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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Do fairies, elves, gnomes, sylphs, etc. exist? Of course they do. Every culture on earth is rich with stories and legends of fairies. But since fairies, just like dragons, do indeed exist, are they then real? The answer to that question depends on the meaning one gives to the word 'real'. Not yet being in my deep philosophical mode, I'll not at this time state my opinion of the meaning of the word 'real', but if fairies do not dwell in the intricacies of the garden-like scene of today's fractal, what then does? The formula that drew the image, TowerMinExp04a, is one I rarely use. It is but one in a remote series of 26 such formulae, which pile up the exponents of Z into exponent towers. The four functions in today's formula merely add variety. I named the image "Fairy Gardens" when a lawn fairy flew past the window while I was trying to think of a name. The image is a bit too busy and fragmented for a very high rating, but the 6, which is a little above average, is satisfactory. As long as my FOTD's rate above a 5, I'm satisfied with them. I'll not divulge at this time whether I believe in magical things such as fairies, and yes even dragons. I will state however that I believe in some things that many consider weird or downright kooky. My beliefs are not limited by the discoveries of science, nor by common sense or reason, though I certainly do occasionally use these attributes. The parameter file of today's image, which is attached to the bottom of this letter, renders in 2-1/2 minutes. For extra convenience, the GIF image file is or soon will be posted to the W.W.Web at the URL: I read recently that the venerable Fractint fractal generating program is over the hill, on its last lap, abandoned by all but a few backward fractalists in favor of more advanced fractal generating programs with glittery advanced features such as true-color, multiple layers, transforms, etc. Well, one would never guess it here at Fractal Central, where the old warhorse program continues to do what it was designed to do -- find fractals. It's not that I have no other programs -- three other fractal generating programs are on my drive. But I rarely use them. Other than true-color, which is Fractint's greatest lack, I feel that the other features of the state-of-the-art programs are leading us from the basic idea of fractals. We are drifting from a "look what I found" attitude to a "look Ma, I'm an artist" attitude. When the fractalist does more work on an image than the numbers, perhaps the resulting image should be called something like computer art, rather than fractal art. I guess I have never been able to make the switch from admiring the things the numbers have done to admiring the things I have done. Maybe my reluctance to embrace the newer programs is due to the fact that I had been working with graphic programs such as Photoshop long before the same image manipulating features appeared included in fractal programs, and I therefore failed to be impressed with such features. (Of course, the features are far less expensive when part of the actual fractal program.) I also find myself amused at the extreme concern on the Fractal-Art list about copyright infringement. Fractals are fun -- they're philosophical, mystical and scientific at the same time. They're not a means of becoming wealthy. Do we really think that someone is going to steal our fractals and get rich from our efforts? If anyone were planning to do this, they certainly would not post their stolen goods on the Web for the whole world to see. I started the FOTD almost exactly 4 years ago for the fun of it. I continue the FOTD 4 years later for the fun of it. If it were not fun, I would have grown bored with the effort years ago and stopped posting. But I have no intention of ending the FOTD in the foreseeable future, because I know that finding fractals will be as much fun in 2005 as it is in 2001 and was in 1997. The fractal weather today was a big improvement over yesterday. A warm sun brought the temperature up to 61F (16C), and brought out the fractal cats into the yard for an afternoon's romp in the new grass. The rush is easing somewhat, but there's still lots to be done. Between other stuff I'll find time for another FOTD in 24 hours. Until then, take care, and watch out for the fairies as you trim your newly greened lawn. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fairy_Gardens { ; time=0:02:30.77--SF5 on a P200
reset=2001 type=formula formulafile=tower.frm
formulaname=TowerMinExp04a function=sqrt/sinh/acos\
h/tanh passes=1 center-mag=1.39458/-1.16573e-015/3\
.617023/1.0776/90 params=3.91/0/3.75/0/-3.215/0
float=y maxiter=250 inside=bof60
logmap=yes periodicity=10
colors=000zzzVLRD9Q00N00P00R00T01V13X34Y46_67a89c9\
AeBCfCDhEFjFGlHInJJoKLqMMsNOuPPwQQxPPuOOrNNoMMlLLj\
KKgJJdIIaII_HHXGGUFFREEODDMCCJBBGAADAAB7A95A82A70A\
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NO7OP8PR9QTARUBSWCTYDTZJWYPYYV`Y`bXfeXkgXheWecVcbU\
``UY_TWYSTXRQVROUQLSPIQPGPODNNAMM8KM5JL2IK0IK1KO2N\
S3QW4T_5Wb6Zf7aj8dn7fp8gq8fq8dq8bq9_q9Xq9Vq9TqARqA\
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E9aFAaGAbHBbJBcKBcLCcNCdODdPDeRDeSEfTEfTEfTEfTFcTF\
`TFYTFVTFSTEPTEMTEJTDGTDETDFUCFTCGSCGQBGPBHOBHNBHP\
AHQAHR9HS9HT9HU8HW8HX8HY7HZ7H_7H`6Ha6Hc6Hd5He5Hf5H\
g4Hh4Hi4Hh1Kg0Mh0Ng0Og0Pg0Qg3Rg5Sg7TgAUgCUfEVfGWfJ\
XfLYfNZfQ_fS`fU`eWagXVjYT
}
frm:TowerMinExp04a {; Jim Muth
z=pixel, c=p2+(p3*pixel):
z=z^fn1(z^fn2(-z^fn3(z^fn4(-z+p1))))+c,
|z| <= 100
}
END 20.0 PAR-FORMULA FILE==================================
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times.
