Calculated Beauty in Mandelbrot space
Author: Steve Kayner
Date: June, 1994
Keywords: fractals fractal Rocky Mountain Digital Peeks graphics program application software review
Text: Calculated Beauty in Mandelbrot space by Steve Kayner, SMUG Member Calculated Beauty: A Journey Through Mandelbrot Space... is a CD-ROM disc for viewing, creating, and just generally fiddling around with fractals in a carefree way, in a non-math setting. Just about now, you're probably saying, ''Steve, what the heck is a fractal, and why would I want to play with one in a carefree way, much less in a non-math setting?'' To which I would be forced to say, ''Well, I'm certainly no expert, but follow along here, and I'll give you a brief explanation.'' According to The Mandelbrot Fractal Companion, an excellent freeware HyperCard stack by Evan and Joleen Yeager, a fractal is: ''a geometric figure that consists of a central theme which repeats itself on an ever reducing scale. Each successive replication is in a specific ratio or scale to the original. Such a ratio can easily be expressed as a fraction thus the term fractal is derived.'' The math involved in fractals is based on complex numbers, which are combinations of real and imaginary numbers. Imaginary numbers are tricky because they involve the square root of -1. Intuitively, the square root of -1 shouldn't exist. I suggest you not even try to imagine it, because you may suffer a serious math anxiety attack. Real numbers are easy, because they're really real, and they sometimes show up in sufficient quantities on our paychecks to make the difference between Spam, and ham. They didn't teach fractals when I was in school. In fact, the math for generating fractal images is so intense, that it wasn't until about 1975 that the computers necessary to explore the topic became available. Simpler shapes, and the math behind them were known much earlier, but it took some real nerd-power to get into the heavy stuff of fractal imagery. A guy named Benoit Man-delbrot spread the word of fractals to the world when he published his work The Fractal Geometry of Nature in the early '80s. Not long after that, they started showing up as land-scapes in movies like Star Trek II, The Wrath of Khan, and The Last Star Fighter. When I got my first com-puter a few years ago, one of the things I enjoyed doing was playing around with fractals. At the time, I was using an IBM clone that was not very fast, but had a math coprocessor. It could generate images over periods of time ranging from 15 minutes, to several hours. I soon tired of it because it took so long to generate images. The Calculated Beauty CD-ROM helps get around this time problem by including a nice library of pre-generated fractal images in the PICT format that can be viewed using the MandelGallery program. MandelGallery can also be set to run a slide show of images, and will display any PICT images that the user chooses. There are also countless more potential images composed of the results of fractal math, stored in a format called ''counts,'' or ''dwells.'' These files are viewed and manipulated using the MandelDisplay program. Images generated by MandelDisplay can be exported at higher resolution, in the PICT format for use with other programs. The Calculated Beauty CD-ROM contains over 6000 square feet of images at 72 dpi. The images are made up of 130,000 Tiles of 160 x 120 pixels each, equating to thousands of hours of computing time. Larger images, called Mosaics, are built up of about 10,000 Tiles each. The program allows the user to zoom in on the Mosaic images, even beyond the calculated depth of the counts, but that requires time for further computation. A floating point unit (FPU) can make a big difference in the speed of the calculations. MandelDisplay has a wide range of controls for generating images and sounds. Checking out the menus without reading the documentation makes it seem mysterious and scientific. There are menu items for ''Mosaic Unveiling'', ''Duration Quantizing'', and ''Use Log10 for Colorizing''. We're not talking KidPix here... The program ships with a large number of predefined palettes for changing the colors of the images you can generate. There are also tools for creating new palettes and for modifying existing ones. MandelDisplay can generate sounds from the count files, and provides a set of tools for refining the sounds to help make them more or less ''music-like.'' There are a variety of different instruments to use as voices for the sounds. The results of fractal math won't automatically emit symphony quality material. In fact, the results of calculations using imaginary numbers can't be expected to generate anything more than imaginary music without some serious tweaking. The Calculated Beauty CD-ROM ships in a standard jewel-case with no paper manuals. There is plenty of documentation on the disc in the form of DocMaker and MS Word files. Both versions are full of color screen shots, but I preferred the DocMaker format because it ran much faster. There are also several good shareware programs included on the disc, for further fractal gratification. Among them are Mandella v8.7, MandelZot v4.0, Fractal! v1.2, and a demo of Mandelbrot (the last frontier). PopCorn v1.0.1 is also included for viewing a lengthy fractal-zooming QuickTime movie. To use MandelDisplay, you'll need a CD-ROM drive, a 4MB Mac with at least an '020 processor, and at least a 16 color display system. A floating point unit (FPU) is also recommended, although a version of the program that will work without an FPU is included on the disc. The publisher does not recommend systems like the LC's, or the Classics, because they have no FPU, and run at less than 20MHz. Additional memory may be needed to save images at higher resolutions for use in other programs. Calculated Beauty [street price $28.95 (EduCorp)] is available from: Rocky Mountain Digital Peeks P.O. Box 1576 Nederland, CO 80466 Compuserve: 73565,446 Educational Inquiries: perdue@csn.org
Copyright © june, 1994 by Steve Kayner