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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I enjoy trees, and since real trees are fractal in nature, it should be no surprise that tree-like figures are found in fractals. Today's image pictures one of these fractal trees. I originally had named the picture "Tree", but since the tree in the picture is but one of an infinity, I finally decided on the name "Fractal Forest". The image is almost, but not quite, part of a Julia set of the (-Z)^1.618034+C Julibrot figure. It is not a Julia set because the direction of the slice is rotated 1.8 degrees from the Julia direction. This slight rotation makes little difference in the overall appearance of the image, though it does give the 'tree' a more stylized appearance. This type of image is quite common in the world of fractals, and it is closely connected to a rocky-landscape type of image that I occasionally investigate. In a day or so, I'll give an example of the rocky landscape hiding in today's tree-like image. I used John Goering's formula to draw the image and do the rotating. This formula can draw more orientations within the Julibrot than any other I know of, though there are still some directions that it cannot reach. The attached parameter file renders in a couple minutes, which is fast enough for all but the busiest fractaliers. For those busy fractaliers, the GIF image will soon be posted on Paul's web site at: The fractal weather today was near-perfect, with blue skies, puffy clouds, and a happy-cat temperature of 82F (28C). Unfortunately, the cats were so happy that they spent most of the day sleeping. As for me, I'll have to spend most of the day working. And the day is just starting. But I shall return with a new FOTD in 24 hours or so. Until that glorious moment arrives, take care, and enjoy the day. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_Forest { ; time=0:02:54.55--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=SliceJB-new-min passes=1 center-mag=0.\
224291/2.56739e-016/12.49983/1.0776/90 params=0.51\
/0.5/0.5/0.5/1.618034/0/-1.153365/0/0/0 float=y
maxiter=1800 inside=0 logmap=5 periodicity=0
colors=000FFQFFQFFPFFPFFPFFOFDOFDOFDMFDMFDLFDLFDLF\
DJFDJFDIFDIFCIFCGFCGFCGFCFFCFFCDFCDFCDFCCFCCFAAFAA\
FAAFA9FA9FA9DA7DA7DA6DA6DA6D94D94D93D93D93D91D91D9\
1D90D90D90D70D70D70D70D70D70D70D70D70D70D70D60D60D\
60D60D60D60D60D60D60D60D60D60F70G90IA0JA0JC0LD0MF0\
OF0PG0PI0QI0SJ0TL0TM0VM0XO0YP0_P0_Q0`S0aT0cT0cV0dX\
0fX0gY0i_0i`0j`0la0mc0ld0mc0mc0mc0mc0mc1mc1mc3mc3m\
c4oc4oc6oc6oa7oa7oa9oa9oaAoaApaCpaCpaDpaDpaFpaGp`H\
p`Ip`Jr`Kr`Lr`Mr`Nr`Or`Pr`Qr`Rr`Sr`Ts_Us_Vs_Ws_Xs_\
Ys_Zs__s_`s_au_bu_cu_duYeuYfuYguYhuYiuYjvYkvYlvYmv\
YnvYovYpvXqvXrvXsxXtxXuxXvxXwxXxxXyxXzxXzxXzzYzyXz\
xXzvXzuXzsXzrXzpXzoXzmXzlXzjXziXzgXzfXzdXzcVzaVz`V\
z_VzYVzXVzVVzTVzQVzPVzOVzMVzLVzJVzIVzGTzFTzDTzCTzA\
Tz9Tz7Tz6Tz4Tz3Tz1Tz0Tz0Tz0Tz0Tz0Uz0Uz0Vz0Vz0Wz0Wz\
0Xz0Xz0Yz1Yz1Zz3Zz3_z4_z4`z6`z6az7az9bzAbzAczCczDc\
zDczFczGczGczIczJczLczLcz
}
frm:SliceJB-new-min {; by John R. H. Goering, July 1999
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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