Robert P. Munafo, 1999 Feb 2.
Whenever using a pixel grid to represent an image which has higher detail than the grid can show, there is the risk of encountering aliasing errors. The most well-known aliasing error is a Moire' pattern. This does not happen often in the Mandelbrot Set, although views that produce it can be found.
Other less drastic aliasing errors affect single lines. A single line can occur either as a filament or as the thinnest part of a cusp. Filaments will suffer most if they are straight, e.g. the .F(1/2B*) of an island mu-molecule. Examples of these are easy to produce.
Aliasing errors are extremely dependent on the precise alignment of the grid with respect to the image. For this reason, it is not possible to give precise coordinates that will yield views with aliasing errors. However, the following descriptions will help you find some:
- get a view that shows seahorse valley R2.C(1/2), and make sure the real axis is also in the view (so you see the very thinnest part of the cusp). Then adjust the real component of the center position a little bit at a time. The idea is to get the thinnest part of the cusp to fall between two rows of pixels.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2023.
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2008 Feb 18. s.27