Fractal visionaries and enthusiasts:

Today's venture into the hyper-dimensional world of fractals takes us to the northern valley of the large period-4 bud on the northeast shore line of the main bay of the Mandelbrot set.

But where is the valley?

The brilliant stripe across the bottom part of the image is the valley.  It bears no resemblance to a valley because it is viewed from the side, at an angle close to the Julia, where Mandelbrot elements extend to infinity in two dimensions.

The spirals in the image are rather curious.  Above the stripe of the valley, they curve clockwise, while below the stripe, they curve counter-clockwise.  This shifting curvature is a situation common to the spirals in the vicinity of all valleys.

I named the image "Dance of the Numbers".  The numbers that create today's image certainly do appear to be dancing.

The rating of a 7-1/2 includes a half-point bonus for the work I did on the colors.

The calculation time of 3-1/2 minutes has been carefully extrapolated from the 14 minutes the image actually took to run on the P200mhz machine.

The day broke with dense freezing fog here at Fractal Central, and most of the morning remained gloomy, but just before noon the sun suddenly burst through, leading to a near-perfect afternoon with cloudless skies and a temperature of 54F 12C.  The fractal cats, never worrying about climate specifics, spent the day relaxing in the warm sun.

The humans simply got through the day, with FL recovering from a mild bug and me frustrated with the CD player, which suddenly died last evening, most likely from a burned-out laser.  The next FOTD will be posted in 24 hours.  Until then, take care, and where are our saviors now that we need them?

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


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

DanceOfTheNumbers  { ; time=0:03:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=t periodicity=6
  center-mag=0/0.131074/3.138989/1/-90/0 float=y
  params=90/90.07/92.48/89.01/0.2438/0.5139/-0.0081/\
  0.5024/2/0 maxiter=25000 inside=0 logmap=yes
  colors=000EHsD0qCJoB0mALk90j8Nh70f6Pd50b4R`30Z2TX1\
  0W2VV20V3XV30V4ZV40U5`U50U6`U60U7_Y80`9Yc90fAViB0l\
  BSoCArDRqDApCToBAnAUmAAmEUmHAmKUmOAmRUmUAmXXcZAU_W\
  JaAIbUHcAGeRFfAEhPDiACjNBkACkQCkADlTDlAElVElAFmYFm\
  JGm_GmMHnbHnQIndInTIobHpTHp_GqOGrUFrKFsNEsEEtHDuED\
  uBCv8Cv6CrAGnEKjIOgMRcQV_UZWYbTaePeiLimHjqEktHjpJi\
  oLenObmQZlSWkVWjXWiZWhaWgcWedWceWafW_gWYgWWgVaeUZc\
  TWaSU_RRYQOXPMVOJTNGRMEPLBNK8MK6PK9RKCUKFWKIZKL`KO\
  cKReKTgJMiIFkGGmEGoCHqBHrCHrCIrCIqDIpDJoEJnEJmFKlF\
  KlFKhHIdJH`KGYUFUqEQmDMmCJmBFmABm98m8HmEPmKYmPemVm\
  j_imdeqjatoYwtczycztczpczkczgczcczZczzczzczzczzczz\
  czzczzczzczzczzczzczzczzczzczzczzhzzhzzhzzhzzhzzhz\
  zhzzhzzhzzhzzhzzhzzhzzhzzhzzhzzmzzmzzmzzmzzmzzmzzm\
  zzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:SliceJulibrot4   {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=z^(real(p5))+c
  |z|< esc }

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