Fractal visionaries and enthusiasts: 

We have found the strange Z^(2.003)+C rectangle in the Julia sets and in the Mandelbrot set.  But what about the four remaining perpendicular directions through the Julibrot?  Well, as today's image shows, the rectangle also appears in the Oblate orientation, where, with the proper stretching and skewing, it makes quite a striking appearance.

At first glance the image appears to have origin symmetry, but a close inspection will reveal that the symmetry is only apparent, and not exact.

I named the image "Oblate Rectangle" for the obvious reason.  The rating of a 7-1/2 includes the usual bonus for my coloring work, which creates a good part of the overall effect.

The calculation time of 3-1/2 minutes might seem slow to those who are growing bored with rectangles.  The web sites bring total relief from boredom however.

The next three FOTD's will feature the rectangle in its remaining three aspects.  Then we'll move on to other fractal wonders.

A near perfect day prevailed here at Fractal Central today, with a temperature of 75F 24C and a Photoshop (aka Kodachrome) blue sky dotted with small, puffy white, chamber-of-commerce cumulus clouds.  The fractal cats enjoyed the outside conditions from inside, spending much time on the shelf in the southwest window, where the sun, at its lower angle, is again starting to come in.

The humans made it through the day without incident.  The next FOTD image will be posted in 24 hours.  Until then, take care, and, if the world is a dream, then the evidence that it is a dream is also a dream.

Jim Muth
jimmuth@earthlink.net


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

Oblate_Rectangle   { ; time=0:03:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/3620/\
  0.01375/0/-77.0000000000000995 params=0/0/90/0/\
  -1.7435/0/0.000175/0.073883/2.003/0 float=y
  maxiter=72000 inside=0 logmap=54 periodicity=6
  colors=000K8aKAcKCeKEgKGiKIkKKmKMoIOqGPsEQuBQwDRvE\
  RuGSuHStJTuKTvLTwNUxOUyQVzRVzSVzUWzVWzXXzYXz_Yz`Yz\
  aYzc_zd`zfbzgcziezhezhdzgbzgazg_zfZzfZzeXzeWzeVzdU\
  zdSzdRzcRzcQzbPzbQzbSzaUzaWzaYxc_ve`tgaribpkcnmdmj\
  ehgfdeg_bhW`iSYjN_kJblEemAho6kqMnsaquVtwPwyJzzDwwK\
  tuQqsknqWkoihmwekubis_gqXeo_crRanI_k9`g0if1gd1eb2d\
  `2bZ3aY3_W4ZU4XS5VQ5UP6SN6RL7PJ9RH7SI6NJ4JK0EL3KL5\
  QL7QL9RLBRLDSLFSLHTLJULIVKHWJGZIFaHEdGEgFFfIGfKHfM\
  HeOIeQJeSJeUKdXLdZLd`MdbNcdNcfOchPbkPbmQboRbqRasSa\
  uTawTayDczCczCczCczCczBczBczBczBczAczmZzmZzmZzmZzm\
  ZzmZzmZzmZzmZzmZzmYzmXzmWzmVzmUzmUzhPNkPOnPPpPPmOM\
  mOKmNImNFmMDmMBmL8mL6mK4mK2mJ6mI9mHDmGGmFKmENmERmD\
  UmCYmB`mAdm9gm6km9jmBimDimGhmIhzKgzMgzPfzRfzTezVez\
  Ydz_czaczdbzfbzhazjazm`zo`zq_zuZzs_zq_zo`zn`zl`zja\
  ziazgbzebzdbzbcz`czZdzYdzWdzUezTezRfzPfzSfzRgzQizP\
  jzNkzMmzLnzKozIqzHrzGszDs }

frm:SliceJulibrot4   {; draws all 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), esc=imag(p5)+9
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=z^(real(p5))+c
  |z|< esc }

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