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Sept. 4, 2012: Rectangle Toyland Aug. 31 Sept. 5 2012 FOTD Home
 Rating 9

rectangle toyland

Fractal visionaries and enthusiasts: 

I'm back!  Let the fractal celebration begin!

I bring with me a rectangle.  Yes, it's the strange little rectangle in the Z^(2.003)+C Julia sets.  Only today we do not see the pure, unadulterated rectangle, we see the rectangle as it appears when viewed slightly off-center in the imag(Z) direction and rotated 2 degrees toward the Oblate orientation.

From this angle the rectangle cannot be described; it must be seen.  To begin, it is no longer rectangular, though it does retain four relatively well-defined sides.  And it is no longer empty, but filled in its upper part with chaotic debris.  The outer parts surrounding the rectangle are no longer unbroken.  They have begun to stretch out and break up as part of the main bay of the nearby Mandelbrot minibrot comes into view.

The result rates a 9, most of which is due to the random coloring feature of Fractint.  My part involved nothing more than a minor tweaking of a few color registers.

The name "Rectangle Toyland" came about when shut off my thinking apparatus, a thing I do often.  The calculation time of  > 1-5/6 minutes will pass swiftly once a recognizable part of the image appears on the screen.

High humidity and lots of clouds left much to be desired here at Fractal Central today.  Occasional periods of rain kept things wet.  The temperature of 84F 29C felt much warmer due to the humidity.  The fractal cats passed the day keeping watch over the local pigeons, while the humans spent the day clearing a minor work backup.  The next FOTD will be another venture into rectangle land, and will be posted in about 24 hours, (with no guarantee given or implied).  Until next time, take care, and intelligent people realize there are no such things as ghosts.  Too bad the ghosts have not heard the news.

Jim Muth
jimmuth@earthlink.net


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

Rectangle_Toyland  { ; time=0:01:50.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1 inside=0
  center-mag=0/0/100 params=88/0/90/0/-1.7435/0.0001\
  /0.000175/0.073883/2.003/0 float=y maxiter=3600
  logmap=-54 periodicity=6
  colors=000YQwYQwWRuURtSRsRSrPSqNSpMToKTnITmHUlFUkD\
  UjCUiBReAOa9MY8JU7HR6EN5BJ49F36B34855B76D97GB8ID8L\
  F9NHAQJBSLBVNCXPD_REaTEcVFaXG_YHZ_HX`IWbJUcKTeKRfL\
  QhMOiNNkNLlOKnPIoPHnQKnRNnSQmSTmTWmUZmValVclWflXil\
  YlkYokZrk_uk_wjcsifohjkgmgfqcft`ip_lm_niZqfZsbYv_Y\
  xXYuYWrZUoZSm_Qj`Og`MeaKbbI_bGXcEVdCSdAPe8Ne6SiBXm\
  G`pKetPiwTfxZdxdbxj`xpZxu_wt_ws`wr`vqavpavobuobunc\
  umctldtkdtjdtjaqhZngWkeTidQfcNcaKa`HZZEWYknzjnzjnz\
  jnzinzinzhnzhnzhnzgnzgnzgnzfnzfnzenzenzenzdnzdnzcn\
  zcnzcnzbnzbnzbnzanzaoz`oz`oz`oz_oz_ozcozcozcozcozc\
  ozcozcozcozcozcozcozcozcozcozcozcozmozmozmozmozmoz\
  mpzmqzmrzmszmtzmuzmvzmwzmxzmyzmzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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