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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: At first glance, today's fractal, which I have named "Fractal Coronette" closely resembles yesterday's "Snakings" image. But actually, today's picture is totally different. Where yesterday's image was all bof60 inside fill, today's consists entirely of the old-fashioned flat equal-escape-time bands. I gave today's image its name when I noticed the solar eclipse effect in the upper right corner. Today's image was created with the M-Mix4 formula when I added 11 parts of Z^(-11) to Z and set the Fractint engine to the task. Although the resulting fractal had Minibrots all through it, I chose an area that had none. The converging arms, which draw the eye to a dead-end in the upper right corner, make quite enough impact without the need for one of those ubiquitous midgets. The image may be seen by running the attached parameter file or by downloading the JPEG file from: The fractal weather was sunny today, but an unseasonably cool 56F (13C) made a jacket the outfit of the day, and made the fractal cats shift to curl-up mode. While taking a break this afternoon, I picked up a copy of the Jan-Feb, 1996 issue of "Skeptical Inquirer". (I realize that it's a strange magazine to read for idle diversion while eating lunch, but then I'm a strange person.) In the letters section of the magazine I found the following statement, which was in a letter written by a professional behaviorist psychologist: "Consciousness is not something a person has; it is something a person does. . . . Consciousness is the behavior of observing one's own behavior." and in another letter: "To date, as far as I know, there has been no replicable experiment demonstrating the existence of consciousness. There likely will never be one because consciousness is just a word. There is simply nothing to prove. . . . Consciousness is the ether of the nineties." (I doubt if the writer of either letter could tell us what it is that anesthesiologists suppress at surgical operations.) When I read non-sensical statements such as these, made by supposedly clear thinkers in a magazine devoted to reason, I am a little less puzzled as to why mysticism is gaining popularity, while reason appears to be on a downward slide. And now, reason tells me that we've come to the end of another FOTD. It is reasonable to assume that the next FOTD will appear in 24 hours. Until then, take care, and sometimes reason is unreasonable. Jim Muth jamth@mindspring.com |
START FORMULA==============================================
MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END FORMULA================================================
START PARAMETER FILE=======================================
Fractal_Coronette { ; time=0:03:02.18 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=mandelbrotmix4 function=ident passes=1
center-mag=-0.02936019747837555/+0.1065182154805637\
0/620.751/1/180 params=11/-11/1/1/0/0 float=y
maxiter=1800 bailout=25 inside=0 logmap=10
symmetry=none periodicity=10
colors=000GFGVUthUu`UuTWs<4>JefHgdFia<3>7pT<13>FWRG\
VRHTR<3>JNQJLPKKP<2>LFPMEPKFU<3>P9DQ89R75S61<11>QKI\
QMJPOK<3>OSQOTROUTOVUOWVQXX<2>LTUKRTIPSHNRFLQ<3>9EM\
8CL6BK<3>14G<4>DDWFFZHGa<2>OMjQNmQPoSPsTQs<21>q`Cr`\
Asa8<3>wb1<17>MkiKlkIln<3>Anw<3>Lpm<3>WrnZrn`so<2>i\
tp<3>hvqhwrgwsgxtgxugbW<5>eh_ei`dj`<2>dmbdnbbl`<15>\
NWEMVDLUB<3>HQ6GP5FO3EN2<3>kkituw<6>o_foXdnUa<3>lGS\
kDQjAOj7Li4Jj0G<3>f4Je5Jd6Kc7Lb7La8MZWn<5>WVs
}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Fractal_Coronette { ; time=0:03:02.18 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=mandelbrotmix4 function=ident passes=1
center-mag=-0.02936019747837555/+0.1065182154805637\
0/620.751/1/180 params=11/-11/1/1/0/0 float=y
maxiter=1800 bailout=25 inside=0 logmap=10
symmetry=none periodicity=10
colors=000GFGVUthUu`UuTWs<4>JefHgdFia<3>7pT<13>FWRG\
VRHTR<3>JNQJLPKKP<2>LFPMEPKFU<3>P9DQ89R75S61<11>QKI\
QMJPOK<3>OSQOTROUTOVUOWVQXX<2>LTUKRTIPSHNRFLQ<3>9EM\
8CL6BK<3>14G<4>DDWFFZHGa<2>OMjQNmQPoSPsTQs<21>q`Cr`\
Asa8<3>wb1<17>MkiKlkIln<3>Anw<3>Lpm<3>WrnZrn`so<2>i\
tp<3>hvqhwrgwsgxtgxugbW<5>eh_ei`dj`<2>dmbdnbbl`<15>\
NWEMVDLUB<3>HQ6GP5FO3EN2<3>kkituw<6>o_foXdnUa<3>lGS\
kDQjAOj7Li4Jj0G<3>f4Je5Jd6Kc7Lb7La8MZWn<5>WVs
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 19.6 PAR-FORMULA FILE==================================
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times.
