Fractal of the Day
by Jim Muth

Towers of Hanoi ©
Jim Muth's fractal image in GIF format (640x480).

FOTD -- September 07, 2006   (Rating 6)

Fractal visionaries and enthusiasts:

Today's FOTD image takes us to East Valley, aka Elephant Valley, where we check the elephants, the goofy-looking eyes and noses, and the typical East Valley brain-like patterns.   What's this, you see none of this stuff?   That's because we're looking at the valley from an entirely new direction, roughly from above the screen.

The generous stretching (1380 times) in the vertical direction was necessary to bring out the detail.   Without stretching, the image would consist of little more than a few horizontal lines.   As it is, the scene looks like two oriental towers.

I named the image "Towers of Hanoi" after a mathematical puzzle I saw in the 'Believe it or Not' comic strip many years ago.   The goal of the puzzle is to take a peg with 64 discs stacked on it, which increase in size toward the bottom of the pile, and transfer the stack of disks to another peg, with the largest disk again on the bottom.   At no time may a larger disk be placed on top of a smaller disk.   There is a third peg to make the transfer possible.

Priests in the temple of Hanoi have been working on the puzzle for thousands of years, and when the transfer is completed, the world will vanish in a thunderclap.   But there is no cause to worry, for 10^64 transfers are needed to do the job.   Making one transfer per second, the priests would need something like 3*10^53 years to finish their task.   But I only hope no one finds a short cut.

The rating of a 6 was given without much thought.   The speedy render time of 34 seconds is true on my fractal machine.   The completed GIF image has been posted for convenience on the FOTD web site at:
A picture of the new fractal cats is posted there also.

A brief shower in the early afternoon did not spoil an otherwise fine day here at New Fractal Central.   Generous sun and a temperature of 75F 24C kept the new fractal cats happy.   Actually, I think the toy bird we picked up this morning at the Pet Mart kept them happier than the weather, which they usually ignore.   The standard treat of tuna for Cassie and cheese for Nico finished a near perfect day for them.

My day was busier than yesterday but still under control.   Unfortunately, I can not say the same for Friday and the week-end.   I expect a big job to arrive late tomorrow, which will be due next Wednesday.   It might force me to miss a few FOTD's.   But never fear, the daily FOTD is in no danger of vanishing forever.   (Of course, that's what the crocodile hunter said . . .)   Anyway, until the next FOTD appears in 24 hours, take care, and try to keep your technology under control.

Jim Muth

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

Towers_of_Hanoi    { ; time=0:00:34.28--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=multirot-XZ-YW-new center-mag=0/-0.027\
  83359565155030/1380.708/0.0009649 params=0/45/2/0/\
  0/0/0.28/0.0001 float=y maxiter=10000 inside=0
  logmap=58 symmetry=yaxis periodicity=10
  jI8V97FEpFAdB7T73H3ZVBNM7 }

frm:multirot-XZ-YW-new {; Jim Muth
  ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
  z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
  |z| <= 36 }

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

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