Fractal visionaries and enthusiasts:

Today's image is (no guarantee) the last of the series of near-Julia Mandelbrot valley images.  This one shows the valley of the north bud of the large minibrot on the west branch of the filament that extends from the north bud of the Mandelbrot set.

The effect is much the same as the previous images, though there is more decoration around the almost-Julia set.  The name "Hourglass Spirals" refers to the hourglass-like shape of the two spirals on either side of the center.

It is tempting to think of these fractal spirals as 3-D things such as short curved lengths of string.  But they are actually 2-D slices of 3-D spaces that curve and twist in 4-D space.  As with all 4-D stuff, the entirety of the spirals is impossible to visualize.  As mere humans, our consciousness is limited to the 3-D experience.

I decided to give today's image, which is likely the last of the series, a rating of a 7.  We have been mired in this series longer than I had intended, and there are many unusual slices of the Julibrot that we have not yet checked.  Tomorrow's image will begin the exploration of these.

Today's image calculates in under 7 minutes, not fireball fast, but certainly faster than some FOTD's, which have taken days to complete.

The last I heard, Paul was still in the hospital, recovering from an infection.  He has enough access to the FOTD web site to post the FOTD discussions.  But since he is using a new-fangled laptop machine running Vista, which panics as the sight of the Fractint program, he cannot run the parameter files.  I am sending the finished GIF images to him while he is in the hospital, from where he can post them to the FOTD web site.  Hopefully, the web site will be up to date shortly.  As always, the site may be accessed at:

       http://www.Nahee.com/FOTD/

A few too many clouds and a bit too little sunshine here at Fractal central on Monday kept the fractal cats from reaching maximum contentment.  The temperature of 54F 12C was just about normal.  My day was normal also.

The next FOTD will be posted in 24 hours.  Until then, take care, and I hear that within 25 years everyone will have their own private autogyro for their daily commute.

Jim Muth
jamth@mindspring.com


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

Hourglass_Spirals  { ; time=0:06:51.18-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 passes=1 center-mag=0/0\
  /11.7/1/87/0 params=89.9/0/89.9/52.5/-0.15436/\
  1.0371225/0/0 float=y maxiter=40000 inside=0
  logmap=8 periodicity=6
  colors=000CKVDLUEMSFNWGOTHPRIQOJRMJSJKTIMUJNVIOWIQ\
  XHTYGVZGY`F_aFabEdcDfeDifCkgCnhBpjAskAul9wm9zlCzlE\
  zlHzlJxlMvlOtlRtlTslWslYsl`rlbrlerlgqljqllqlnokmnj\
  lmikkijjhiifhgdhfegedfcbecadcaccaccabcbacc`cc_ccZc\
  cZccYccXccWccVccUcbUcaYc`acZecXicWmcVqcUpcUpcUpdUp\
  dUpdUpeUpeUoeUofUofUofUogUogUogUnhUnhUnhUniUniUnjU\
  nkUmlUlmUkmUjmUimUhmUhmUgmUfmUemUfmUgmUhmUhmUimUjm\
  UjmUkmUlmUlmUmmUnmUnmUomUpmUpmUpmUqmUrmUsmUtmUumUv\
  mUwmUxmUymUxmUxmUxmTxmSxmRwmQwmPwmOwmNwmMwmLvmKvmJ\
  vmIvmHvmGumFumEumDumCumBuiEteHtaKsYNsUQrSRrQSrOTsM\
  UsKUsIVsGVsEWtCWtAXt8Xt6Yt4Zu2_u0`u0bz0dz0ez0ez0fz\
  0fz0gz0hz0hz0hz0iz1jz3jz4kz5kz7kz8qzArzBrzCszEszFs\
  zHuzIuzKuzLuzMuzOuzPuzRuzSuzSuzUzzVzzWzzXzzYzzZzz`\
  zzazzbzzczzdzzezzgzzhzzizzizzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:SliceJulibrot2   {; draws most 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),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=sqr(z)+c
  |z|<=9 }

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