Fractal visionaries and enthusiasts:

I named today's image "Cubic or Quadratic" because I'm uncertain what it is.  The minibrot at the center is clearly a cubic one, with its main bay divided into two large sections.  But the hexagonal pattern around the minibrot is divided into 6 parts, where one would expect it to be divided into one of the powers of 3, such as 3,9,27....  Clearly the quadratic element is still playing a major part in the action.

The parent fractal is an everyday Mandelbrot set.  The value of 1000 given to the real(p1) parameter assures the cubic corruption lies quite deep.  At a magnitude of over 3*(10^11) however, today's image lies well within the range of cubic corruption.

The image is located in a bit of debris in a tiny minibrot on the west branch of the filament extending from the large period-3 bud of the parent Mandelbrot set.  I rated it at a 7-1/2 because I had too little time to give it the coloring it deserves.

The calculation time of 6 minutes borders on slowness, but relief may be found on the FOTD web sites.

Total sunshine on the fresh 1-1/2 inches (4cm) of snow made today quite brilliant here at Fractal Central.  The temperature of 41F and light winds kept the outdoors quite comfortable.  The fractal cats approved of the weather but did not like the cat footprints that appeared overnight in the snow in the back yard.

FL and myself heartily approved of the weather but were too occupied with the more mundane tasks of the day to enjoy it.  The next FOTD will be posted in 24 hours.  Until then, take care, and fight to make the world safe for fractals.

Jim Muth
jimmuth@earthlink.net


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

Cubic_or_Quadratic { ; time=0:06:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=JulibrotMulti2 function=recip passes=1
  center-mag=-0.142935711425101/+1.018936551710222/\
  3.22728e+011/1/-35/0 params=3/1000/0/0/0/0/0/0/0/0
  float=y maxiter=3600 inside=0 logmap=662
  periodicity=6 mathtolerance=0.05/1
  colors=00000A00B00B00C00D00E00F00G10H20I40K60M70O9\
  0RA0SC0UD0VF0XG0YI0_J0`L0bN0cO0eQ0dR0cT0aU0`W0_X0Z\
  Z0X_0Wa0Va1Vb3Uc5Ud7Ud9TeBTfDTgFSgHShJSiLRjMRjORkQ\
  QlSQmUQmWPnYPo_PpaOpcOqdOrfNshNsjNtlMunMvpMwrLxtLy\
  vMzuOztQzsSzrUzqWzqYzqczqczqczqizqjzqkzqlzqrzqszqm\
  zrmzszztzzuzzvzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzzmzzmz\
  zmzzmzzmzzKRCHKDFBDGAFHCGHBHIBIJCKJCLKIMLNNLOOMOQM\
  PRNPSOVTOVUP`WQ`XQaYRaZT``Sa_Ra_RbZQbZQcYPcYOcXOdX\
  NdWNeWMeVMeVLfUKfUKgTJgTJhSIhSHhRHiRGiQGjQFjPGiLFj\
  NFjPEjQEkSDkUDkVClXClZBl_BlaAmcAmd9mf9nh8ni8ok7qz7\
  rz6sz6zz8zpAzzBzzDuzFtzGooImoKlnLgnNcnOZnQUmOPcNKU\
  LFKJAAH55F00zmnzeom`ojSofDoc6oalpVgoOcnI_nBWm5Sm_W\
  2W`FTeRQjcNnoKmtHmyUgzfaze`vd`sc_ob_laZh`Ze_YbZYZY\
  XWXXSWWPVWMPTXKRfjtumzajz`gz_dzZazYZzXWzWTzVUzUczT\
  czSczRmzQmzPmzOzzNzzKzzNzzPzzSzzUzzXzzZzz`zzZzzXzz\
  VzzUzzSzzQzzOzzNzzHzzAzz3 }

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=========================================