Fractal visionaries and enthusiasts:

In yesterday's FOTD, I commented that there were upside-down elephants in the detail under the arch of hollowed-out outline elephants.  In today's image I pick out and concentrate on the primary upside-down elephant.  The name "Primary Elephant" identifies the pachyderm that marches proudly before us in today's image, with its sub-elephants and their sub-sub-elephants lined up in its back.  I have never before given as much prominence to a single so-obviously fractal elephant!

As all Mandelbrot enthusiasts know, each elephant in East Valley stands guard over its particular Mandelbrot bud.  So where is the bud that is being guarded by the elephant in today's image?

Notice the narrow brilliant horizontal band across the lower part of the image.  The broad dark horizontal area between this band and the brilliant white area behind the elephant's upper parts is actually the bud, or what is left of it.  The bud has been stretched to infinity by viewing it in the Rectangular direction.

Mandelbrot features are compact in the C planes, but extend to infinity in the Z planes.  The Rectangular plane consists of the compact imag(c) dimension plus the infinite imag(z) dimension, resulting in an open circular Mandelbrot bud stretched in one direction to infinity, which appears as an infinitely long black open stripe with parallel sides.

Although the image is the third visit to the same part of the East Valley complex, the central elephant is so well defined that I rated the image at a 7.

A slight drawback is the calculation time of almost 11 minutes, which is long enough to give impatience a chance to raise its fickle head.

The heavy rain moved out and the sunshine returned here at Fractal Central on Friday, while the temperature took a drop to 70F 26C.  The fractal cats spent their afternoon lounging in the sun on the kitchen floor.

My day was relatively slow.  A bit of water did seep into the fractal basement on Thursday night, but FL with her mop quickly took care of that.  The next FOTD will be posted in 24 hours unless an antiquing expedition develops on Saturday, when the FOTD might be delayed.  Until whenever, take care and befriend a lonely fractal.

Jim Muth
jamth@mindspring.com


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

Primary_Elephant   { ; time=0:10:55.81-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=t
  center-mag=-0.011023301/+0.168393972/2097/0.1113/\
  90/69 params=90/0/0/90/0.28/0/0.5/0/2/0 float=y
  maxiter=32767 inside=0 logmap=10 periodicity=6
  colors=000kpThpVeoWcmYak__iaYgeWeiUdiRchSbhQakObnM\
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  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
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  czvhzslzppzmtzjxzgzzdzzczzbzzawz`tz_qzZnzYkzXhzWez\
  VbzU_zTXzSUzRRzQOzPLzPGzOIzOKzOMzOOzOPzORzOTzNVzNX\
  zNYzN_zNazNczKazNdzPgzSjz }

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