[Fractint] FOTD 24-07-12 (Wrecked Rectangle [8])

24 Jul 2012

      FOTD -- July 24, 2012 (Rating 8)

Fractal visionaries and enthusiasts:

Today's image gives an unexpected view of one of those strange 
rectangles in certain areas and at certain orientations of the 
Z^(2.003)+C Julibrot.  It shows that these figures are not 
really rectangles at all.

To create the distortion, I first found a minibrot very close to 
the X-axis of the Mandelbrot plane, with rectangles in its 
surrounding pattern.  Then I calculated the Julia set of this 
Mandelbrot rectangle.  Surprisingly, the Julia set of the 
rectangle is a concave octagon.

To produce the effect of two pentagons connected by a narrow 
thread, I double rotated the orientation of the slice 0.0021 
degrees from the true Julia direction, which is the point where 
the octagon is ready to split into two rectangles.

The result is today's image, which I have named "Wrecked 
Rectangle".

I rated the image at an 8, because of both the brilliant colors 
and the mathematical interest.

The calculation time of 55 seconds will seem to pass in the 
blink of an eye once the strange geometric object at the center 
comes into view.

Find the image already finished at:

      <http://www.crosscanpuzzles.com/Archives.html>

Find high-definition variations at:

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

Find thousands of back images at:

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

A typical partly cloudy midsummer day passed uneventfully here 
at Fractal Central.  The temperature of 91F 33C was a bit on the 
hot side, but a refreshing breeze and relatively low humidity 
kept things bearable.  The fractal cats spent most of the day 
lounging in their cat cubes; the humans spent the day attending 
to assorted tasks, which is true for almost every human on earth.

The next FOTD will be posted in 24 hours.  Until then, take 
care, and the dangers that the media are not reporting are 
likely to be more dangerous than the things they *are* reporting.

Jim Muth
jimmuth@earthlink.net

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

Wrecked_Rectangle  { ; time=0:00:50.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=+0.000023902\
  45110228/-0.00011070773475015/3164.17/1/-87.5/0
  params=89.9979/0/89.9979/0/-1.74323693381586/\
  1.24151879e-007/0/0/2.003/0 float=y maxiter=360
  inside=0 logmap=84 periodicity=6
  colors=000GD5GB0EA0HA0HA0HA0HA0HA0HA0HB0HG0HI0HJ0H\
  Q0Lc2HZ0EX0BU09T06Q04P01N00L00H00G00E00D00B0090080\
  0000600E00L09U0Le0zz0Xn0ETD0Bc00z00z01z05z09z0Gx0L\
  v0Qs0Xq0en0ll0si0zg0ze0vi0in0Zs0Pv1Gz61zB0zG0zH0zJ\
  0zJNzLNzNNxNNvPgsQgqQgnTglUgiUsgXzeXzcTz`Pz`Nz`JsZ\
  HgZEUZBQZ9PX6LX5HX26X00U00U00U00X00UH0TlJT`LLQLEHN\
  89N22P00P00J00E0KD0KH0K40K00K00K00K00K00U10U10U24U\
  48c5Ec5Jc9LcDNcHPmLQmQTmUTmNNmHJmBGm6Dm29z06z04z01\
  z00z00z10z40z80zD0zH0zG0zG0zG0zG1zG6zGDzGJzGQzGZzG\
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  1H00H00J00L00N00P00T00P09N0QL0lG0iJ0gN9eQPcUgcZz`X\
  xZUvXUqUTnTQiQQgPPcNN`LNXJLUHJQGJPEHLDHJBJJBLL9PN8\
  QN8TP6UQ6XQ5ZT5`U4cU4eX2gZ2iZ1n`0qc0sc0ve0xg0zg0zi\
  0zl0zl0zn0zn0zl0zl0zl0zi0zi0zi0zg0zg0zg0ze0ze1ze1z\
  e1xc0gL0gJ0gH0gG0gE0zN1gD }

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