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Thank you for downloading this fractal learning tool.
Adam Smith is reachable (but not tangible) at: smithab@mailbox.syr.edu for bug reports, suggestions, comments, whatever....
If you use my program, send me e-mail! Especially if you use this as a fractal teaching tool. Yes, you are obligated : )
Why version 5.0 is so <explicit adjective> special:
This is the first 'fat' binary release with code for PowerMacs and FPU-equipt 680x0 Macs.
New smaller application size means less time to download, more time to play!
New This Release (from version 3.1):
•30% Faster calculations of all sets on PowerMacs! RISC Optimized!
•Implementation of the 'Divide and Conquer' Mariani-Silver algorithm we love so much. Hold down the control-key when choosing 'Fractalize!' to see approximations.
•Window contents now scale themselves when the window size is changed!
•Real-time Julia Set Calculations (Hold down Option and click-and-hold-and-drag in the fractal window, zooming is not implemented for Julia sets.)
•Full-Screen view up to 832 by 624.
You can now save images that are exactly the size of your screen (for deskpicts, startups etc…)
•Choices window sizes: (in addition to full-screen view)
(640 by 480) and (320 by 240) on a really big monitor
(480 by 360) and (320 by 240) on a standard 640 by 480 Apple monitor
even smaller on a 512 by 384 monitor (but nobody uses these right?)
Use zoom box to toggle window size.
•Has Option for maintaining Aspect-Ratio. If you turn this off, you can stretch and warp the fractals, but when you turn it back on it won't reverse the damage (it locks on the current H:W ratio!)
•New "About…" dialog, cool :-P
•New command key equivalents and menu appearances.
•Calculates the default view on program launch ('cause it's fast)
•New HSV palattes (They look uglier in the default view, but look cool when you zoom way in)
I am currently working on the palattes to find a good compromise for better looking julia sets.
•Eats more RAM for a 832 by 624 buffer. Now a whopping 2.6Mb RAM slammer!
•Uses RAM much more efficiently however. (old versions wasted perfectly good RAM with unecessary buffering)
Running Floating Fractals:
You should be able to simply double click to launch.
Do not use this product with any "non-prescription" drugs.
Files that comprise Floating Fractals:
ReadMe "Floating Fractals" (You are reading this now)
Floating Fractals 5.0ß (FAT)
Required Hardware Configuration:
A good mac.
More specifically, a color Macintosh with 3 Free MB of RAM and an FPU (881/882/882subset)
Floating fractals will not run satisfactorily with FPU emulators!
PowerMac and Monitor with Thousands of colors recommended (of course).
This program will run fastest in Thousands or Millions of colors mode.
Some transparent features may also require Quicktime.
Best calc. times (640 by 480 Mandelbrot set @ 100 iterations) :
/Div. and Conq./ PowerMac 7100/66 1.03 seconds :-)
Centris 650 25MHz 11.35 seconds >:-[
Using Floating Fractals:
I got sick of detailing the program's use in each release. Sorry. My time is better spent programming than re-writing these docs. I think my program is pretty self explanatory. Play with all the menus and have fun : )
The Main Viewing Sector (opened upon launch) choose an appropriate size for itself on your screen with a maximum size of 640 by 480 on monitors supporting 832 by 624 or larger displays.
You may have to pump up the iteration multiplier if you zoom way in. If out-of-set areas are not solid-colored, for example, or if the set is black and blotchy. A setting of 2500 for Maximum iterations should be enough for most of life's problems.
The Fractals:
The Mandelbrot Set: The famous one of the bunch. Hooray :-|
The Drawn and Quartered Mandelbrots: The Mandelbrot Set, with a hyperbolic-type singularities at the origin (division by zero!) will calculate slower that other fractals.
The True Delta Set: A manipulation of the Mandelbrot function. Contains miniature likenesses of itself and of the Mandelbrot Set (Look Hard!).
Others: Atemporal manifestations of my 3rd Stage Guild Navigating Mind. These contain interesting spiral and fluid-like space-time discontinuous tensor manifold fields. (Whatever!)
Now, Fractalize! and enjoy.
Technical Notes:
The name "Floating Fractals" refers to only two things, and could thus be considered a condensed form of "Floating-Point Numeric Fractal Generator".
Code was generated with Metrowerks’ CodeWarrior C for PPC.
I used my trusty 7100/66 16/250 to test the 601 code, and on occasion,
our school's Q650's and a Q800 to test the '040 code. I also compiled the SANE version for 68K so that I could test the 68K application on my 882-less PowerMac in emulation-mode, but this only proved that PowerMac emulation of the 68LC040 is more stable than a real '040!
Other than what I have checked, there has been little testing of this program. Bugs are likely, especially on computer configurations that are non-standard or not available for me to test this program on. Runs OK on my IIvx too.
Floating Fractals is from my original C source. It uses a true RGB palatte, selected according to escape time (not by true point potential, however), and calculated from an HSV hue or value ramp. All GWorlds are 16-bit. All calulations are done with 64-bit doubles on the Powermacs. The other sample Fractal Sets provided, I made up. Most are not really near-self-similar like the Mandelbrot set, but they have some neat patterns within.
Floating Fractals has a formula that determines how many iterations are to be done, based on the real number range of the viewing area. The number of iterations is proportional to some
log of the real number range. I provided a simple scalar control over this function, Iteration Multiplier. This allows you to multiply the number of iterations in cases where you do not feel that the picture is accurate enough.
Shortcomings:
1. The calculation routine locks up the interface and only offers the standard Command-period abort. I most likely will not fix this any time soon. On PowerMacs, calculation time is short enough that no one would want to background it (about 0.95 seconds for the default image on an 832 by 624 monitor on my 7100).
2. My algorithm for finding solid color areas is bit of a hack. For speed on the 68K machines, I don’t do a thorough check of block border pixels. For this reason, You may see solid block artifacts once every 17,000 years. Too Bad.
3. Creates PICT files with it's own application signature, but cannot re-open them. Oh well.
4. Still has no practical, real-world applications.
5. Still doesn't cure cancer either, sorry.
Possible Bugs/Acknowledged Problems:
1. Problem: Using the divide and conquer algorithm, block sizes often become odd-sized, and are thus no longer even divisions of the window size. This will not affect the resultant image, but is an internal problem for memory writes nonetheless, and may inhibit features in future versions.
2. Problem!: I hacked this App between my engineering finals. Hey it was free, OK?
3. Problems: I still use too many exclamation points in my documentation!!! I dont yous spelcheking eathir.
Thanks to: (finally!):
•“The New Galactic Emperor” Garth Henning here at syr.edu for his help with function pointers and RISC optimization and for his numerous tips that kept me away from my debugger.
•Dave Hochhauser at kent.edu for his time spent beta testing and optimizing my core routine code, and for animating my marquee.
•Tony Yang at tufts.edu for his on-line help in the aesthetics dept. and the time he spent testing out early versions.
•Thanks to everyone else who tried out my program but may not wish to be mentioned by name.
•No thanks to Davis, whose contempt for mac hackers shames the institution of public education!
The Fine Print (Read Carefully!)
Floating Fractals 5.0ß by Adam Smith, Dec, 1994. You take the risks, should any exist. I am not a computer scientist (yeah!); I am a janitor at Syracuse University, Techno-MIDI junky and former //e programmer who just thinks PowerMacs and Fractals are cool beans!) This software is freeware, but I retain all my rights to it. You may not use this software for any commercial purposes without consent from its author (me). As this is a learning tool, distribution without the accompanying documentation is strongly discouraged, as is distribution of code-stripped single CPU copies. No, I am not really a janitor! Have you seen my dog 'chugs' ? Quickdraw, Macintosh and Power Macintosh are registered trademarks of Apple Computer, Inc.
