This article is from the Fractal FAQ, by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by others.
Fractint's speed (such as it is) is due to a combination of:
1. Using fixed point math rather than floating point where possible (huge
improvement for non-coprocessor machine, small for 486's).
2. Exploiting symmetry of the fractal.
3. Detecting nearly repeating orbits, avoid useless iteration (e.g. repeatedly
iterating 0^2+0 etc. etc.).
4. Reducing computation by guessing solid areas (especially the "lake"
area).
5. Using hand-coded assembler in many places.
6. Obtaining both sin and cos from one 387 math coprocessor instruction.
7. Using good direct memory graphics writing in 256-color modes.
The first four are probably the most important. Some of these introduce
errors, usually quite acceptable.
 
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