What do you get when a creationist visits the Galapagos? »« Those dang comments


  1. Jacob Schmidt says

    Ahaha, I like that. Thanks, tomfrog.

    The electric sheep screen saver is an interesting little toy. It plays a fractal, but it mutates them with other fractals online. If you leave your computer on over night to download and mutate at random, you’ll have quite the collection of morphing fractals in the morning.

  2. DLC says

    I created one of those in mathcad once. It was spectacular watching the system try not to hang while drawing it. I loved mathcad. it was so damn useful for things. /sigh.

  3. says

    A primer on Mandebrot’s fractal geometry was published in the College Math Journal in 1987 and is posted here. (And Mandelbrot’s middle initial is reportedly just that — a middle initial. It doesn’t stand for anything more.)

  4. says

    Huh. They claim that all numbers move either to zero or infinity under the Mandelbrot transformation, but that’s a simplification at best. Some numbers go into a cycle.

    Outside the boundary, the numbers do indeed go off to infinity. Inside the boundary, the numbers either converge to a cycle or converge to zero.

  5. Louis says


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  6. says

    Damn, I feel about a thousand times smarter than I did when I woke up now. Excellent early morning coffee viewing.

  7. says

    If you have a decent computer, go online and look for Fractal eXtreme. It’s shareware (current price, $10) but even just the trial version is very nice. And if you have a 64 bit machine multi-core processors and a high definition monitor…. Trust me on this.

  8. Alex says

    Interestingly, fundamental quantities in physics such as the strength of the strong force or the fine structure constant scale with fractal dimension depending on the “magnification”, rather like the length of a seashore.

    Maybe it means something :)

  9. Jonathan Dresner says

    Could have done without the Jungian absurdities towards the end, but otherwise decently done.

  10. lpetrich says

    Very beautiful. I think that the attraction of the Mandelbrot set and of fractals in general is because they have a real-world sort of appearance. It’s especially nice that these objects can be generated with very simple algorithms, though they require a lot of number crunching to display them.

    That’s a big contrast to traditional geometry, whose shapes are much oversimplified compared to many real-world objects. But fractals need not be opposed to traditional geometry. Fractals can serve as algorithms for specifying groups of traditional geometrical shapes. L-systems use lines, for instance.

    There are lots of biological fractal systems.

    Circulatory systems (blood, lymph), lungs, tree branches, roots, …

    I think that this says something about how they are laid down. The biggest ones are laid down directly, while the smaller ones are generated in fractal fashion — as they grow, they branch. Something that ought to interest a developmental biologist.

    It suggests that genes specify algorithms for development rather than anything like architect’s drawings — proteins are produced in architect-drawing fashion, but that’s about it.

  11. Crudely Wrott says

    I’ll second Gregory @ 11. Fractal eXtreme is a powerful and fast way to generate M-sets, J-sets, attractors and other very cool stuff. Zoom movies too, IIRC.

    For a more artful approach try the also very fast and powerful UltraFractal. I’ve had v. 3 in residence on one computer or another for a *long time*. It has a layering feature that can result in spectacularly detailed and subtle images. It also features a boatload of example formulas and help files. All drag and drop, of course, and you have control over everything that can be controlled except that one thing that I never did find.

    For a vintage experience try to find FractInt, from The Stone Soup Group. I first got it on a couple of 4 1/2 inch floppies back when shareware was bleeding edge. Some very clever programers wanted to take advantage of fast integer math to generate a wide range of fractals and they had a lot of success. So much that they kept updating long enough for at least twenty versions. I know this because v. 20 also resides on this computer. Guess what? Runs under DOS!!! I still bring it up from time to time just for the sake of play and nostalgia.
    Oh, yeah. You’ve really got to admire their “contribution” policy from back in the 80s:
    “Don’t want money. Got money. Want Admiration!”
    FractInt does have a built in limit as far as magnification, or, zoom. I forget the number off hand but this should put it in perspective: A screen large enough to show the whole M-set at max zoom would be about the size of the orbit of Saturn.
    Oh, yeah. It does red-blue 3D as well as those weird 3D images made up of colored dots apparently plotted randomly. Wass’call, I think.

    So, try ya some. Today!

  12. inquisitiveraven says

    Fractint is still around. Not sure if any further development is happening, but you can find it here.