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May 18, 1997: Angry Fish May 17 May 19 1997 FOTD Home

angry fish

Fractal visionaries:

The first thing a fractal explorer discovers is that the inside of the fractal lake, where the points are trapped, is a pretty dull place.  You just don't go looking there for interesting images.  True, one can add a bit of color by searching out finite attractors, but the result is still rather dull.

A while back I decided to see if I could do something about this situation.  I wrote a series of experimental formulas called Mystic.  Mystic1 did little of interest, but Mystic2, attached below, was a real winner.  The last line of the formula, g=sqr(g), assures that the fractal itself, with the inside set to a solid color, will be nothing more than a circle of radius one around the origin.  But there's a lot going on beneath the calm surface of that circle.

Set the inside to bof60 or bof61 and the fractal suddenly comes to life.  No longer a solid color, it is filled with intricate fractal detail.  The six variable parameters and one variable function give variety enough to satisfy any fractal explorer.  In today's picture for example, which I named kissfish because it reminded me of kissing fish, set the function to floor and watch the resulting explosion.

In addition to the seven variables, the image can sometimes also be changed by changing the maxiter or the periodicity setting.  This, however, is something I have not yet investigated.

These undersea fractals are also interesting in that they are quite unpredictable.  Different areas have totally different characteristics.  Zoom in on the edge of the circular fractal, and you never know what surprise awaits there.  A limitation exists in coloring possibilities because of the limited number of bands in these pictures, but this can be worked around.

BTW, I think I'm beginning to have second thoughts about longer formulas.  When I joined this list, I said that I liked my formulas as short and simple as possible.  I rarely included as much as a single transcendental function.  But now that I've seen what some of you are doing with longer formulas, I'm not sure how I feel.  I guess I'll just have to see how my future formula writing efforts develop.

Jim Muth
jamth@mindspring.com


START PARAMETER FILE FOR 19.6===================================

frm:Mystic2 {; Jim Muth
a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), k=real(p3), f=imag(p3),
g=pixel, z=(pixel)^a+(b*(pixel))^c:
z=(fn1(z)+(d*(g)))^k+(f*(cos(g)))
g=sqr(g),
LastSqr <= 100 }

Angry_Fish         { ; time=0:00:22.13-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=Mystic2 function=cosxx passes=2
  center-mag=0/0/1.6328 params=2/12/1/2/-10/1 float=y
  maxiter=90 inside=bof60 logmap=yes
  symmetry=xaxis periodicity=10
  colors=000NORETT5XUCWPKVJRTEYS8bQFgNLlLSpJYuGdzEjz\
  HkyLmyOnxSoxVpwZrwaskdmZhhNkbAnXFnVLoUQoSWoR`oPfpO\
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  De`DbbDZcDWeDTgCQiCMkCJmCGoMIiVKddMZmfdn`gpUkqOnrL\
  isIduF_vCUw9Px6KoBMeFNXKP }

frm:Mystic2 {; Jim Muth
a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), k=real(p3), f=imag(p3),
g=pixel, z=(pixel)^a+(b*(pixel))^c:
z=(fn1(z)+(d*(g)))^k+(f*(cos(g)))
g=sqr(g),
LastSqr <= 100 }

END PARAMETER FILE FOR 19.6=====================================