Robert P. Munafo, 1998 Dec 29.
Approximations are one type of Speed Improvement (q.v.). As the name implies, they usually involve making some sort of compromise, presumably for the benefit of improved response during interactive exploration. (See the accuracy page for a discussion of the unrelated theoretical issues involving approximation of the Mandelbrot Set in general.)
Here is a summary of practical approximation techniques used in computing views of the Mandelbrot Set:
Integer Math: write an assembly-language function that does the z->z^2+c computation in 16-bit integer math using registers and the processor's built-in integer multiply instruction. Use it when computing views in which the Magnification is low. (The exact rule is: use integer math when the pixel spacing is greater than the Escape Radius divided by 2^16).
Low Resolution: draw the image at lower resolution (by using "chunky" pixels, or by drawing in a small window).
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017. Mu-ency index
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11