Fractal visionaries and enthusiasts:

Today's image is a "Seahorse Abomination", which is what I named it.

Seahorse Valley never deserved to have such things done to it.  The valley is a nice little place, a four-dimensional complex, so what have we done to the innocent valley to cause the gross disruption apparent in today's image?

To begin, the image is not a Julia set of the familiar Seahorse Valley of the Mandelbrot set.  It is a Julia set of Seahorse Valley of the Quaternion Mandelbrot set, which is actually an eight-dimensional Julibrot complex, with a 4-D Mandelbrot aspect and a 4-D Julia aspect.

I'll not go into details about the wonders of the eighth dimension; I'm still working on understanding the fourth.  But one thing certain is that in 8-D space, 28 two-dimensional planes pass through every point, with every plane perpendicular to all the others.

(There is something puzzling about the two quaternion formulas.  Today's image was created by the type=quatjul formula, which plots Julia sets.  This formula has six variable parameters, all of which are necessary if we are to move off from the screen in the six perpendicular directions.  Yet the type=quat formula, which plots Mandelbrot sets, has only two changeable parameters [plus two unused parameters] both of which have the same effect, giving the impression that the quaternion Mandelbrot set is a simple three-dimensional thing that would result from rotating the classic M-set around the X-axis.)

Be that as it may, today's image, with its minor mathematical interest and only slightly better artistic worth, rates a 6.

The fireball-fast calculation time of under 3 seconds will leave little time to wonder about higher dimensions before the image bursts onto the screen in a blaze of mediocrity.

Sunday here at Fractal Central featured a mixture of sun and clouds, and a very pleasant temperature of 70F 21C.  The fractal cats complained that there was not enough sun then went to sleep on the living room carpet.

After my trip back to the nostalgia-infested land of Old Fractal Central on Saturday, Sunday seemed relaxing.  (Though I still wish the Phillies had won the NL pennant.)  FL occupied herself wondering why I end my FOTD discussions with so many 'silly and unanswerable' comments.

The next FOTD will be posted in the generally accepted 24 hours.  Until then, take care, and if the belief in God and an afterlife is a defense mechanism evolved to enable us to cope with the awareness of our ultimate mortality, how would society react if it were ever demonstrated beyond all doubt that these things do not exist?

Jim Muth
jamth@mindspring.com


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