Brian (quoted by Kenneth) wrote:
<snip> but folks should know that the "universality of the M-set," that is the recurrence of "mini-bugs" or cardioids, at every level of "magnification," is just an artifact of the floating-point ops (IEEE-755, -855, I think). this was (really/partially) confirmed by monsieur M, when he glroriously begged my (only) technical question at a talk for a "general audience." <snip>
This is patently ridiculous and easily refuted. Fractint has a number of different numerical methods of computation: IEEE floating point, integer (fixed point) math, and arbitrary precision, and one can see the same "mini-bugs" with all of them (within their range of magnification). If these "mini-bugs" were artifacts of IEEE floating point, if one changed the math to non-IEEE (e.g. integer math or arbitrary) the "mini-bugs would go away. But they don't. All three math implementations show very similar images. SImilarly, with fractint one can force a higher precision using aribrary precision. Typically when one does this, one gets the same (or very nearly the same) image. When increasing precision does not change an image, that is pretty good evidence that the image is not an artifact of the math implementation. Just goes to show you that anyone can write anything on the internet, whether or not it makes sense. Tim