Fractal visionaries and enthusiasts:

On July 3 we viewed an East Valley elephant from the normal position directly in front of the screen.   On July 4 we viewed the same area from the direction of the past and saw a different aspect of the elephant complex.   Today we rotate the Julibrot so that in our 3-D space the real(Z) axis is perpendicular to the screen, and view the same East Valley area from the left side of the screen, which gives what I call the Oblate view.   The area we see lies invisibly about two feet in front of the screen, and is stretched about 120 times in the vertical direction to make the elephants recognizable.

Well, they're still the same period-30 elephants, but now they appear as gossamer, ethereal things with barely any substance, so fragile that light passes right through them.   And they are changing shape before our eyes.   The one on the left is overweight, while the one on the right is actually anemic.

The elephants are still standing guard over their appointed bud, but we now see the hypercylindrical bud sideways, sliced in a direction that appears to stretch it to infinity.   The horizontal black strip is the bud; the bluish stripe near the bottom of the frame is the valley leading to the bud.   We have found that there are many elephants guarding each East Valley bud, lurking both behind and in front of the screen while we are viewing the buds.

The Mandelbrot elephants have minibrots in the area of their shoulders, while the Julia elephants have Julia sets.   But the oblate elephants have only dry valleys that lead nowhere, and a scattering of 30-pointed stars.

There are many more varieties of elephants to become acquainted with, and in tomorrow's FOTD we'll see what the Rectangular elephants have to offer.

Today's parameter file runs in 4 minutes, but a bit of time may be saved by checking the finished image on the FOTD web site at:
Another perfect day passed uneventfully here at Fractal Central on Sunday.   The near cloudless skies and temperature of 81F 27C were just what the doctor ordered.   (Don't ask which doctor.)   After a Saturday evening of exploding firecrackers, the fractal cats had a peaceful day of recovery.   My day was kept busy by chasing the japanese beetles from FL's raspberries.

Unless something unexpected happens, the next fractal elephants will be posted in 24 hours.   Until then, take care, and fight the threat of global warming hysteria.


Jim Muth
jamth@mindspring.com
jimmuth@aol.com

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

Oblate_Elephants    { ; time=0:03:59.92-SF5 on P4-2000
  reset=2004 type=formula formulafile=basic.frm
  formulaname=SliceJulibrot4 passes=t float=y inside=0
  center-mag=+0.2921149279660176/-0.001977650433172/2\
  484.439/0.007941/0/85.7426211542968275 maxiter=27500
  params=0/0/90/0/0.260821781/0/0/0/2/0 periodicity=10
  logmap=25
  colors=000s9qr6rq3ro3rm5ok7mi9kgBidDgaFdZHbWJ`SLZP\
  NXMPUJRSGTQDVOAXM2ZF5`I7bS9dUBeWDeVFeWKeXQeTWeS`dO\
  bcKdbIcaJb_KaYL`WN_UOZSPYQQXORWMTVKSUISTGSSESRCSQA\
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  ULsQJoMHkIGgEEhACm74r6Bv6Hz6Oz6Uz6Yz5`z6az7az7Xv8S\
  r9Nm9IhADcB8Z83UB4OD5QF6UI7YK7aM8eP9iRAmTBqVBuUDrT\
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  Ga6I`9J_AKZFLYHMXKNWNOWPfeUadNLmXLgaLafLWkIX`GXRzX\
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  JmXHsPGyQHjRIWSJHSK3QLEPMPNN_MOjWYldfmnoowxpsmmqb`\
  pSzj8zXgz`Oz`hzYfzWezUdzqdzhcz_czFJzMUzltzakzprzcj\
  zFvz1EzANzJWzrIzkOzdTzYZzv4z1WzuLzfEzaNzXWzh9zbKzX\
  Uza0zXKzSPzUhzy1zFYzM`zHizLgzPezYizVfzt_zl`zeazZbz\
  LgzNfzPezRdzdzz_rzWjzY8zMXzP`zsNzfAzr_zdazHKzo`zcb\
  zlOz5FzBMzHSzNYz8yzFqzMjz }

frm:SliceJulibrot4    {; draws most 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),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=z^(p5)+c
  |z| <= 9 }

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