May 18, 1997: Angry Fish | May 17 | May 19 | 1997 | FOTD Home |
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\
kpMflOahQXdSR`TMXVHTXNWTSZPYaLbdHZZOVUVbaYjj`qrcyz\
fpz_hzT_yMRyFQvFQrEPoEOkENhDNdDMaDLZDKVCKSCJOCILBH\
HBHEBGAAF7AJADNCFQFIUHKXKNZMQ00h00ekTXnWZrYau_cvBV\
tEWrGWpJXnLYlOYjQZiT_gV_eY`c_`aba_dbYgbWicZf``cZc`\
WfYUhVRkRPmOMpLKsIHuFFxCC0yJ0yJ0xK0xK0xK0xL0wL0wL0\
wL0vM0vM0vM1uN2tO3sP4rQ5qQ6pR7oS8nT8nT9mUAlVBkWCjW\
DiXEhYEhYDdXDaXCZWCWWCTWBQVBNVAKUAHUAEUBLZBRbBXfCb\
jChnCnrCtvCzzEywFyuGysHyqJyoKymLykMyiNxgOxePxcRxaS\
x_TxYUxWVxUUvSTuQStPRrNQqMPpKOoINnHMlFLkEKjCOjGRiL\
ViPZiTbiYehaihemhipgntgrshqshqripqipqjopknoknnlmnl\
mmmljnmfnncoo`opYpqUqrRqsOrsLrtHsuEtvBtw8ux4uy1vz4\
uv8trBsnFrjIqeLpaPoYSnUPqTLtRIwQFyPEuRErTEoVEkXDhZ\
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=====================================