FOTD 29-06-03 (Time Lash [5])

29 Jun 2003

      FOTD -- June 29, 2003 (Rating 5)

Fractal visionaries and enthusiasts:

Today's image was created by the MandelbrotMix3 formula.  This 
formula mixes together and iterates four different powers of Z.  
But it has a down side.  It does not automatically initialize Z 
to a critical point of the formula.  That task must be done by 
hand, and the resulting value entered as real(p5), which is the 
reason I use the formula so rarely.

Formulas such as those calculated by the M-Mix3 formula have 
several critical points, which are points where the function is 
stationary and midgets thrive, so several different fractal 
images can be obtained from the same formula when the critical 
points are calculated by hand.  This is one of the good points.

But big disadvantages are that calculating critical points is 
boring work and the resulting fractals are not that much better 
than those created by the MandelbrotMix4 formula.  Today's 
parent fractal for example mixes various portions of Z^(10), Z, 
(1/Z), and Z^(2).  The resulting image, which resembles a flying 
saucer or Marvin the Martian wearing an army helmet, could just 
as easily been created by the MandelbrotMix4 formula.  The 
unusually precise value of real(p5) is one of the critical 
points of the formula, which I calculated and entered by hand.

The parent fractal has X-axis symmetry, with a tiny East Valley 
just where it should be, and many other valleys that also 
probably hold worthwhile images.  Today's scene is an unusually 
shallow one located in this East Valley.

Today's image rates an average 5, largely because of its 
spectacularly brilliant colors, which I tweaked in a graphics 
program.  Those who run the parameter file need not be concerned 
about missing the enhanced colors.  The colors are fully encoded 
in the parameter file.  The name of the image, "Time Lash", was 
chosen while I was watching a 'Doctor Who' episode of that name 
on TV late Saturday night.

The render time of 1/10 second over 10 minutes on my machine, 
which is nearing the fossil stage, can be cut at least in half 
on newer units.  And as always, the completed GIF image can be 
downloaded for convenience from one of the FOTD web sites at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

Though lots of clouds hung around here at Fractal Central on 
Saturday, they were thin enough to let the temperature reach 82F 
28C -- near perfect cat conditions.  Enjoying the conditions to 
the fullest, the dynamic pair had a peaceful day in the yard.  
The pushy cat from two doors down the hill stayed where he 
belongs for a change, so their peace was uninterrupted.

Today is starting sunny, and the temperature is still near 
ideal, but showers are possible.  It remains to be seen how the 
cats' day will go.  I'm going to spend the day doing as little 
as possible.  If I get ambitious, I might resume work on the 
FOTD CD, which has been nearly but not quite ready for several 
months.  I'll probably end up releasing the CD in imperfect 
form, but I'm not quite ready to give up hope of perfection yet.  
Until next FOTD, take care, and stay in there with the big-time 
thinkers.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com

START 20.0 PAR-FORMULA FILE================================

Time_Lash          { ; time=0:10:00.10--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix3a function=ident passes=1
  center-mag=+1.506891153995481/-0.00013746456513907\
  /205962.1/1/-172.5/2.01858393888976195e-009
  params=0.001/10/1/1/1/-1/0.1/2/-1.403897684563/0
  float=y maxiter=4200 inside=0 periodicity=10
  colors=000z0zz0zz0zv0zP0z0lz0zz0zz0zz0zz0zz0zz0zz0\
  zz2zz6zzBzvGzhKzZPzPUzBZz2cz0hz0vz0zz0zz0zz0zz0zz0\
  zz0zz2zz6qzBhzGZzKPzPBqU2cZ0Pc0Bh02l00q00v00z00z6K\
  6zz0zz0zz0zz0zz0zz0zz0zq0lc0cK0P60G0220G00P00c00l0\
  Xz0Wx0Vw0Uv0Tu0St0Rs0Qs00s00s00t00t00u00u20w20w60z\
  B0zB0zG0zG0zG0zG0zP0qU0Zc0Gh20lB0vK0zU0zc0vZ0lU0cU\
  0ZP0PP0GK0BK02G00G00B00B00600200200000000000000000\
  000000000Z0zzPzzzzzzzzvzzhzvUzZGzG2h00P00600000000\
  00000000000000000000000000000000000000000000000000\
  000000000000000600B00K00P00Z60cG0hK0qU2vc2zl6zvBzz\
  BzzGzzKzzKzzPzzUzzUzzZzzczzczzhzzhzzhzzlzzlzzlzzqz\
  zqzzqzzvzzvzzvzzzzzzzzzzzzzzzzzzzzzzvUzK0z00z00P00\
  0000zz2zz6zzBzzGqzKlzKczPZzUPvZKqcBhc6ch0Zl0Pq0Kv0\
  Gv06z02z00z00z02z2BqUKhqPczZUzhKzlGzP6z62z00z00z00\
  z00z00z00z00z00z00z02z06z0Bz0Gz0Kz0Pz0Zz0cz0hz0lv0\
  qv0vq0zl0zl0zh0zGUzU2zl0z }

frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }

END 20.0 PAR-FORMULA FILE==================================

Jim Muth

Thaddaeus Parker

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