Hi folks. For several months I have been utterly unable to sent messages to this list... I have now discovered the cause of this devistating problem: I typed the address wrong in my address book. (Even that is not beyond doubt - there was a single letter missing. It may simply be that I have a malfunctioning keyboard!) But anyway... I'm back! Yay!! I've just been doing some stuff with the good old cubic function f(z) = z^3 - 3(a^2)z + b. This formula has (IIRC) several critical points, but all bar 2 of them are always within the basin of attraction to infinity. (Corrections, anyone?) The two that (sometimes) aren't are +A and -A. (If I'm not mistaken, 0 is NOT critical for this mapping...) Now, the cubic Mandelbrot is defined as being the set of points (A, B) for which for orbits of Z[0] = +A *and* Z[0] = -A remain bounded. (Compare the classic quadratic Mandelbrot: this is the set of all C such that Z[0] = 0 remains bounded.) Thus, the set M+ is defined as the set of (A, B) for which Z[0] = +A remains bounded, and M- is defined as the set of (A, B) for which Z[0] = -A remains bounded. (I have a feeling the two sets are mirror images or something... not entirely sure.) Then the M set itself is simply the intersection of M- and M+. (Try telling that to fractint!!!) I've got a number of formulas that attempt to draw the cubic M, but none of them seem to work entirely properly. They do, however, draw some rather fabulouse images! Of course, having to navigate a 4-dimensional M set that is really the intersection of the mirror-image M+ and M- sets (which, therefore, are also 4-D) is somewhat confusing to say the least! But the results are well worth it... Out of interest, I would rather like to know 1) if the statements I've made thus far are actually correct, 2) what the "generalised form" for a 4th order polynomial looks like... Hey - keep fractalling ;-) Thanks. Andrew. PS. I've heard it said that z^3 - 3(a^2)z + b is more complex than needed, and z^3 + az + b will work. My reason for using the former is that it draws a much nicer image. (Oh, and finding the critical points is easier ;-)