Fractal visionaries and enthusiasts:

Today's image takes us ever deeper into the world of near-linearity.  The exponent of Z in today's image is 1.009.  Both common sense and instinct tell us that a fractal with an exponent so close to unity can only be a lopsided circle or a featureless ellipse at best.  But as is the case with so many things that are known to be true in the world of science, common sense and instinct are wrong.

The parent fractal of today's scene is an ellipse, that's for sure, but when calculated at the particular height of 4.45 levels up the logarithmic ladder, the ellipse becomes irregular along its edges.  Today's image shows a close-up of some of this irregularity.

I named the image "Tsunami-Plus".  The reason for the 'tsunami' part of the name is obvious.  The 'plus' refers to the shaft of total chaos shooting down and disappearing behind the wave.

The rating of an 8 expresses my opinion of the mathematical worth of the image.  If I had put more effort into the coloring, I might have given the image more artistic value and worked the rating up to an 8-1/2.

The calculation time of 4-1/2 minutes will pass in a flash once the peak of the mighty wave appears, decorated almost like the wave in the famous Japanese drawing.

Sun, clouds and a temperature of 75F 24C made Monday a refreshingly pleasant day here at Fractal Central.  At least the fractal cats thought so.  They reverted to their winter curl-up modes.  The humans spent the day doing routine things such as gardening and serious work.  The next FOTD, likely another in the how-low-can-you-go series, will be posted in 24 hours.  Until then, take care, and all good things must come to an end, but so must all bad things.  In fact, everything with a beginning in time must come to an end in time.

Jim Muth
jimmuth@earthlink.net


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

Tsunami-Plus       { ; time=0:04:31.27-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip passes=t
  center-mag=0.787447/-1.99784/1.8675/1/-77.5/0
  params=1.009/0/4.45/2400 float=y maxiter=5000
  inside=255 logmap=205 periodicity=6
  colors=000U7AV8BW9CW9DXAEXBFYCGZDHZEI_FJ_FK`GLaHMa\
  INbJObKPcLQcLRdNQeOQfQPfRPgTOhUOhVNiXNjYMj_Mk`LlbL\
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  kRSmSOnTLpVHqWEsXAuZ4tY7tX9sWBsVDrUFrUHqTJqSMpROpQ\
  QoQSoPUnOWnNYmM`mLblLdlKfkJhkIjjHlkEpjHnjJljLkjNii\
  PgiRfiUdiWciYah__haZhcXhfWghUgjSglRgnPdvPgpOikNkfM\
  maLpWKrRJtMIxGIvHHtHGrHGpHFnHFlHEjHEhHDfHDdHCbIC`I\
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  Hp9Io9Cr4Jo9QlDWjIbgMheRobVu`ZucSufLuiEul7IjaJk_Jk\
  YL_QNPJPDCR25S36T47T58F0F }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-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=========================================