Fractal of the Day
by Jim Muth

Where are the Elephants ©
Jim Muth's fractal image in GIF format (640x480).

FOTD -- February 22, 2004   (Rating 3)

Fractal visionaries and enthusiasts:

Today's image is not particularly attractive.   I warned that the odd planes of the Julibrot can sometimes be stressful to look at.   But it is still an interesting view of what happens to the elephants in East Valley when the angle of view is changed to something totally new.

In today's image we have stationed ourselves at the origin of the Julibrot, which is also the origin of the Mandelbrot set, and we are looking east toward East Valley.   The four-dimensional Julibrot figure is oriented in our 3-D space so that the X-axis of the image is the imag(z) axis of the Julibrot and the Y-axis is the imag(c) axis.   What we see looking east has been stretched 250 times in the vertical direction.   If this had not been done, the image would have consisted of nothing but a few horizontal lines and bars.

And after stretching the scene, what do we see?   East Valley is sometimes called Elephant Valley because the features there resemble elephants.   The name is well earned.   The East Valley features resemble elephants more closely than the Seahorse Valley features resemble seahorses.   But here we are in East Valley, and "Where are the Elephants"?

The elephants are all around us, but only bits and pieces of them are recognizable.   Look closely and you will see parts of trunks here and there, half-elephants touching trunks, and disembodied parts of bodies scattered about in a totally disorganized manner.   The elephants are here indeed, but we have missed them, for, though they lie very near, they are in the fourth dimension, leaving us only hints of their true nature.

After careful consideration, I decided today's image was worth no more than a rating of a below-average 3.   This rating combines with the render time of 2-1/2 minutes to give an overall value of 119.

The finished image has been posted to Paul's FOTD web site at:from where it may be conveniently downloaded.

The Saturday temperature of 50F 10C was fair enough here at Fractal Central, but the wind, which gusted to over 40mph 64kph was far too much for the cats, who spent most of the day sitting on their shelf by the window, watching the trees blowing and the birds flying by.   An extra treat of tuna in the evening restored their good spirits.

With nothing much to do for the rest of today, I am going to do nothing much.   Sometime this evening I'll see what I can find in the Julibrot that will rate higher than today's 3.   Until next time, take care, and there are more wonders in the fourth dimension than can be imagined by the mind of man.

Jim Muth

START 20.0 PAR-FORMULA FILE================================

WheresTheElephants { ; time=0:02:31.05--SF5 on a P200
  reset=2003 type=formula formulafile=allinone.frm
  formulaname=SliceJulibrot2 passes=1
  params=90/90/0/90/0.27555/0/0/0 float=y
  maxiter=10000 bailout=9 inside=0 periodicity=10
  xZ9xUCxPExKGxeOf_WaTcWMkQ }

frm:SliceJulibrot2   {; draws most slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  r=u*sg+v*ca*sb*cg, s=v*sin(a),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  |z| <= 9 }

END 20.0 PAR-FORMULA FILE==================================

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