Fractal visionaries and enthusiasts: 

Today's image has a math rating of 9, which is an exceptional rating for the mathematical aspect of an image.  The rating is based on the lack of discontinuities.  All images that have a fractal exponent of Z in their generating expression must contain discontinuities.  There is no way around it.

Well, maybe there is!  Today's image takes us into a area of debris polluting the large northern bud of the large minibrot on the main stem of the parent Mandelbrot set, which is corrupted in its depths by Z^(3.5) energies.  The minibrot at the center is purely of order 3.5, but checking the elements beyond the minibrot, I see a ring of seven, arranged nearly perfectly, with no discontinuities in sight.

It's impossible, but there it is, for all the fractal world to stare at in awe and wonder.  But don't be too shocked.  Discontinuities actually *are* in the image, but I have arranged the colors so that the breaks are invisible.

Despite the exceptional math interest, the artistic aspect of the scene is boringly average.  The rating of a 6 will win neither praise nor trophies, but the image is still worth the 50 seconds required to calculate it, if only to see a symmetrical Z^(3.5) fractal not filled with breaks.  Checking the web sites will eliminate the calculation nuisance.

Typical midsummer conditions prevailed here at Fractal Central today, with mostly clear blue skies, a hot sun, and a sweltering temperature of 90F 32C.  Early in the afternoon the fractal cat found a cool spot to stretch out in, and stayed there until evening when the sun went down.  (Sunset was at 8:43pm EDT today here at FC.)  The fractal humans took it easy most of the day, avoiding distractions such as cook-outs.

The next FOTD will be posted shortly.  Those who can see time as an illusion might be able to view the next image at once.  The rest will have to wait.  Until whenever, take care, and as I see it, time is not an illusion.  It is the fourth dimension of space, viewed edge-on.

Jim Muth
jimmuth@earthlink.net


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

Mathematic_Mystery { ; time=0:00:50.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip
  center-mag=-1.759072351009887/+0.01430659715177246\
  /4.875516e+009/1/42.5/0 params=3.5/1000/0/0 float=y
  maxiter=2000 inside=0 logmap=52 periodicity=6
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  d_Re_Oe_Me_JecYjdXjeXj`Vk }

frm:FinDivBrot-2   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }

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