;     Date: Tue, 24 Jul 2012 17:25:58 -0400
;     From: Jim Muth <jimmuth@earthlink.net>
;  Subject: [Fractint] FOTD 24-07-12 (Wrecked Rectangle [8])
;       Id: <1.5.4.16.20120724172911.2a0799da@earthlink.net>
; ---------
; 
; 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\
  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=========================================
; 
; 
; 
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