Fractal visionaries and enthusiasts:

Today's image is quite a discovery, at least as far as I am concerned.  The object at the center of the screen is a minibrot in the Z^(-2)+C Mandeloid.  Yes, I know, or rather, I have assumed that minibrots can not exist in Mandeloids with single negative exponents of Z.  It turns out that I was mistaken.

As today's image shows, minibrots do exist in such Mandeloids.  And they have the expected number of lobes -- one less than the exponent of Z.  In today's image, the exponent of Z is minus 2.  One less than minus two is minus three.  Therefore we find minus three lobes in the minibrot.  I'm not sure what a negative lobe is supposed to look like, it might appear as a peninsula, but why question such a reasonable explanation?

Quite a bit of trickery was needed to bring out the minibrot in today's image.  To begin, I raised the bailout radius to the point where nearly the entire fractal had evaporated.  Then I rendered the remaining scene with the inside set to 'atan'.  Finally, I set the periodicity to its most aggressive setting, which causes the stuff that would normally fill the interior of the minibrot to be skipped over and show up as black.

The resulting image is not exactly correct, but it does show what I assume to be a minibrot lying in a fractal with a single negative exponent of Z.

Since the image is almost entirely of mathematical interest, I could give it no rating.  The name "Lost And Found" describes the adventures of all such negative minibrots.

The calculation time of 2-1/4 minutes is reasonable.  Viewing the finished image on the FOTD web site at:

http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html

will save a bit of effort.

The original FOTD web site may be accessed at:

    http://www.Nahee.com/FOTD/

A preview of spring visited Fractal Central on Friday.  The warm sun and temperature of 68F 20C made it feel more like mid-April than mid-February.  The fractal cats did not bother themselves with time-of-year details however.  They spent the day on their shelf in the sun.

My day was moderately busy, while FL had a slower day.  The next FOTD is due in 24 hours.  Only an unexpected antiquing trip could delay it.  Until next time, take care, and look for the bright side of the darkness.

Jim Muth
jamth@mindspring.com

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