Fractal visionaries and enthusiasts:  

Today's image lies in the fractal that results when the formula Z^(1.5)+C is iterated 379.2424085207679 levels up the complex hyperladder with no function applied.  The odd number of levels indicates that the value was set at random by Fractint's evolver feature.  A very similar image could have been found with a far simpler value, though I lacked time to search for it.

Actually, the complex logarithm has an infinity of values, but this does not mean that an infinite variety of fractals is possible.  The fractals change in a circular manner as the value of 'k' in the complex log formula is changed, and soon begin repeating.

I named today's image "Something New".  I have never before seen features quite like the dark blue ones in today's image.  The filaments extending from them resemble those extending from everyday Mandelbrot buds.  And the filaments in the image have identical mini dark blue mini-features lying along them.

The rating of a 7 is average.  The artistic value is not that great, nor is the mathematical interest.  Extra coloring effort might have raised the rating a half point or so however.

The calculation takes 2-1/2 minutes to finish.  Significant time may be saved by viewing the finished image on one of the web sites.

Near total sun with a temperature of 45F +7C made today unusually pleasant for the time of year.  The fractal cat enjoyed the sun; the humans enjoyed getting the work finished.

The next FOTD will be posted in a day or two.  Until whenever, take care, and the surest sign of a dysfunctional group is when its members begin fighting among themselves instead of working together to solve their common problems.

Jim Muth
jimmuth@earthlink.net


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

Something_New      { ; time=0:02:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident inside=0
  center-mag=+1.52637522907494/+0.5716577695720915/\
  1.263153e+009/1/-90/0 params=1.85/0/379.2424085207\
  679/0 float=y maxiter=3600 logmap=381 periodicity=6
  colors=000E7SF8TG9UHAVIBWJCXKDYLEZMF_NG`OHaPIbQJcR\
  KdSMeVOeZQeaSfeVfiXflZgp`gvYbt`esbgrejpglojopkrolq\
  nlqmlqllqklqklqjlqilqhmqgmqgmqfmqemqdmqcmqclwcmqcm\
  kcnecn`cnVcoPcoJfrGdpFcoEanD`mCZlBYjAWi9Vh8Tg7Vf4S\
  f6Re5Rd5Rc5Rb5Qa5Q`5Q`5Q_5QZ5PY5PX5PW5PV5Ya2PV5GO8\
  WBG7HABJBFKCJLCNMDQNDUOEYPEaQFdRFhSGlTGpUHxJLuPJsV\
  Hq`GofErlDvrBzz8vwAruBnsCkqEloFmlGnjHnhJofKpdLpbMo\
  _IkZHhYGeXFbWF_VEXUDUTDRSCORBLQBIPAFO9CN9AQ89T78V6\
  7Y56_45b34d23g12i06h6AgCDgIHfOKeTOeZRddVcjYcoV`kTY\
  gRVcPT`NQXLNTJLQGIMEFICCEAAB877643420GWBES9CP8BM79\
  J68G56C4493362131iBHeAFb9U_8UW7UT7UQ6UN5UJ4UG3UD3U\
  92K61K30KKTKSEKFNKCJKAFc7Bc57c23cGMm8BmJYmHVzGTzFR\
  zEPzDNzBLzAJz9Hz8Ez7Cz5Az48z36z24z12zIYzGUzEQzCMzA\
  Iz8Fz6Bz47z23zKKzq`zlXzfTzaQzWMzRIzLEzGBzA7z53z1zz\
  0qz0hz0_z0Rz0Iz09zGazEZzDWzCTzBQz9Nz8Kz7Hz6Ez4Bz38\
  z25z12zVrzRlzOgzLazIXzFRz }

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