Fractal visionaries and enthusiasts:  

The formula that created today's image, the JuliaBC, is one of the original two 'branch cut' formulas submitted about 12 years ago, if I remember right, by Andrew Coppin.  The other branch cut formula, the MandelbrotBC, simply shows the critical Mandelbrot aspects of the same fractal expressions.

The purpose of the two formulas was to take advantage of the multi-valued nature of the complex log function and make an animation of the fractals that result when the other log values are iterated.  The MandelbrotBC formula in particular, and its descendants, have produced many FOTD fractals over the years.

Today's scene shows one of the Julia sets that result when the formula Z^(1.3)+C is iterated 52 levels up the hyperladder with the floor function hard coded into the formula.  The particular value of C is -0.4,-0.2.

The name "Fractal Rat's Nest" describes my first impression of the scene.

Thanks to the 'fmod' inside fill, the art value rates an 8.  The math value rates a reasonably respectable 7.5, since I use the Julia branch-cut formulas far less often than the Mandelbrots.

The calculation time of 1-1/2 minutes will pass fast when the interesting part of the image starts to appear.  And checking the web sites can make the time pass even faster.

Today brought a lot of sun and, for a change, a temperature of a couple degrees above freezing to Fractal Central.  The older fractal cat enjoyed the sun, while the younger cat was thankful to be rescued from the doctor, who convinced her to stay away from the kind of tomcats that have been prowling the area.  The humans comforted the younger cat as soon as she arrived home.

The next FOTD will be posted sometime between 24 and 54 hours from now.  Until whenever, take care, and

Jim Muth
jimmuth@earthlink.net


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

Fractal_Rat's_Nest { ; time=0:01:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=JuliaBC passes=1 center-mag=-0.19265/\
  -0.145174/0.8445339/1/57.5/0 params=1.3/0/52/0/\
  -0.4/-0.2/0/0 float=y maxiter=1000 inside=fmod
  proximity=0.04 periodicity=6
  colors=000L8QL9SLAULBWLCYLD_LEaLFcLGeLHgLIiLJkLLmL\
  NoLPqLQrLSrLUrLWrLYrL_rLarLcrLerLgrBYrBYrBYrBYrBYr\
  BYrBYrBYrBYrBYrBYrBYrBYrBYrksrksrksrkqrkqrkqrhorfo\
  rbmr`mrXmrXkrVkrVirVirTirThrRhrRhrQfrQfrOdrOdrOdrM\
  brMbrK`rK`rI`rIZrGZrGZrGWrDWrDUrBUrBUrATrATr8Rr8Rr\
  8Rr6Pr6Pr4Nr4Nr2Nr2Lr0Lr0Lr0Jr0Jr0Hr0Hr0Hr0Fr0Fr0D\
  r0Dr0Dr0Cr0Cr0Cr0Ar0Ar08r08r08r06r06r04r04r04r04r0\
  4r04r06r08r0Ar0Cr0Dr0Hr0Jr0Lr0Nr0Pr0Rr0Ur0Wr0Zr0`r\
  0br0fr0hr0ir0kr0mr0or0sr0ur0wr0yr0zr0zr0zr1zr3zr5z\
  r7zr9zrBzrDzrFzrHzrJzrLzrNzrPzrRzrSzrTzrUzrVzrWzrX\
  zrYzrZzr_zr`zrazrbzrczrdzrezrfzrgzrhzsizujywkxxmxy\
  pwzswzvvzwvzvwztwyqxxnxwlyukzsjzrizrhzrgzrfzrezrdz\
  rczrbzrazr`zr_zrZyrYyrXwrWwrVurUurTsrSsrRqrQorPorO\
  mrNmrMkrLkrKirJirIhrIhrIfrGfrGdrGdrGbrGbrG`rD`rDZr\
  DZrDWrDWrDUrBUrBTrBTrBRrBRrBPrANrANrALrALrAJrAJr8H\
  r8Hr8Fr8Fr8Dr8Dr6Cr6Cr6Ar }

frm:JuliaBC   { ; by several Fractint users
  e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)),
  r=real(p2)-q, C=p3, Z=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|< p4+100 }

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