Fractal visionaries and enthusiasts:

In yesterday's FOTD I wondered whether the Julia aspect of the image held rectangles.  Since then, my curiosity has gotten the better of me.  To satisfy the curiosity, I calculated the Julia aspect and, as the name of today's image implies, found no rectangles.  I did find the same basic large shape however, plus lots of other unexpected smaller shapes, only a few of which appear in today's image.  An outzoom or two will reveal many more of these unexpected shapes.

The most obvious shapes in the image are the two scalloped-edged squares that appear ready to merge.  A very slight change in the real(c) parameter (real(p4)) will either merge them or move them farther apart.

The rating of a 7 indicates that I consider the image only adequate.  More work on the color could have made an improvement.

The name "No Rectangles" obviously indicates that I found no rectangles.

The calculation time of only one brief minute will try the patience of no one.

A mix of sun and clouds, low humidity, gentle breezes and a temperature of 81F 27C made the day delightful here at Fractal Central.  The fractal cats' thrill came when we put out their cat cubes and let them have their fun.  Other than the cats' fun, little of note happened in the humans' world.  The next FOTD will be posted in 24 hours.  Until then, take care, and is it the Tea-Party's fault or the Progressives' fault?

Jim Muth
jimmuth@earthlink.net


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

No_Rectangles      { ; time=0:01:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=JulibrotMulti2 function=recip float=y
  center-mag=+0.0009022201/+0.0696080662/4811.939/1/\
  0.5/0 params=2.5/100/90/0/90/0/-1.7506789/0/0/0
  maxiter=1500 inside=0 logmap=86 periodicity=6
  colors=0009O_9Ra8Uc8WdAVdCUdETdGSdIRdKQdMPdOOdQNdS\
  MdIPi9Rn0Ts5Vt9WtDXtHYtLZuP_uT`uYauabuecvidvmevqfv\
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  OOgNNeNLdNKcMJaMI`MH_PJYRKWUMUWNSZOR`QPcRNeTLhUKjV\
  ImXGoYEqZDp`FpbHpcJpeLogNohPojRolTomVnoXnqZnr`ntbn\
  udjpggkicfl`anXXqUSsQNvNIxOFvOCuP9tP6sP4rR7lTAfUDa\
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  d`rearc`ob`ma`k`_i__gZ_eY_cXZaWZ_VZYUZWTYUSYSRYQQY\
  OPWRPUUPTWORZOP`OOcOMeNKhNJkNHmMFpMErMCuMBwNDxNExN\
  GxNHxNJxNKyNMyNNyNPyNQyNRyQTwSUvVWtXXs_Zra_pdaofbm\
  idlkekhbge_dbXa_UZXRWUOTSLPPIMMFJJCGG9DD6AB37R45e4\
  4XKFPZPHmZOh_Vd`a`ahXafWW }

frm:JulibrotMulti2  {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p2*0.0055555555555556),
  b=pi*imag(p2*0.0055555555555556),
  g=pi*real(p3*0.0055555555555556),
  d=pi*imag(p3*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),
  aa=-(real(p1)-2), bb=imag(p1),
  c=p+flip(q)+p4, z=r+flip(s)+p5:
  z=(bb)*(z*z*fn1(z^(aa)+bb))+c
  |z|< 6 }

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