["Minibrots" of Mandelbrot set a floating point artifact?] Well, *most* real number cannot be represented exactly by floating point math because of the finite width of the mantissa (think of 1/3 in decimal or 3/5 in binary). Therefore nearly any iteration calculation will accumulate errors, which causes the computed values to "drift away". But: As others already have pointed out, if the "fine structure" of the Mandelbrot set were an artifact, then a change in number format (64 bit, 80 bit, arbitrary precision) should at least shift those minibrots around, if not deform them beyond recognition. Strangely enough, whatever hard-, whatever software is used, they always reside in the same spot, easily found on machine B using coordinates calculated on machine A. In "Chaos and Fractals: New Frontiers of Science" by Peitgen/Jürgens/Saupe (1992) there's a whole chapter dedicated to this question (p. 575 ff. under "Numerics of Chaos: Worth the Trouble or Not?"): As it turns out, although the small rounding errors while iterating cause the calculated orbit to wander off the real one, it is provable that, *because* of the limited size of each error at every iteration, there *always* will be *another* real orbit close to the calculated one - and its starting point will be near the starting point of the calculated orbit, too! In short, we might not get the behavior of the point at the *exact* pixel coordinates, but of one that is so close, it in all likelihood will lie in the area of the same pixel anyway. The true reason why there are tiny Mandelbrots in the Mandelbrot set (and in other complex iteration maps, too) is the fact that polynomials of high degree (and many other functions) often have small areas in their domain where they look just like the quadratic map. BTW, an interesting site regarding the math of the MSet: http://www.people.nnov.ru/fractal/MSet/Contents.htm Regards, Gerald