007
  11. Wayne J. Cosshall

    Matt Clara Guest

    Look into Vue. They have something called EcoSystem materials which can
    generate vast fields of whatever 3D objects you'd like, if you make your
    own, or if you use the presets, with fields of flowers and grasses, trees,
    rocks, small villages, farmland, and more. There are two images I created
    in Vue on the front page of my website. I also own Bryce, but like Vue
    better. They are both still slow to render BIG images. I have two gigs of
    ram but the only way I can get Vue to do anything over 3200 x 2400 is to
    render it out in parts and then recombine in Photoshop.
    Matt Clara, Apr 30, 2007

  12. Lovely idea, but it's about five times the price of Bryce - which is
    affordable for recreational use, not commercial. Vue Infinite is a bit
    too expensive for our needs!

    David Kilpatrick, Apr 30, 2007
  13. Wayne J. Cosshall

    Matt Clara Guest
    It is more expensive than Bryce, but not five times. It's also better than
    Bryce, by about 10 times. Bryce has changed a little over the years, where
    Vue makes huge jumps in R&D, and will likely continue to do so--ecosystems
    are just that, a huge jump. I would not be surprised to see Bryce bought up
    and incorporated into one of the other 3D software vendor's code, by and by.
    Matt Clara, Apr 30, 2007
  14. Wayne J. Cosshall

    Matt Clara Guest

    My apologies if I appear to dis Bryce entirely; I still have several images
    on my site created in Bryce, including: (ferns were painted in post
    process with Corel Painter 6)
    (and a few others which should probably be taken down)

    I don't think they compare favorably to my new Vue images
    (, though, but that could have to
    do with experience and a more developed eye (largely due to photography, I
    might add). Also, as I said before, Bryce doesn't change much, whereas Vue
    does, and that makes Vue the more exciting program, both to use and to watch
    (some might say the same is true of Canon, though I believe that's a finer
    point). Having said that, you may wish to watch Vue Easel for the day that
    ecosystems are incorporated therein. It's only $89, and frankly, I thought
    I'd read that Vue Easel 6 had ecosystems, and that's what I was suggesting,
    not Infinite. Vue espirit 6 allows you to load ecosystems--not sure if that
    means you can't make them or whether it includes a preexisting library of
    them--and it's running $199 (which just happens to be what I paid for my
    copy of Bryce 3D in 97/98).
    Matt Clara, Apr 30, 2007
  15. Wayne J. Cosshall

    Alan Browne Guest

    Too bad you miss the point that nature suffers both chaos and entropy so
    "pure" Mandlebrot sets are not seen (at least not for long).

    You're also missing the very important point that while perfect
    symmetry, repetition, nesting and so on are very easy in mathematics,
    the complex of nature wild is not easy to model.

    Introduce subtle noise or impulses into a Mandelbrot set and you will
    get terminations, variations and so on that begin to better mimic nature.,-76.294556&spn=1.638258,3.669434&t=k&om=1
    is but one of thousands of examples you can find of natural
    Mandelbrot-like sets in nature.

    Alan Browne, May 1, 2007
  16. Wayne J. Cosshall, May 1, 2007
  17. Wayne J. Cosshall, May 1, 2007
  18. Wayne J. Cosshall

    Mr.T Guest

    Possibly true, but I bet the actual data you have to support such a claim is
    Although the same claim can probably be made for most modern software
    without necessarily being wrong.

    Mr.T, May 1, 2007
  19. Wayne J. Cosshall

    Toby Guest

    In fact, turbulent flows (ie most flows in nature, streams etc) are
    self-similar (eddies of various sizes coexist), frustrating our
    attempts to understand it in a deep way (for some definition of
    "deep"). Other examples of this type of self-similarity abound.
    Someone even got a Nobel prize in 1982 for exploiting this self-
    similarity in a particular field of physics.

    But those levels of self-similarity are quite limited, compared to the
    infinte levels of self-similarity in a pure Mandelbrot fractal. Tree
    branchings exhibit the same self-similarity, but only up to a point.

    Toby, May 1, 2007
  20. Wayne J. Cosshall

    Robert Coe Guest

    My latest column is up with some thoughts about the links between
    : landscape photography and fractal images:

    IIRC, Mandelbrot's original paper on fractals emphasized their similarity to
    landscapes, notably to the shape of coastlines.

    This is the first time I've seen Cosshall's column. He presents some
    intriguing ideas, but someone should introduce him to a good proofreader. ;^)

    Robert Coe, May 1, 2007
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