Fractal visionaries and enthusiasts:

Today's image rates only a 5, but this is for its artistic aspect, which I admit is not too great.  It's mathematical aspect is far more interesting however.

While casually rotating the colors of today's scene, and ready to move on to a more promising image, I caught a fleeting glimpse of an unsuspected pattern buried in the chaos that fills the screen.  I bit of tweaking revealed that I was not mistaken. The pattern definitely is there -- unlike anything I have seen before.  But it takes special coloring to reveal the underground pattern, which is nearly invisible with normal random coloring.

The parent fractal consists of a circle with a trapezoidal shape nearly filling it and a large distorted Mandeloid inside the trapezoid.  Most of the distortion in the Mandeloid lies in the higher-order buds, which are elongated to ridiculous lengths.  Today's scene lies in the northern branch of Seahorse Valley of the Mandeloid.

The image is filled with both minibrots and disappointing dry valleys that look like they hold minibrots but go flat before a minibrot appears.  I have already checked a few minibrots and found them to be disappointing.  This does not mean that no great minibrots lie in the depths, but it is not a good way to start searching.

The name "Patterns in the Mist" refers back to the original scene before I began work on the colors, when the dark underground pattern was virtually invisible.

The calculation time of 2-1/2 minutes will pass in a flash, especially for those who have something else to do while waiting.

Tuesday turned out really not too bad here at Fractal Central.  The morning fog cleared off by 10am, leading to a sunny day with light winds and a temperature of 63F 17C.  For some reason, the fractal cats were active unusually early, and settled into their afternoon naps well before noon.  My day was rather busy but satisfying.  FL was also busy.  The next FOTD will be posted in 24 hours.  Until then, take care, and the supernatural does not exist, that is unless we are talking about what the human brain is supposed to do. 

Jim Muth
jamth@mindspring.com


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

PatternsInTheMist  { ; time=0:02:31.61-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip
  center-mag=-0.741183021/+0.043160417/3242/1/\
  -12.5/0 params=-3/10/0/0 float=y maxiter=7500
  inside=0 logmap=68 periodicity=6
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  3TL4TL5UM5UM6UN7VO7VO8VP9WP9WQAXRBXRCXSCYSDYTEYUEZ\
  UFZVGZVGYUHXTIXTJWSKWSLVRLUQMUQNTPOTPPSOQSOQRNRQMS\
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  8Q0AR0DS0FT0IU0KW0NX0QY0S }

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