At 12:29 AM 5/1/04 -0400, Hiram Berry wrote: <snipped>

After "Fractal Nonsense", which I think you also rated a 5, I don't put much credance in your ratings Jim. That one, which showed a morphologically sextic midget in the main filament of a fractal with a quartic generator, showed something fundamental about Mandeloid generation and thus ought to be ranked somewhere near the top of the scale regardless of whether your colorist's skills were in evidence that day or not.

I think I had a whole series of images leading up to the spurious sextic midget, which should indicate that I noticed something mathematically unusual in it. My ratings are entirely subjective, and depend largely on my mood at the time I rate the images. Perhaps I should give my images two ratings -- one for artistic worth, the second for mathematical interest.

A while back you chided Sherlok Merfy for not initializing z on a critical point in one of his fractals.

The chiding was kind of hard to resist, especially in light of the cute spelling he came on with, and words and phrases such as 'SherLok', 'Merfy', 'private instigator', and 'brewhaha', etc. in his internet addresses. No harm was intended, and I doubt that SherLok was seriously offended.

That would seem to imply that you value the concept of purposeful intent in fractal creation, rather than just randomly trying a lot of parameter combinations in hope of hitting something interesting.

I aim for a blending of random discovery and purposeful intent. IMO, when fractals are over-planned, much of the surprise and therefore the fun is lost.

I suppose you wanted Sherlok to understand how to apply the Fatou Theorem to generate a maximal set of fractal points.

Not so. I have no idea what the Fatou Theorem is. The rest of the letter demands more careful consideration. It has some valuable ideas in it. Jim M.