Fractal visionaries and enthusiasts:

The valley on the east side of the Z^2 Mandelbrot set is sometimes called Elephant Valley.  The radicals found there rather convincingly resemble elephants.  Every bud has one elephant standing over it, trunk raised and curled in defiance.  The Z^3 Mandeloid has two elephants guarding every 2-lobed bud in its Elephant Valley; the Z^4 Mandeloid has three elephants guarding every 3-lobed bud, etc.  The series continues, with the elephants growing ever more numerous and smaller, always numbering one less than the exponent of Z.  But what happens when the exponent of Z is reduced?

The same series continues.  Today's image shows the elephants, or what is left of them, in the Elephant Valley of the Z^(1.5) Mandeloid.  We have half an elephant guarding every half-bud.  And it happens to be the front half of the elephants that remains.  The image shows disembodied elephant trunks scattered everywhere, but not a single whole elephant.  With little thought, I named the image "Scattered Trunks".

The parent Mandeloid is a rather shapeless thing that came about when I returned to the 'MandelbrotBC2' formula and checked East Valley of the fractal that results when the expression Z^(1.5)+C is calculated 1.5 levels up the logarithmic ladder.

Today's scene lies on the south side of the valley, where the front halves of the elephants remain.  (On the north side of the valley their rear halves remain, but elephant rumps are far less impressive than elephant trunks, so I chose to check the trunks.)

I rated the image at an 8, mostly for its mathematical interest.  The coloring is a bit flat, though it is smoother than usual and its flatness does give an atmospheric effect.

The calculation time of 2-3/4 minutes is rather slow by FOTD standards.  This is where the FOTD web sites stampede to the rescue.

Partly cloudy skies and a temperature of 46F +8C made today an un-notable one here at Fractal Central.  The fractal cats were annoyed by the come-and-go sun, and settled by the house heat early in the afternoon.

FL and I had a day as uneventful as the weather.  Yes, I know it makes boring reading, but I have to tell it like it is.  The next FOTD will be posted in 24 hours.  Until then, take care, and one thing absolutely certain is that the end of the world is coming, just like those 'scare' shows say.  The only question is when.

Jim Muth
jimmuth@earthlink.net


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

Scattered_Trunks   { ; time=0:02:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 center-mag=+0.17056338/\
  -0.00784447/757/1/33.1/0 params=1.5/0/1.5/0 float=y
  maxiter=15000 inside=0 logmap=30 periodicity=6
  colors=00010c20d31e42f54g66h79i8Cg9FfBIeCLdEOcFRbH\
  UaIW`JY_K_ZLaYMcXPeWPgVOiULkTGmNBoIApJCqLFrQLsWSta\
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  UVJUVJUVJUVJUVJUVJUVJUVJUVIUXHUYGU_FU`EUbDUcCUdBUf\
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  8zm8zm8zm8zm9zmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAz\
  mAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmA\
  zmAzmAzmAzmAzmAzmAzmAzmAz }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100, p=real(p2)+PI
  q=2*PI*floor(p/(2*PI)), r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

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