Fractal of the Day
by Jim Muth

Squarely Chaotic ©
Jim Muth's fractal image in GIF format (640x480).

FOTD -- August 07, 2006   (Rating 6)

Fractal visionaries and enthusiasts:

Today's image is a scene in the Z^sqrt(2)+C fractal as it appears 41 levels up the logarithmic ladder.   (The ladder is infinite.   Regardless of how far one climbs up or down it, they can come no closer to the top or bottom, for there is no top or bottom.)

I named the image "Squarely Chaotic" because the exponent of Z is the square root of 2.   I rated the image a 6 because I could find nothing in it that might earn a higher rating.

The parent fractal consists of a large double-lobed bay vaguely resembling a termite and surrounded by considerable chaos.   Since termites are bad news if they get into the house, I left the word out of the name.   Today's scene is located at the inland edge of the chaos on the north-northeast shoreline of the bay.

The image is not the best of all time, but the brief render time of 1-1/2 minutes means that not much effort will have been wasted if the image fails to please its viewer.   And as always, the finished GIF image will soon be posted to the venerable FOTD web site at:
Another very pleasant day prevailed Sunday here at New Fractal Central on Sunday.   The all-new fractal cats made the most of things by watching birds and squirrels, and stretching in the sun that comes in the front window during the afternoon.   In the evening I gave them their treat of tuna, but Nicholas seems to prefer cheese (sharp cheddar only) to tuna.   Maybe he was a cow in a past life.   Cassie is satisfied with her tuna treat.

My day was peaceful enough, but Mindspring still does not have its dial-up access under control in this area.   I guess it's about time to think of a switch.   The next FOTD is due in 15 hours.   Until then, take care, and walk on the enlightened side of the fractal.


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

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

Squarely_Chaotic   { ; time=0:01:26.12--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 center-mag=+0.2624741533\
  9993670/+1.0374591869810080/159400.7 periodicity=10
  params=1.4142/0/41/0 float=y maxiter=30000 inside=0
  colors=000900F00L0898`E5VI4RM1MzR0oH0b891i`EMRC`Iz\
  _YCl0HV5LFCy`5lO9`BEbz0Ys0V`5SICs00j05c09X0E_0YV0S\
  S0MHziusbeRSl8ef5_`4TV1O0zF9VHp0vb0b005BXxr8uc4`e0\
  m0f0s0Sm0Xg0`b0eX0gb9MgT1EEEEEMMEX4HO09UL2Qz0xv0ro\
  0mg0ib0eCRP0p9HcoCXi8Rc4LY0FSFLPTPMgTJzYIf40bEClOR\
  vYezfsLHOuVijL`_9RO8SrxXcTPz0Yp0Tg0PY0LyYmlMb`BSLJ\
  BMCEO5Hx00l00`04rJ8c9E0SSPJsPEiP9`P4R0Bs9V0EM0IF0M\
  69i9v_4bJS0ME6cue_f_XSTSEOzb0xS0lI2`8Buz4ii9_MEOvg\
  Pf`PSVPEOg`0`O4VBB`zXVYPOvpPfgPS_PERzzv000060540C2\
  0J19z40x20l10`09Xx0Tg0ST0RE9E1vJ0bl64zgjoS`bERbz2V\
  XBbb0YS0VI0S880vPBSLz20x10l14`0BYrOO0I4R09J0FC0L58\
  zz2Mz0Om0OX1PF98zjEpxJPb909zzrH0xL0bL`FMOHOBIT0858\
  xeH0_B0T56v`BmREeIFX8H_zxXslT`bRISxzTolRfXOYFLe1``\
  0VX0RS0M0`16R5CI9J8EzP6lCCRI0PC5P89P4EBz0Fo0IY0MH9\
  Cy0Hc0LJ6`08zz0mX8zzMxrLl_J`HI0Y00P08H4H8BbX0YL0T9\
  56lVC_RHOOLBL000200E08400 }

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




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