Certain combinations of a, b, c and d produce quite striking pictures. Some of my favorites are included as sample files. On color or gray-scale systems, PlotDotAt (x,y) becomes DarkenDotAt(x,y) using a palette of equally spaced shades of gray. The resulting plots have an attractive diaphanous quality, but they take a while to "grow". Please be patient. My approach has been to search for interesting parameter sets in black & white and then let a color plot run in the background.
I've tried to use standard Mac interface conventions. When the mouse pointer is in Cliff's window, it changes to a hand shaped cursor. You can click and drag to move the picture around inside the window. Click and drag in the grow icon at the window's bottom right corner to shrink or enlarge the window. Click in the zoom icon in the window's title bar to enlarge the window to fill your screen.
The File menu's Open… command lets you load a set of parameters from a text file. The Save… command saves the current parameter set as a Teach Text file. The format is quite liberal so you can use Teach Text to add notes to the file. The Save PICT… command saves the image as a PICT file, and the Copy command in the Edit menu copies it to the clipboard. Use the Adjust Parameters… command in the Cliff menu to change a, b, c, d and n. The Get Info command tells you how many iterations have completed and how fast Cliff's going.
Requirements:
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Cliff runs on any Mac with System 7, but requires the 32Bit QuickDraw extension with System 6. Cliff comes in two flavors: Cliff.SANE and Cliff.881. Cliff.SANE uses the slower (but more accurate) Standard Apple Numerics Environment routines to iterate the function. Cliff.881 is much faster, but requires a floating point co-processor and a 68020 processor or better. One megabyte of memory is enough for eight bit deep (256 color) displays. You may have to increase the memory allotment for deeper displays.
References:
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These simple iterated mappings are the subject matter for an entire computer art/math book Dr. Pickover will be publishing in about a year. He has written extensively about this and related topics:
Pickover, C. (1990) Computers, Pattern, Chaos and Beauty.
St. Martin's Press: NY. (Tel: 1-800-221-7945)
Pickover, C. (1991) Computers and the Imagination.
St. Martin's Press: NY. (Tel: 1-800-221-7945)
Pickover, C. (Sept, 1992) Mazes for the Mind.
St. Martin's Press: NY. (Tel: 1-800-221-7945)
Hargittai, I. and Pickover, C. (1992) Spiral Symmetry.
World Scientific: NY, London, Singapore. ISBN 981-02-0615-1 (USA Office: World Scientific, 687 Hartwell St., Teaneck, NJ 07666-5309 (Toll-free: 1-800-227-7562, Fax: 201-837-8859); Singapore Fax: 3825919.)
Sorry, neither Gem City Software nor I can accept liability arising out of use of this program including (but not limited to) the time you waste playing with it. Happy hunting!