Fractal visionaries and enthusiasts:  

Today's image is a simple blow-up of a small part of yesterday's Seahorse Valley image.  I named it "Buds in Buds" because it holds two different types of buds.  The first type, filled with the stripes, is obvious.  The other type is the stripes themselves, which are actually Mandelbrot buds seen from the side and stretched about 50 times in the horizontal direction.

The art, which most people consider the most important aspect of fractals, rates a humdrum 5.  The math aspect, which I sometimes consider more important, rates a quite respectable 8.

The calculation time of 5-1/2 minutes will seem fast at first, but will slow significantly as the rendering continues.  Of course, the web sites can make the viewing far more pleasant.

A mix of sun and clouds with a temperature of 37F +3C made today right on the mark for the second day of the year.  The fractal cats soaked up the sunlight when it was falling on their shelf and waited hopefully when clouds blocked the sun.  The humans settled down to prepare for another year of surprises.  When the next FOTD is posted in a day or two, little will have yet changed.  Until then, take care, and if fractals hold as much hidden meaning as is often claimed, what then of the human beings who worked out the math?

Jim Muth
jimmuth@earthlink.net


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

Buds_in_Buds       { ; time=0:05:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrotSqr passes=t
  center-mag=0.369319/-0.531478/14.674/1/135/0
  params=88/88/88/90/-0.75/0/0/0/0/0 float=y
  maxiter=42000 inside=0 logmap=5 periodicity=6
  colors=00054L65K76K87K98K99MAAOABQ9CS9EU9GW9IY8K_8\
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  UlHUmHUmGUmGVmFWmEYnE_oDapDdrCgsCitBkuBmvAowAqx8ty\
  7wz6zz5zz3zz2zz1zz0zzTzzU }

frm:SliceJulibrotSqr   {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=z*z+c
  |z|< esc }

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