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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: On and off over these past several days I've been searching for the ultimate fractal tree. I think I found its shape this afternoon, though the complete properly colored tree still eludes me. The simple formula (-Z)^1.075+C led the way. I found the tree growing in an oblique slice of the Julibrot of this formula, at the coordinates C=4,Z=1.9. The orientation of the slice is totally oblique, but closest to the Julia direction. I like this fractal tree because it is not symmetrical, but has instead the near-symmetry and imperfections of a real tree. Unless I'm mistaken, the tree even has a few broken limbs that need trimming. Since the formula contains 5 complex parameters, patch 13 or 14 of fractint version 20.0 must be used to do the calculation. And the calculating formula, SliceJB-new-min, is a small rewriting of the SliceJB formula posted in July 1999 to the Fractint list by John Goering. Taking advantage of the two additional complex parameter entries in patches 13 and 14, I have added a variable initialization of Z and a variable exponent of Z. In coloring the image I made no effort to be realistic, choosing instead a striking magenta and green palette for the tree, surrounded by a dull blue and brick-red background. Perhaps a bit optimistically, I named the result "The Ultimate Tree". I say optimistically because I doubt if today's image is the last tree I'll post in my current tree series. After considering the picture's strengths and weaknesses, I gave it an above-average rating of 7. The parameter file renders in 2 minutes if you have the proper version of Fractint. It downloads in about the same time if you don't. The image file ready for download may be found at: The fractal weather today was very perfect, with sunny skies and a temperature of 78F (25.5C), which brought out the best in the fractal cats. I'm still trying to recover from yesterday's unexpected outburst of fractal philosophy. It's really exhausting when one spreads such wisdom. And much more is brewing, but not yet finished. It might appear tomorrow, it might not appear for a week. Keep checking the Philofractal list; you wouldn't want to miss the enlightenment. I find that I'm out of things to say, so there's nothing left to do but shut down the fractal shoppe, call it a night, and see what kind of junk I can find on the telly. Until next time, take care, and only my humility prevents me from telling how great I am.  Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Ultimate_Tree { ; time=0:02:00.30 -- SF5 on a P200
; Version 2000 Patchlevel 14
reset=2000 type=formula formulafile=critical.frm
formulaname=SliceJB-new-min passes=1 center-mag=0.18\
3845/0.0285631/2.806587/1.2255/90/-6.088
params=0.4502/0.4315/0.3702/0.3897/1.075/0/4/0/1.9/0
float=y maxiter=1500 inside=0 logmap=30 periodicity=9
colors=000H8A<2>M6AN6AO68<13>76K66K56L<3>16O<23>n3dp\
3er3f<3>z3h<3>sBOqDIpFDnH8mI3<25>mhTmiUmjV<3>mnZ<2>x\
oW<14>klajlaikb<3>fkcelddld<3>aneUo`MoW<17>IxLIxKIyJ\
<4>HzGHzGHzF<14>9zC8zC8zB<3>6zB<15>NzJOzKPzK<3>TzMVz\
K<8>PzaPzcOze<2>NzkMzmNzm<16>HzoHzoGzo<2>FzoFzoEzq<4\
>IzjJziKzh<3>NzcEzdBzj<2>GzY
}
frm:SliceJB-new-min {; adapted from John R. H. Goering
pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1),
b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a),
cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d),
sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg,
s=v*sin(a), c=p+flip(q)+(p4), z=r+flip(s)+(p5):
z=(-z)^(p3)+c
|z|<=100
}
END 20.0 PAR-FORMULA FILE==================================
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