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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Since space is unbounded though not necessarily infinite, and today's image reminds me of a globular cluster in space, I decided to give today's image an unbounded rating. Regardless of what this means when applied to a fractal rating, today's image is different enough to be well worth a look. I named the image "Cosmic Un-Conquest" in sympathy with mankind, who, because he must carry a clumsy physical body with him wherever he goes, will never conquer even the solar system, much less the infinite multiverse. A temporary mind of limitless fancy trapped in a body of wet kleenex can do little more than sit here on earth, look up at the night sky and wish it were otherwise. But such is not the case with fractals, where we can venture wherever our computers and fanciful minds can take us. In today's case we journey to the land of Z2/(Z^(-2)+11)+C, which at first appears to be a blank screen consisting totally of inside stuff. But, as the 'bof61' fill reveals, this inside stuff is active. Today's image is unusual in that it is dependent on both the screen resolution and the choice of passes. Whenever one of these is changed, a different image will result, since different dots will be chosen or passed over. Perhaps the biggest drawback in the image is its rather slow calculation time of 10 minutes. But this drawback may be turned into an advantage by visiting the FOTD web site at: Fine midsummer weather prevailed here at Fractal Central on Wednesday, with a cat-pleasing temperature of 82F 28C and sunny skies. In my department things went pretty well also. As for the next FOTD, it will be posted in 24 hours, perhaps not as cosmic as today's but interesting nevertheless. Until then, let your mind soar where your body cannot. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Cosmic_Un-Conquest { ; time=0:10:07.25-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot passes=1 float=y
center-mag=-1.1400168468679/+1.308367613934373/\
1.048206e+007 params=0/0/0/0/0/0/0/0/-2/11
maxiter=1500 inside=bof61 logmap=yes periodicity=10
colors=000Fm4Em4Dn4Cn4Bn4Bo5Ao59p58p57p56q55q54q53\
r52r52r5Mp7eq8do9dnAcmBclCbkDbjEaiFagG`fH`eI_dJ_cK\
ZbLZaMZ`NYZOYYPXXQXWRWVSWUTVTUVRVUQWUPXTOYTNZSM_SL\
`TJ_SK`RL`RMaQNaQObPPbPQbORcOScNTdMUdMUeLVeLWeKXfK\
YfJZgJ_gI`hHahHbhGciGdiFdjFejEfkEgkDhkCilCjlBkmBlm\
AmnAnn9on9oo8poAqpzzzAsqAtqAuqAvrAwrAxsAysAyu3yt3y\
s3yrUUU3yqzpc3yo3yo4yn4ym4ym4ylkhz4yj4yj4yi5yh5yg5\
yg5yz5ye5ye5yd5yczmb6yb6ya6y`6y`6y_6yZzyY7yz7yz7yz\
7yz7yz7yz7yz7yz8yz8yz8yz8yz8yz8yz8yz8yz00000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
0000000000000000000000000 }
frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots
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),
aa=-(real(p5)-2), bb=imag(p5+0.00000000000000000001),
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)/(z^(aa)+bb)+c
|z| < 1000000 }
END PARAMETER FILE=========================================
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times.
