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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With an unexpected load of work to get out, I have time for only a short discussion of today's image. The image is a scene in Seahorse Valley. It looks nothing like the familiar valley because it is sliced through the Julibrot in a new direction. To visualize the direction, imagine the Seahorse Valley area of the M-set extending as a 3-D figure in front of and behind the screen as it would when the real and imaginary parts of Z are perturbed equally. Then imagine a horizontal slice through this 3-D figure cut 0.05 above the X-axis. And then imagine yourself looking down on this slice from above. Or better, forget the imagination. From this angle, Seahorse Valley appears as a 'bridge' spanning the width of the Julibrot. The impossibly straight edges are typical of scenes in the odd planes. There is an explanation for why this is so, but it will have to wait until I have more time to write it. Until then, enjoy Seahorse Valley as you have never seen it before. I named the image "The Golden M". The reason for the name is obvious when the image is seen. The rating of an average 5 combines with the render time of 16 minutes to give an overall value of 31. The value may be increased by downloading the finished GIF image from: The sun shone and the temperature rose to 46F 8C on Wednesday here at Fractal Central. The cats enjoyed the pleasant conditions to the best of their ability, and when the sun went down, came inside without complaint. Only a small treat was needed to satisfy their meager desires. Today is starting cloudy, but it is still mild. It will be another good day for the cats. For me, it remains to be seen how the trip into the fourth dimension will go. But however it goes, whatever I find there will appear as the next FOTD. Until then, take care, and keep your feet on the ground and your head in the clouds. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
The_Golden_M { ; time=0:16:10.54--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2 passes=t logmap=yes
center-mag=-0.00128325508607199/-0.000000000000004\
55/159.0018/0.01505/90/-5.05012698326368081e-014
params=45/90/0/0/-0.75/0.05/0/0 float=y
maxiter=100000 inside=0 outside=summ periodicity=10
colors=000NuPNrQOpSOmTPkVPhWQfYQcZR``RZaSWcSUdTRfT\
PgUMiUKjWJiXIiZHh_GhaFgbEgcEgeDffCfhBeiAek9dl8dm8d\
bIaTRZJ`W9iTDeVHbWL_XPXYTUZXR_`OadLbhIclFdpCet9fw6\
gqHdlRbg`_hjYmqWmoTmmQmkNmiJmgFmeBmd8meAmfCriAml9m\
n7uq6xr5uo4sk4qh4qe4pc4oa4n_4mZ3mY3nX3oW3pV3qU3rZ3\
rV3rT7mRBhOFcMIZJMUHQPFUKFXEH`8Id7Kh6Mk5No4Ps3Rw3S\
z8XrD`kIddNhYSmRXqKauDfy6bu9_qCXmFTjIQfKYbNJ_QGWTD\
SV9PYaL`mHmcEeUHrcKmcMcmKccScEUcHXcJZcLacfdhQfmSim\
VlmXnmZqm`smZpmYmmWmmVmmTmmSmmQmmOmmNmmLcmacmZQmXO\
mUMmRKmPImMGoKEpGGqDHrAJr7Ks4Ls8NtCOtGPtKRtOStSTtW\
Vt_WtcXtgZtk_to`tsbtwctzdtxfqvgouhmsjmqkmplmnmmlon\
kpoiqphrqfqrepsdotcnubmvalw`kxblycmzdnzfozgpzhqzir\
zkszltzmuzovzpwzqxzryzpzzozzmzzlzzjzzizzhzzfzzezzc\
zzbzz`zz_zzZzzbzzezzhzzkzznzzozzpzzpzzqzzqzzrzzszz\
szztzztzzuzzvzzvzzwzzwzztzzrzzozzmzzjzzhzzfzzczzaz\
z_zzYzzWzzUzzSzzQzzOzzMzz }
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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