Fractal of the Day
by Jim Muth

Extremely Deep©
Jim Muth's fractal image in GIF format (640x480).

FOTD -- March 30, 2005   (Rating 9)

Fractal visionaries and enthusiasts:

Caution.   Today's image is the slowest of all time.   Unless you can afford several days of computer time, do not attempt to generate today's image from the included parameter file.   Download it from the FOTD web site.

In yesterday's FOTD discussion I announced that I had found a scene extremely deep in Seahorse Valley, but that it would take several days for my fastest computer to render it at full size.   Well, I underestimated the ability of my fast P4-2300 machine when it is running straight DOS.   When I booted it with DOS 6.22 and set it to the task of calculating the full sized image, it finished the job in under 3-1/2 hours, running at about 23 times the speed of the P200 and not needing to be kick-started back into high speed mode every half hour or so.   This speed is somewhat of a surprise, since 2300 divided by 200 equals 11.5, which is only half of 23.   I guess the 2300 does twice the work per cycle, at least with the high-speed Mandelbrot formula.

The render time in the parameter file has been adjusted to reflect the time it would have taken my standard P200 unit to calculate the same scene.   Needless to say, very few will wish to devote almost 3-1/2 days computer time to the calculation of today's image, which is why I sent it on ahead to the FOTD web site at:where it may be viewed at once.

Today's image is located extremely deep in Seahorse Valley, at a distance of only 0.00000799... from the mystical point on the X-axis.   It shows a midget on the west shore of the valley.   The almost unbelievable narrowness of the valley at this point is demonstrated by the X-value of the scene, -0.7500000000975.

The iteration count of the large areas of purple is over 1,100,000, which is one of the reasons the image is so slow.   The other reason is the maxiter, which at 450,000,000 is over 1/5 of the absolute maximum of which Fractint is capable.   And even this extreme maxiter fails to close all the spurious holes in the image.   The magnitude of 3*10^12 is not all that unusual, but I have included the mathtolerance entry in the parameter file to insure that anyone who decides to render the image from the parameter file does so at the correct magnitude.

Searching for seahorses in the image is futile.   I have no idea where they have gone, but they have totally vanished.   What we have instead is a midget surrounded by a spider-web network of filaments, organized into nodes with peanut-holes at the center.   The pattern of filaments around the midget is also surprisingly irregular.   The expected powers-of-two organization of elements is there, but it appears to be breaking down.   I wonder whether the 2-4-8-16... arrangement breaks down entirely even deeper in the valley.   I rather doubt it, but I also doubt that I will soon be going deeper into Seahorse Valley.

I named today's image "Extremely Deep", which is nothing more than a description of its location.   The rating of a 9 reflects the mathematical interest.   The artistic merit alone is probably closer to a 6.

I think that with today's image I have satisfied my curiosity about what lies hidden this deep in the Mandelbrot valleys.   Tomorrow's FOTD will return us to the world of more conventional fractals.   I have yet to conclude the tour of the Elliptic orientation of the Julibrot, but I might stop off briefly in the MandelbrotMix4 formula for a bit of refreshment before returning to the fourth dimension.

A perfect early spring day on Tuesday brought out the playfulness in the neighborhood kids and the fractal cats as well.   The duo actually started chasing each other around the yard, much as they did many years ago when they were young cats.   It brought a twinge of nostalgia to me as I wondered if this was the last time I would see the nearly 15-year-old pair carrying on like kittens.   Even though I had to call a few extra times to coax them indoors when evening came, I gave them an extra treat of tuna.   They ended the day sleeping side-by-side on the couch.   This morning is starting hazy but even milder.   I expect another good day for the duo.

For me it will be work first, then fractal play.   The next fractal will playfully appear in 24 hours.   Until then, take care, and be at ease in the abstract realm of numbers.

Jim Muth

START PARAMETER FILE=======================================

Extremely_Deep     {; time=80:45:00.00--SF5 on a P200
  reset=2004 type=mandel
  292361711339 params=0/0 float=y maxiter=450000000
  bailout=9 inside=0 periodicity=10 mathtolerance=/1
  NzzRwzUszXoz_htiltlotomup }

END PARAMETER FILE=========================================

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