Fractal of the Day
by Jim Muth
FOTD -- December 31, 1998
Fractal visionaries:
The weather turned very cold today here at Fractal Central. The afternoon temperature of 22F -6C and 30 knot winds made fractal hunting the preferred activity. And whenever an activity is preferred, I do it. So today I hunkered down and hunted fractals.
But before getting to the fractal, I have a joke of the day to tell. The joke is a get-rich-quick letter I found in my e-mail box this morning. Here is a shortened version:
START LETTER=======================================
Dear Friend:
Are you tired of not having the money to live the life you
deserve? I was until I determined to do something about it.
After many months of failures, I finally discovered a secret
program that requires little effort and virtually forces people
to give me money! I am now willing to share this secret with
you. To show that you seriously want to be wealthy, please send
seventy-five (75) dollars to me.
END LETTER=========================================
Posting to Usenet as I do, I receive many such letters, but this letter is one of the most blatant. As I read the letter, I wondered, "how am I supposed to get rich by giving money to someone else?" Then I thought, "is there anyone who needs to prove that they would prefer to be wealthy?"
True, the one who sent the letter does indeed have a secret method of getting money, and that secret method is to get people to send 75 dollars to him. But the greatest question is, will anyone actually be taken in by this scam? If no one responded to such letters, there would not be so many of them floating around on the internet.
While I'm writing my check, 
I'll take a few minutes to talk about the topic of the day, which is fractals. Today's fractal is a scene in the area around Z^(-1.618). It's a simple midget with overlapping areas of widely separated iteration. The gaudy colors remind me of the decorations at a New Year's Eve party, so I named it "Happy New Year".
The parameter file is a slow one, so I advise downloading it from Usenet at:alt.binaries.pictures.fractalsor from the WWW at:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow, I'll return with another fractal and another few words of wisdom. Until then, take care, and don't get stung. Don't reply until you receive a letter that reads, "please show that you want to be wealthy and I'll send money to you!"
Jim Muth
jamth@mindspring.com
START FORMULA================================================
MandelbrotMix7 {; 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=pixel:
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| <= l
}
END FORMULA==================================================
START PARAMETER FILE=========================================
Happy_New_Year { ; 4-1/2hr on 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1
center-mag=-0.27079874054616540/+0.36014196341808110\
/4.903311e+008/1/-174.999 params=1/-1.618/-1/-1.619/\
1000/0 float=y maxiter=24000 bailout=25 inside=0
logmap=668 symmetry=xaxis periodicity=10
colors=000HBMZ3F5qIOfJeXJZcPgYNoSLRrw<2>oVTqWcV8OiGL\
iMYnNTsNO0bpUV_w0dw9UuZvwcSwYPwSMb7YiDTpIOWR9XAEDHL\
<2>lMJEay2gv<2>iSTOoCe`G5reOgYWIGeFdrJzOox<2>nUTzlYJ\
dUXZQjTMMsiZh`kYSEW_`RRUP1wW6hTAwQFzTs<2>wOSJlxXcjjV\
XOexVOV<2>pNMJD`cISu3JxBm<2>wKQWMUeNQnNMMkR<2>nTLh0x\
pAc`SMlPK4s`iZJM9e<2>nKOHcLbVKO5MeEKJ9y<2>mKTYFU<2>q\
LLGCoaIZe77nFDDS0t5ix84wC8wGCwKGu_uvVhwRWaBalHSr8qtD\
evIUlURpROtPLvsK`EVlJPtlIibJ0YFKUHcQI3eL<2>iRJ60nXBZ\
T7MgOe96HnjxqdmsZczgTkV5<2>tPGfhkYjqPlw<2>KkpB`j3QeQ\
27SfcchkoirzzzfaoOUe5MXKW_YdaddXvdQjdSqdNzdArdyudced\
fZddkeUbfgihZpjRml8<2>upHBqxOrm_scktTvuxwvjwwX8xzQyk\
fzXkzHqzIYzhfz_ozRDzA9zeZzUqzZszTuzOAz`uzgvzVbzqizep\
zU1zPJzQczMSzfgzVXzN2zLDzBTzEhzHrzmtzbvzTrzXtzSvzNKz\
tYzgjzV1zmwz7wzDPz4`z9lzEqzVszRuzNczzpz5bzyhz\
nmzcrzTzzG
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Happy_New_Year { ; 4-1/2hr on 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1
center-mag=-0.27079874054616540/+0.36014196341808110\
/4.903311e+008/1/-174.999 params=1/-1.618/-1/-1.619/\
1000/0 float=y maxiter=24000 bailout=25 inside=0
logmap=668 symmetry=xaxis periodicity=10
colors=000HBMZ3F5qIOfJeXJZcPgYNoSLRrw<2>oVTqWcV8OiGL\
iMYnNTsNO0bpUV_w0dw9UuZvwcSwYPwSMb7YiDTpIOWR9XAEDHL\
<2>lMJEay2gv<2>iSTOoCe`G5reOgYWIGeFdrJzOox<2>nUTzlYJ\
dUXZQjTMMsiZh`kYSEW_`RRUP1wW6hTAwQFzTs<2>wOSJlxXcjjV\
XOexVOV<2>pNMJD`cISu3JxBm<2>wKQWMUeNQnNMMkR<2>nTLh0x\
pAc`SMlPK4s`iZJM9e<2>nKOHcLbVKO5MeEKJ9y<2>mKTYFU<2>q\
LLGCoaIZe77nFDDS0t5ix84wC8wGCwKGu_uvVhwRWaBalHSr8qtD\
evIUlURpROtPLvsK`EVlJPtlIibJ0YFKUHcQI3eL<2>iRJ60nXBZ\
T7MgOe96HnjxqdmsZczgTkV5<2>tPGfhkYjqPlw<2>KkpB`j3QeQ\
27SfcchkoirzzzfaoOUe5MXKW_YdaddXvdQjdSqdNzdArdyudced\
fZddkeUbfgihZpjRml8<2>upHBqxOrm_scktTvuxwvjwwX8xzQyk\
fzXkzHqzIYzhfz_ozRDzA9zeZzUqzZszTuzOAz`uzgvzVbzqizep\
zU1zPJzQczMSzfgzVXzN2zLDzBTzEhzHrzmtzbvzTrzXtzSvzNKz\
tYzgjzV1zmwz7wzDPz4`z9lzEqzVszRuzNczzpz5bzyhz\
nmzcrzTzzG
}
frm:MandelbrotMix7 {; 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=pixel:
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| <= l
}
END 19.6 PARAMETER-FORMULA FILE==============================
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