Fractal of the Day
by Jim Muth

Pebble in the Pond ©
Jim Muth's fractal image in GIF format (640x480).

FOTD -- March 13, 2007   (Rating 9)

Fractal visionaries and enthusiasts:

For a change, today's image most definitely does deserve both a name and a rating.   I named it "Pebble in the Pond" for obvious reasons, and rated it at a 9.   No special formula was needed to create the effect of ripples on a pond.   It was all done with nothing more than old-fashioned equal iteration bands and clever coloring.   Finding a real fractal that looks like rippling water is far more satisfying, at least to me, than writing a formula that creates artificial ripples in any image.

What we have in the image is the familiar Seahorse Valley of the classic Mandelbrot set.   I realize that nothing even vaguely resembling either the valley or its Julia set appears in the image, but this is a view of the valley from an entirely new and unimaginable direction, and four-dimensional thinking is needed to visualize what is going on here.

I'll not get into a lengthy discussion of the fourth dimension at this time.   I have discussed this mathematical abstraction at length numerous times in past FOTD's.   But one thing for certain is that the image is lightning fast, and will finish in only a few seconds.   Considering its rating of a 9, this is the best FOTD value in many weeks.

Those who do not render may see the image on the FOTD web site at:
With enough sun and a temperature of 57F 14C, the weather outside was delightful here at Fractal Central on Monday, but the fractal cats did not notice.   They were more interested in something they seemed to hear around the kitchen cabinet.   I heard nothing, but the hearing of a cat is very sharp, and they might have heard a mouse or something in the woodwork.   They must still remember the mouse that came out of the hole by the radiator in the hall last autumn.

My day was once again quite busy, but hopefully, the end is in sight.   There is no guarantee however.   The next FOTD is due in 24 hours.   The big question is whether it will appear when it is due.   Until that mysterious moment arrives, take care, and when wondering about the great mysteries of life, don't ask what or when -- ask why.   That is the real and most difficult question.


Jim Muth
jamth@mindspring.com
jimmuth@aol.com

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

Pebble_in_the_Pond { ; time=0:00:29.96--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=multirot-XZ-YW-new center-mag=0/-0.130\
  564/2.314276 params=90/40/2/0/0/0/-0.75/0 inside=255
  float=y maxiter=100000 symmetry=yaxis periodicity=10
  logmap=yes
  colors=000Q0hR2iS5jT8kUPnVSmWTnXVoYXpZZq_`r`bsadtb\
  fuchvejwfkwglxfkzekwdjvciubhtagrafq`ep_doZcnYbmXak\
  X`jW_iVZhUZgUYgTXfSWdRVcRUbQTaPS`OR_NQYMPXMPWLOVKN\
  UJMSILRHKQGJPGIOFHNEGLDFKCEJBDIBCHABG9AE89D78C67B5\
  6A55944733622511400320640860A80AA09C09E08G07I07K06\
  M36O65Q94SB4U93X83_62b41e31h10g6Ie5Hc5Hb5H`5G_5GY5\
  GY5GX5FW5FW5FV5FV4EU4EU4ET4ET4DS4DR4DR4CQ4CQ4CP4CP\
  3BO3BO3BN3BM3AM3AL3AL3AK39K39J39J39I28H28H28G27G27\
  F27F27E26D26D26C26C15B15B15A15A1491481481371371361\
  3602502502402301301201201100100000zzQnzmmzmlzmkzmj\
  zmizmgpMfoLemKdlKcjJbiJahI_fIZeHYdGXbGWaFV_FTZESYE\
  RWDQVDPUCOSBNRBLQAKOAJN9IL9HK8GJ7EH7DG6CF6BD5AC59A\
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  LOEKNDJLCHKCGIBFHAEF9CE8BC7AB68A678567455334222111\
  0ENuDMsDLrL4dL4dL3eL3ezzz }

frm:multirot-XZ-YW-new {; Jim Muth
  ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
  e=exp(flip(real(p1*.01745329251994))),
  f=exp(flip(imag(p1*.01745329251994))),
  z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
  z=z^(p2)+c,
  |z| <= 36 }

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




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