Fractal of the Day
by Jim Muth
FOTD -- December 14, 1998
Fractal visionaries:
Today was a near perfect one for a fractal hunt, as a gray cold day with steady light rain always is. The temperature of 45F 7C made it just a bit too chilly to stay outdoors, but just right for plopping into a computer chair and typing "fr" (I run Fractint from a batch file.)
I found today's fractal early -- before the bell for the morning service rang at the church two blocks away. In fact, I found it at 10:50am, at the end of my first fractal search of the day. I began the day's fractalling by examining the East Valley area of the (-Z)^2 Mandeloid, wondering what happens to the midgets in the elephant trunk spirals as the exponent is set to ever lesser values.
My goal was to reach an exponent of 1.618..., but at that value I found the spirals had totally vanished. Backing off a bit, I first caught sight of spiral tendencies at (-Z)^1.65. Once I found the spirals, it was a simple matter to locate the midgets. I named today's picture "Embryonic Midget" because it is a picture of a midget not yet fully formed.
When the exponent of Z is 1.65, the spiral arms converge in powers of 1.65. Therefore we should find spiral arms numbering 1.65, 2.72, 4.5, 7.4, 12.2, etc. as they converge on the midget. The arms in today's fractal are highly fragmented, so an accurate count is impossible, but if all the fragments of the outer series of arms were added, the pieces would total something like 7.5 arms.
The midget itself holds much of interest, but if the full detail is to be seen, a fast machine is necessary -- unless one is willing to wait hours for the picture to trickle onto the screen.
Today's fractal is far more reasonable timewise. It draws in a few minutes. If a few minutes is too inconvenient, the GIF file has been posted to:alt.binaries.pictures.fractalsand to the Web at the URL:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Having found today's FOTD early, (and tomorrow's as well), and having no other immediate jobs to do, I got a chance this afternoon to sit and ponder further about the impossibility of my existence. But the unanswerable question remains unanswered. I do not know why, when I was born, that infant was me instead of simply one more someone who is not me, as all infants before and after have been.
Most likely, I'll ponder this question off and on for the rest of my days, as thinkers and non-thinkers have done for thousands of years. Of course, I shall find no answer, but finding the answer to the great mystery or not, I'll certainly find many fractals in the years to come.
That's it from 39N 77W for today. Tomorrow's fractal will be a geometrical one. To see the geometry, check here in 24 hours. Until then, take care, and never forget that fractals are fun.
Jim Muth
jamth@mindspring.com
START FORMULA================================================
MandelbrotMiN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=(-z)^(b)+c,
|z| <= 16
}
END FORMULA==================================================
START PARAMETER FILE=========================================
Embryonic_Midget { ; 20min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=slices.frm
formulaname=MandelbrotMiN passes=1
center-mag=+0.83644173784573540/-0.19333812277513170\
/1.590641e+008/1/-95 params=1.65/0/0/0/0/0 float=y
maxiter=12000 bailout=25 inside=0
logmap=112 symmetry=none periodicity=10
colors=000CRE<2>AWFAYF8`I<3>Da6Ag1<3>IT7JP8KN9<2>LHD\
JFEJCGI9HJ6IK4JJ5LJ5ML6NN6OP7PP7QR7R<16>3Eg<14>BHp6E\
o<21>scvudvzfx<22>WacUe`<11>XNqTLq<6>sOw<8>JXWFYT8XR\
LYQTZP<9>rcHqdGpfKogIhdG<5>XjSWkUWlWUmYNm_Ima<9>KmuK\
mwKmxKmyImz<22>_mzdmz<13>7mz<17>PmzHmz<9>smz<2>pmz
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Embryonic_Midget { ; 20min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=slices.frm
formulaname=MandelbrotMiN passes=1
center-mag=+0.83644173784573540/-0.19333812277513170\
/1.590641e+008/1/-95 params=1.65/0/0/0/0/0 float=y
maxiter=12000 bailout=25 inside=0
logmap=112 symmetry=none periodicity=10
colors=000CRE<2>AWFAYF8`I<3>Da6Ag1<3>IT7JP8KN9<2>LHD\
JFEJCGI9HJ6IK4JJ5LJ5ML6NN6OP7PP7QR7R<16>3Eg<14>BHp6E\
o<21>scvudvzfx<22>WacUe`<11>XNqTLq<6>sOw<8>JXWFYT8XR\
LYQTZP<9>rcHqdGpfKogIhdG<5>XjSWkUWlWUmYNm_Ima<9>KmuK\
mwKmxKmyImz<22>_mzdmz<13>7mz<17>PmzHmz<9>smz<2>pmz
}
frm:MandelbrotMiN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=(-z)^(b)+c,
|z| <= 16
}
END 19.6 PARAMETER-FORMULA FILE==============================
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