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.

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\
  gzGqzGzzGzzEzzEzzDzzDxzBszBqzBnz9lz9iz8ez8cz6`z6Zz\
  6Xz5Tz5Qz5Pz5Nz5Lz5Jz4Lz5Hz6Gz8Dz9B5B84B64D42E21G1\
  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=========================================