Fractal visionaries and enthusiasts: 

Today's scene lies in the Mandeloid fractal that results when the formula Z^(1.5)+C is iterated 1.5 levels up the logarithmic hyper-spiral with no function applied.  This parent fractal resembles a Mandelbrot set with an oversized main bud on the north shore line of the main bay.  Today's scene is located on the southwest shore line of this oversized bud.

I rated the image at an 8 because it is one of the finer minibrot scenes I have found in the fractals with exponents between 1 and 2.  Although the pattern around the minibrot is filled with discontinuities, they are arranged so that the pattern appears quite regular, with some rather attractive curly filaments extending outward from the minibrot.  The unusually brilliant colors also help with the rating.

I sometimes wonder whether fractals like today's are actually true fractals at all.  It seems to me that the MandelbrotBC3 formula invents a new kind of math, and while using it with its various functions, I am exploring possible alternate mathematical systems rather than real fractals created with accurate math.  It really doesn't matter however.  The images are fractals, with all the characteristics of fractals, and real or not, they can still be unusually attractive.

Do not be deceived by the name "Silver Horizon".  The image is not one of those fantastic fractal scenes on other planets.  It is a surprisingly attractive scene of just another irregular <2 >1 minibrot.

The calculation time of 2 minutes is near the fractal average.  The web sites can cut the wait notably.

With partly cloudy skies, a temperature of 77F 25C and high humidity, today seemed more like an early August day than an early October day.  The fractal cats would have preferred more sun, but they still found enough comfort on their chair by the southwest window.  Except for a midday visit by the dryer repairman, who did his job quickly, the humans had a typical day.  The next FOTD will be posted at the right time.  Until whenever, take care, and I get the feeling that something is wrong with the world, but I can not track it down.

Jim Muth
jimmuth@earthlink.net


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

Silver_Horizon     { ; time=0:02:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident
  center-mag=+0.1154933507434394/+0.9603539171372509\
  /7.500726e+008/1/-115/0 params=1.5/0/51/0 float=y
  maxiter=2500 inside=0 logmap=257 periodicity=6
  colors=0009P07O05N03L02K02J00I00G00F00E10D20C20B52\
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  7G58J59K5AL5BO5CP5DQ5ES7FV7GW7IX8J_8Ka8Lb8Nd9Of9Ph\
  9QjASmAToAVpAVrBTpCSoDQoEQmFPkGOkIOjJNhKLhLKfQKeWJ\
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  kz0kz0kz0kz0kz0kz0kz0kz0kz0zz0zz0zz0zz0zz0zz0zz0zz\
  0zzozzmzzkzzazzZzzXzzVzzS }

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