Fractal visionaries and enthusiasts:

The oversized parent Mandelbrot set of today's scene has been corrupted by Z^23 energies.  On the surface, the corruption barely shows, but only one zoom into the depths will show that, in its depths, the parent is anything but a typical Mandelbrot set.

Today's image lies in a minibrot on the prominent filament extending northwest from the large period-2 but of the parent near-Mandelbrot set.  This minibrot is morphed about halfway between a Z^2 and a Z^23 one, with lots of interesting nooks and crannies to investigate.  Today's scene is located in the area of what once was the northwest shore line of the main bay.

I frequently mention directions when writing about minibrots in the FOTD discussions.  When I do this, I consider the minibrot to be lying in the 'normal' orientation of the classic Mandelbrot set, with the main spike pointing west and Elephant Valley on the east side of the heart-shaped main bay.  North is then up, and south is down.  We really could use a good atlas of the Mandelbrot set, describing and naming all the valleys and buds, etc.  Several probably are on the internet, though I have never made a search.

I named the image "A Very Common Object" because objects like the one in today's image are almost universal in corrupted parent fractals such as today's.  This of course assumes that the things appearing in fractal images are actually objects at all.

The rating of an 8 seems appropriate for a rather nice illustration of such a common object.

An early taste of spring came to Fractal Central today, as the sun shone in and out of the clouds and the temperature reached a relatively balmy 54F 12C.  The fractal cats took advantage of the sun when it was shining by finding the sunniest spots and stretching out like only cats can do.  FL and I simply had another routine day, which means a day that would be boring to describe but was not too bad to live through.

The next FOTD will be posted in 24 hours, come rain or shine.  (Rain is expected.)  Until then, take care, and aliens from outer space, spirits of the dead, lake monsters, sasquatches wandering the woods, etc. etc. might or might not be real, but one thing modern science has shown is that the world extends far, far beyond the things we can observe with our senses or instruments.  And it's getting so confusing that even the word 'real' is losing its meaning.  (As philosophers have always debated and I have always suspected.)

Jim Muth
jimmuth@earthlink.net


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

A_VeryCommonObject { ; time=0:00:15.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=JulibrotMulti function=recip
  center-mag=-37.56466262894342/+10.3069228272142/\
  3.19272e+011/1/-22.5/0 params=23/30/0/0/0/0/0/0/0/0
  float=y maxiter=1800 inside=0 logmap=24
  periodicity=6 mathtolerance=0.05/1
  colors=000rCYoBWmAUj9Sg8Qd7Ob6M`5KZ4IX3GU2FS2DQ1BO\
  1AM08K07J3BI5EH8HGALFCOEFREHUDJYCM`BOcAQg9Tj8Vm8Xp\
  C_lGaiKcfOecSg`WiY_lVcnSgpzkzzozzzzzzzzzzzzzzizzfz\
  zdbza_z_WzXTzVQzSMzQJzNGzLDzMHzNLzOPzPTzQWzR_zSczT\
  gJUjKVnLWrLXvMYyMTvQPsULpYHm`Djd9gh5dl1aoGzTNzUUzU\
  `zUgzUnzUlvWkvYju_iuahucfteetgdticskbsmasoXqnSzmOz\
  lJzkFzjAzi6zh8ze9zcAz`CzZDzWEzUGzRHzPIzMKzKLzHMzFV\
  zLczRkiWlgUmfTneSocRpbPpaOq_NrZMsYKtWJuVIuUHjOP_zX\
  PzdEzlFzmFzmGzmGznHznHznKznMznOznQznSznUdnWjnYpn_u\
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  OjXOjZPkaPkc5ykFrhPkeYdbgY_pRYdTXTzWHzVLzvNzsPzqRz\
  oTzmUzkWzhYzf_zdagbcm_bj`aha`eb_zbZzcYzdYzdXzeWzfV\
  zgUzgTzhSziWzeUzgSziQzjOzlMznKioIpqHwrJtpLqnNnlPlj\
  RiiTfgVdeXacZZahmNddU`X`XOfTzmPzsJzgEzX8zM0z82zA3z\
  B4zC5zD6zE7zG8zH9zIAzJBzK }

frm:JulibrotMulti  {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p2*0.0055555555555556),
  b=pi*imag(p2*0.0055555555555556),
  g=pi*real(p3*0.0055555555555556),
  d=pi*imag(p3*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), aa=-(real(p1)-2),
  bb=imag(p1)-0.0000000000000000001,
  c=p+flip(q)+p4, z=r+flip(s)+p5:
  z=z*z*fn1(z^(aa)+bb)+c
  |z|< 100000000 }

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