Fractal visionaries and enthusiasts:

Today's image lies in an everyday Mandelbrot set that has taken on order-7 characteristics in its deeper depths.  To find the scene we start at the period-4 bud on the northeast shore line of the parent M-set then go to the largest minibrot on this bud's filament network.  This minibrot is still a reasonably normal one, but when we check the minibrot on this minibrot's main stem, we find that it is well along the way of morphing into an order-7 minibrot.

Zooming in even farther, we check the area where the larger minibrot's main stem joins the smaller morphing minibrot, an area we might call the East Valley area of the smaller minibrot. We notice that the main stem branches into a series of shallow spirals before it enters the actual bay.  We check one of these spirals.  By the time we have gone deep enough to find an even smaller minibrot in the spiral, the minibrots have all totally morphed into order-7 shapes.  Today's image shows one of these order-7 minibrots.  The curved arms radiating from the minibrot indicate that the scene lies on a shallow spiral network.

But all this confusing verbal description totally fails to give a visual impression of today's image.  To enjoy the image, it will be necessary to run the included parameter file, which runs in 5-2/3 minutes.

The name "7-armed Heptafractal" was of my own invention.  Anyone who knows exactly what it means also knows where the Tropic of Sir Galahad is located and what the song 'Stairway to Heaven' is all about.

The rating of 7-1/2 indicates that I consider the image a little better than normal, but nothing to write home about.

Heat returned to Fractal Central on July 16 as the temperature reached 88F 31C.  The day was saved however by the humidity, which remained on the dry side all day.  The fractal cats passed the day lounging on the living room floor, avoiding the sunlight that occasionally filtered through the trees.  At post time on the 17th, the weather was looking like a repeat of the 16th.

The day of the humans on the 16th was acceptable, as are most days here at FC.  The next FOTD will be posted in 24 hours, but hopefully, by the end of the week, we'll have the FOTD back on its traditional every-day schedule.  Until next time, take care and have fun dreaming of trips into interstellar space.  You're surely never getting there in person.

But isn't it curious that we have evolved the ability to dream dreams and feel desires that have no chance of being realized.  One would wonder what the evolutionary advantage of such a frustrating ability might be.

Jim Muth
jimmuth@earthlink.net


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

7armedHeptafractal { ; time=0:05:38.74-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip inside=0
  center-mag=+0.355833037442585/+0.6498625194640629/\
  5e+012/1/-25/0 params=7/1000000000000.0/0/0 float=y
  maxiter=3200 logmap=-714 mathtolerance=0.05/1
  colors=000SAUTBUUBUUBUUBUUBUUBUUBUUBUUCUUCUUCUUCVU\
  DWUDXUDVUEUUEUUEUUFUUFUUFTUGTUGTUHTUHSUISUISUJRVJR\
  VJRVKSVKTVKTUKUUKVUKVUKWUKXSK_UMXWOVYQT_SQ`UObWMdY\
  Jf_HgaFicCkeKkgPkiUkkZkmckohkqlkomkmnkkokipkgqkerk\
  cskatl_ulYvlWwmUxmSymQzjPwhOtfOqdNnaNk_LiYKhWIfTHd\
  RFbPE`AEAADAADABCA9CA6BA6BA4AA5AF9BJCBHFBGICFLDEOF\
  ERGDUHDXHB_H9cI8hI6mI4rI3vI1zI0vH3rG6mF8hEBfDDdCGb\
  BJ`ALc9OX8Qc7TT6Wc5YP4`c5cN4bc4bP4bc4bQ4bc4bS4bc4b\
  U4bm3aV3am3aX3am3aY3am3a_3am3a`3am6`Y8`mA`WC`mE_UH\
  _zJ_SL_zNZQPZzSZOUZzWYMYYz_YKbYzdXIfXzhXGjXziYJiYz\
  iYMiYziYOiYziYRjYzkYTlYzmYWnYzoYZqYztY`wYzzWzzY_z_\
  zzaWzczzeRzgzziLzjzzjPzjzzjSzjzzjWzzzzjYzzzzfzzzzz\
  czzzzz_zzzzzXzzzzzTzzzzzQzzzzzMzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzEzzAzzBzzBzzAzzAzzAzzCzzEzzGzzIzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:FinDivBrot-2   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }

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