Infinite Dwell Limit
Robert P. Munafo, 1999 May 18.
A "more perfect" picture of the Mandelbrot Set can be obtained by using an infinite dwell limit.
In order to avoid an infinite loop in the iteration process, some method of orbit detection must be used.
The infinite dwell limit method takes much longer than a standard finite dwell limit method. For a typical view of the whole Mandelbrot Set it takes about 10 times as long, and the slowdown is even worse as you zoom in. This is because orbit detection algorithms don't work well near the Mandelbrot Set's boundary. Points near the boundary might iterate 10,000 or even 1,000,000 times before an orbit is detected.
As a result, infinite dwell limit is only used for pixel counting or in cases where it's really important to create an image that has no inaccuracies resulting from dwell limit.
This is one type of speed improvement (see that article for more).
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2012. Mu-ency index