Fractal visionaries:

Yesterday, I said that I would post something never before seen as today's fractal.  That's a rather hard promise to keep, but I think that I've come a bit close with today's picture.

The two well-known planes have distinctive features, which become familiar with only a small amount of exploring.  The Mandelbrot planes have their familiar buds, valleys, stars, spirals, tendrils and of course, their midgets.  The Julia planes have everything the M-planes have except the midgets.  In addition, the Julia planes have those silly looking double spirals with the big noses, and are self-similar all the way down, which sometimes makes their exploration a bit dull.

Until I found today's fractal, I considered the other four sets of planes rather dull also.  But I suspected that this couldn't be true, because everything of interest that appears in the Mandelbrot and Julia planes also appears in the other four sets of planes, but sliced in a different direction.

Today's fractal is named for what it is -- the first interesting and unique object I have found in the XW plane.  As would be expected, it combines features of the Julia and Mandelbrot planes.  The chains of Mandelbrot buds twist around those silly big-nose, pop-eyed features so characteristic of Julia sets.  And everything is stretched and distorted as is always the case in the odd planes.

Today's finished image has definitely been posted to a.b.p.f. and a.f.p.  I have already seen it there.  Anyone who can't find it on those groups has a problem with their news server.  I know that some servers are slow at picking up articles.  Sometimes it takes over a day for the Fractal of the day headers to appear on the AOL newsgroups list.

One more thing needs to be discussed.  There is confusion as to which axes are the X, Y, Z, and W axes in these odd plane fractals.  I think of the Mandelbrot axes as X and Y, and the Julia axes as Z and W, while others consider the Julia axes as X and Y and the Mandelbrot axes as Z and W.  This situation leads to the confusion.

But there is never confusion between the planes when the names Mandelbrot and Julia are used to describe them -- the names make the planes unmistakable.  By giving names such as Julia and Mandelbrot to the other four sets of planes, all this confusion could be avoided.  (I would suggest the Muth planes for one of the directions, but my humility prevents me from doing so. ;-)

Anyway, while I'm considering names for the four odd sets of planes, I'll dump the cat out of the chair and ensconce myself in front of the TV to watch one of those great old sci-fi films.  By tomorrow, I'll have discovered other interesting scenes in the odd planes, and one of them I'll post.

Jim Muth
jamth@mindspring.com


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END 19.6 FILE===============================================