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February 11, 2012: Pentagram Feb. 10 Feb. 12 2011 FOTD Home
  Rating 7

pentagram

Fractal visionaries and enthusiasts:

Today's FOTD image is named "Pentagram".  It has nothing to do with werewolves or Satanic rituals however.  The name refers to the near perfect pentagram star surrounding the central quintic minibrot.

The parent fractal is a Mandelbrot set with Z^5 corruption so severe that it appears even on the surface, in the form of bits of debris in the interior of the buds, with a trace of this debris also in the main bay.  Today's image lies in the debris cluttering the north part of the main period-2 bud of the parent M-set.

The rating of an everyday 7 is all I could give the image.  It's not all that impressive mathematically and it proved very difficult to color, but despite the rating the star around the minibrot is certainly worth a look.

The calculation time of the parameter file is just over one minute, fast enough to keep impatience at bay and insure that little time will have been wasted if the image bombs.

The weather took a definite turn for the worse here at Fractal Central today.  Dawn broke with heavy clouds.  Showers of snow began at midday and continued through the afternoon, growing even heavier at post time.  The temperature hung around 34F +1C, so the pavements remained merely wet, but on the grassy areas the snow piled up to one inch, 2cm.  The fractal cats enjoyed the big fluffy flakes for a while, then retired to the warmest places they could find.

The humans, FL and I, took a short afternoon trip to a nearby antique emporium, making it back just before the temperature dropped.  The next FOTD will be posted in 24 hours.  Until then, take care, and I hear that married people tend to be happier than unmarried people.  Does this mean that marriage brings happiness or that fewer want to marry unhappy people?

Jim Muth
jimmuth@earthlink.net


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

Pentagram          { ; time=0:01:10.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=JulibrotMulti2 function=recip passes=1
  float=y center-mag=-1.054400978411/+0.062210075561\
  /7.995e+008/1/-26.25/0 params=5/500/0/0/0/0/0/0/0/0
  maxiter=2400 inside=255 logmap=46 periodicity=6
  colors=000zzzwwotulrtnpsolroiqocpoZooTmoOloIkoDjo8\
  io9fk9chA`dAYaBVZBSVCPSCMPDJLDGIEDFEABF78F45E99DDD\
  CIHCMLBRPAVS9_W9c_8hc7lg5ri7pj9njBljDkjFijHgkJfkLd\
  kNbkPakQ_kSYlUXlWVlYTl_SlaQmcOmeNmgLmiJmiHnjImjImj\
  ImkImkImkImlJllJllJlmJlmJlmJlnKknKknKkoKkoKkoKkpLj\
  pLjpLjqLjqLjqLjrMirMirMisMisMitLksMirNgqNfpOdoOcnP\
  amP`lQZkQYjRWiRVhSTgSSfTQfTPeUNdUMcVKbVJaWH`WG_XEZ\
  XDYYBXYAWZ8VZ7U_5U_4T`6S`7Ra8Qa9PaAPbBObCNcDMcELcF\
  LdGKdHJdIIeJHeKHfLGfMFfNEgODgPChPDgQDfQDeQEeQEdQEc\
  QFcQFbQFaQGaQG`QG_QG_QHYRHXRHWRHVRHUSITSISSIRSIQTI\
  PTJNTJMTJLUJKUJJUKIUKHVKGVKFVKEVIHWHKXGNYFPZES_DV`\
  AYbCXaDWaFW`GV`HU`JU_KT_LTZNSZORZPRYRQYSQXTPXVOXWO\
  WYNWZNV_MVaLVbLUcKUeKTfJTgITiISj0Sj0Tk0Sk0Rk0Rl0Ql\
  0Ql0Pm0Om0Om0Nn0Nn0Mn0Lo0Lo0Ko0Kp0Jp0Ip0Iq0Hq0Hq0G\
  r0Fr0Fr0Er0Ep0Do0Dm0Dl0Cj0Ci0Cg0Bf0Bd0Bc0Ba0A`0AZ0\
  AY09W09V09T08S08Y0_a0bzz0 }

frm:JulibrotMulti2  {; 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),
  c=p+flip(q)+p4, z=r+flip(s)+p5:
  z=(bb)*(z*z*fn1(z^(aa)+bb))+c
  |z|< 6 }

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