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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Though today's image might not be the most beautiful scene ever discovered in the Z^2+C Julibrot, it must be one of the most unusual. Viewing the image, we once again find ourselves in the East Valley area, but what has happened to the valley we know so well? Where are the elephants? In today's image there is not the slightest sign of the ponderous pachyderms that live in the vicinity. Don't panic. The elephants have not stampeded off. They have simply been squashed beyond recognition, leaving us with something that resembles a surrealistic mathematical hill standing on an alien planet, under a very earthly blue sky, complete with a haze layer near the horizon. Nothing beyond the basic equal-iteration bands has been used to render the scene. The only extraordinary aspect of the image is the fact that it has been stretched in the vertical direction almost 100000 times. Things become quite squashed as we near the tip of East Valley and view it from the unimaginable direction of today's image. The stretching I did on the image was necessary so that it would consist of more than a straight, featureless razor-edge. I named the image "The Fractal Hill". It does rather resemble a hill, and it most certainly is a fractal. I put some extra effort into coloring the scene, which raises its rating to a 7. When the render time of over 10 minutes is considered, the overall value comes in at a 67. And when the pre-rendered image is downloaded from Paul's web site at: With lots of sun and a temperature of 50F 10C, Sunday was fair enough here at Fractal Central. The cats must have thought so also, because they spent over three hours lounging in the yard, and when they came in, only a small bit of tuna was needed to keep their moods up. Today is starting sunny and pleasant once again. We shall see how the cats' day goes. For me, it will be another relatively uneventful day -- that is unless finding a great fractal can be considered a big event. Regardless of what happens, the next FOTD will appear in 24 hours. Until then, take care, and there's a hill beyond the hill beyond the hill . . . Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
The_Fractal_Hill { ; time=0:10:23.02--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2 passes=1
center-mag=+0.25009805052166050/+0.519661012667224\
50/28984.82/9.451e-005/90/3.64113739159677152e-011
params=45/90/0/0/0/1e-006/0/0 float=y
maxiter=100000 inside=255 logmap=297 periodicity=10
colors=000PNzQOzRPzSQzTRzUSzVTzWUzXVzYWzZXz_Yz`Zza\
_zb`zcazdbzeczfdzgezhfzigzjhzkizljzmkzmlzmmzmmzmmz\
mmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmm\
zmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzm\
mzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmz\
mmzmmzlmzlmzkmzkmzkmzjmzjmzimzimzimzhmzhmzhmzgmzgm\
zfmzfmzfmzemzUmLUmMUkLUjLUiLUgLUfLUeLUdLUbLYaLZ`M_\
ZOZYQYXSXWUWUWVTYUS_TQaSPcROhQNrPLkOKbNJZKHSKGSKFS\
KESKCSKBSKASK8SK7QK6OK5MK3KK2IK1IK0IKANKKSPUXUbaZa\
aiaacaaUaaUaaA`aB`aB`aC`aC`aDcaE_aE_aF_aF_aG_aHWaH\
ZaIZaIZaJZaJZaKYaLYaLYaMYaMYaNXaOXaOXaPXaPXaQXaRWa\
RWaSWaSWaTWaUVaUVaVVaVVaWVaWVaXWbXWbYWbYWbYWbZWbZW\
b_Wb_Wb_Xb`Xb`XbaXbaXbaXbbXbbXbcXbcYbcYbdYbdYbeYbe\
YbeYbfYbfYbgZbgZbgZbhZbhZbiZbiZbiZbjZbj_bk_bk_bk_b\
l_bl_bm_bm_bn`cm_bm_bm_bm`em`emaemaembembdmcdmcdmc\
dmccmccmccmccmcbmcbmcbmcb }
frm:SliceJulibrot2 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
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)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z| <= 9 }
END 20.0 PAR-FORMULA FILE==================================
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