Fractal visionaries and enthusiasts:

Today's image is named "Totally New Aspect", which means it is a totally new aspect of the Mandelbrot set, or more correctly, of the Z^2+C Julibrot.  The scene lies near the Seahorse Valley area of the M-set, near a point where a number of heavy arms converge.  The image has been stretched and skewed to bring it as close as possible to a recognizable aspect of the M-set.

The M-set is a 'connected' object, in one piece.  Every minibrot is connected to the main body of the set by an infinitely thin filament, giving the set only one infinitely long and convoluted shore line.  Yet in today's image we see ring-like elements that are obviously not connected.

Most likely these elements are connected to the main body of the Julibrot somewhere in the fourth dimension, though I am not sure if it has ever been demonstrated whether the Z^2+C Julibrot is or is not connected.

The rating of a 6 is adequate for a FOTD, but implies nothing outstanding.  The calculation time of 2-2/3 minutes is within reason.  The finished image is or soon will be available on the currently active web site at:

http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html

the original web site is located at:

http://www.Nahee.com/FOTD/

though it is not up to date.

Thursday brought a mix of sun and clouds to Fractal Central, with a temperature of 39F +4C, which was a virtual repeat of Wednesday.  These conditions gave the fractal cats the choice of lying on the shelf in the window, where the warmth of the sun was intermittent, but the view was better, or on the shelf in the hallway, where the warmth was guaranteed, but the view was boring.  Nicholas chose the window; Cassie chose the hallway.

The humans had a typical day, wrapping up the straggling odds and ends.  Actually, today, the 31st, is the end of the first decade of the 21st Century, but in the popular mind, the decade ended a year ago.  The next FOTD will be posted in 24 hours.  Until then, take care, and the last time I checked, none of the people I know were Boltzmann brains.  (I'll have more to say about these hypothetical disembodied brains floating around in outer space sometime in the future.)

Jim Muth
jamth@mindspring.com


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

Totally_New_Aspect { ; time=0:02:40.28-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 passes=1 float=y
  center-mag=-0.06323373791458239/+0.152854337845338\
  30/63.53143/86.095/-90/-10.3180927723985381
  params=100/0/90/0/-0.7525/0/0.5/0 maxiter=1500
  inside=0 periodicity=0 mathtolerance=0.05/1
  colors=0002jZ3lY4lX5lX6lW7lV9lVAlUBlTClTDlSElRFlRN\
  oQUqP`sOgvNnxMuzMpyLkyKfyJayJXxISxHNxGIxGMuHQsHUqH\
  YoHamHejIihImfIqdIubIpaJlaKhaLd`M_`NW`OS_PO_QJ_RFZ\
  SBZT7ZT8VV9SWAPXBMYCJZDG_ED`FAaJKVNUPRbIVlCZu6WoAU\
  jDSdHQ_KOUOMPRKJVIEYG9`IDaKGaLJaNMaOPaQSaSVbTYbV`b\
  WcbYfbZibXj`WkZVlXTmVSnTRoRPpPOqNNrLLsJKtHJuGIsHIr\
  HHqIHpIGnJGmJFlKFkKFjKDfPBcT9_Y7Xa5Tf4Qj7ShAUgDWeG\
  XdJZbM`aPb`ScZVeYYdWYbVY`UYZGZXF_VF`TEaREcSDeUDfVD\
  hWCsjCqiBohBmgAkfAheAedJbcRZaZV_fRZeNZeJZdF_dD_fC_\
  gBZhAYiFZfK_cP_`T`ZY`WbaTfaRe`Te_Ve_XeZZdY`dYbdXdd\
  WfdWhcVjcUlcUncTpcTqeUpgUpiUpjUplUpnUppUoqUosUouUo\
  wUoxUo`wf_wd_wc_vaZv`Zv_ZuYYuXYtVYtUXtTXsRXsQWrOWr\
  NWrMVpKUoITnJSmLRlNQkPPjRQiTRhVRhXUi_Xia_icbieeigh\
  iikikmjnmjpmjrljtljvljxljzjaqhTifK`dBTbCUaDU`EV_EV\
  YFVXGWWGWVHWTIXSIXRJYQKYOKYNLZMMZLMZNNYOOXQPWRRVST\
  UUVUVXTWZSY`RYbQZdQMfTAhW }

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