Fractal visionaries and enthusiasts: 

For years I was disappointed with the higher order fractal images, especially the minibrots, which to me at least, with a few minor differences, all look the same.

Then, totally by accident, I stumbled upon the DivideBrot series of formulas.  These formulas somehow combine higher order energies with quadratic energies in such a way that the higher order energies affect only the deeper sections of the fractals.

Today's image is a typical scene quite deep in its parent fractal, which on the surface is an everyday Mandelbrot set.  We need to go only a small distance down into the parent before we spot trouble however.  The large minibrot on the main stem is already breaking up, its main bay filling with debris.  Today's image lies in the debris strewn about the northeast part of its main bay.

I rated the image at an 8, mostly because the prominent order-7 minibrot at the center is one of the most unusual high-order minibrots I have yet found.  I might have added a half-point for the coloring, but a second thought said the present rating is high enough.

The name "Coma Fractrailis" is an invented phony latin phrase, which is supposed to mean 'fractal with commas'.  The seven elements arranged around the minibrot strongly resemble commas.

The calculation time of one minute will be faster on modern SOTA machines and slower on older ones.  All timing uncertainty may be eliminated however by checking the web sites.

A mix of sun and clouds, and a temperature of 61F 16C, made conditions near ideal here at Fractal central today.  Fractal Nicholas appreciated both the warm sun on the shelf in the southwest window and the blowing leaves, which are still falling.  It was apparent however that he missed Cassie sitting nearby.

The fractal people had a not-too-cheery day.  It's still rather glum here at FC with only one lonely cat trying to keep things active.  The next FOTD will be posted before too much time passes.  Until whenever, take care, and look to the light.

Jim Muth
jimmuth@earthlink.net


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

Coma_Fractrailis   { ; time=0:01:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip passes=1
  center-mag=-1.749144546273318/+0.00657273175035928\
  /1.140195e+013/1/-13.25/0 params=7/10000000/0/0
  float=y maxiter=1800 inside=0 logmap=66
  periodicity=6 mathtolerance=0.05/1
  colors=000ABU9DZ7FZ4HZ2JZ0LZ4N`8QaCTcGWdJ_eNbgRehV\
  hjYlkaqliuzqzzoxzmtznquonrpkmqhmrelsbkt_kuXjvUjsRh\
  qPgnNflLeiJcfHbdFabCY`AUY8PW6KV4FS2AO0AK3AE5AC87AA\
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  hdcjeblfanf`pg_qgZmeZjdYgcYdbXaaXZ`WW_WTZVQYVNXUKW\
  UHVWLUXPUYSUZWU`_UabUbfUcjUemUfqUguUhxUcwRZvOUuLPt\
  IKsFFrCAq95p61p35q78qBCqEFqIJqMMqPJoSHnUFmWClYAj_8\
  ia5hc3ge1fg1ik8jm8km9lm9mmAmmAmmBmmCmmCmmdiNdiNehO\
  ehOfhPfhPghPhgQhgQigRigRjfSjfSkfTkfTleUzeUzeUzeVze\
  VzdWzdWzdXzdXzcYzcYzcZzcZzcZzaYz`Xz_WzZVzYVzWUzVTz\
  USzTSzSRzRQzPPzOOzNOzMNzLMzJLzILzHKzGJzFIzEIzFHzGH\
  zHGzIGzJFzKFzKEzLEzMDzNDzOCzPCzPBzLBzMAzNAzO9zP9zQ\
  8zQ8zR7zS7zT6zU6zV5zV5zT8zRAzPCzPEzPGzPIzPLzPNzPPz\
  PRzZTzZVzZXzZVzZTzZRzZPzZNzZLzZJzZHzZFzZDzZEzZEzZF\
  zZFzZGzZGzZFzZFzZFzZFzZFzZFzZFzZFzZFzZFzZFzZFzZFzZ\
  FzZFzZFzZFzZFzZFzZFzZFzZF }

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