Fractal of the Day
by Jim Muth
FOTD -- December 13, 1998
Fractal visionaries:
Today started sunny, but grew increasingly cloudy as the afternoon progressed, until by nightfall it was totally overcast and threatening rain. The temperature of 45F 7C made it the first day in a month on which the temperature was not above average.
Of course, it was a perfect day for hunting fractals as well as pondering the mysteries of existence. Unable to decide which path to follow, I both hunted and pondered. The fractal I found is a scene in the Z^1.5 Julibrot.
Experienced fractalists know that the Z^1.5 Julia set with a C-value of -0.195 appears as a trilobite shaped figure with tree-like objects spotted around the edge. These fractal trees are totally missing in the Mandelbrot view of this area, causing me to wonder what happens to them as the view is rotated from Julia to Mandelbrot.
I found that rotating the view as little as 1 degree from the Julia plane causes the lovely symmetrical trilobite and its surrounding trees to totally break down. What, I wondered, would this scene look like in the odd planes.
Having already written a formula that does this rotation, I set out to follow the shadow of the trees as far as I could. I ended up in an oblique odd plane closest to the Elliptic direction.
Today's FOTD, which I have named "Tree from the Side", is a side view of one of the tree-figures in the Z^1.5 Julia plane. I cranked up the colors a bit in Photoshop, but made no other changes. The GIF file of the finished product has been posted to the newsgroup:alt.binaries.pictures.fractalsand to the WWW at:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
In addition to fractal hunting, I did some pondering today. What set me off was a newspaper article that appeared a few days ago. That article reported that Japanese scientists have successfully cloned four cows. If we have reached the stage where we can clone cows, can cloning people be far behind?
One of life's greatest mysteries is the simple question, "why am I me and not someone else?" This is the question that brought the angel to earth in the film "Wings of Desire". The scientific answer is that the existence of each individual one of us is an accident, brought about by an almost impossibly fortuitous arrangement of particular genetic material, or of DNA or perhaps of individual atoms.
This answer seems the only one possible, but it does not really answer the question. It leaves one unsatisfied. Identical twins, even quintuplets, start with the same atoms, the same genetic material, the same DNA, yet they are different individuals. They are not the same person in several places at the same time. And now we are soon to have clones.
Theoretically, it would be possible to create a million, a trillion, even a googol of clones of an individual. Given an eternity, there could be an infinity of identical versions of that person filling an infinity of universes. There is no limit, yet they would not be the same awareness. They would be an infinity of unique awarenesses in identical bodies. They would look the same, but would they behave the same? I know two identical twins, and they do not behave as though they were the same person.
What then is the total number of unique awarenesses possible? The answer, apparently, is an infinity. This means that the chance of any individual happening by accident is one divided by infinity, or zero. Therefore it would appear that it is impossible for any of us to exist.
Of course, each of us does exist, so there must be a flaw in my reasoning. I guess it's back to my pondering chair to search for that flaw. But flawed or not, I'll be here again tomorrow with another fractal if not an answer. Until then, take care, and think fractals.
Jim Muth
jamth@mindspring.com
START FORMULA================================================
mult1-5-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=z^1.5+c,
|z| <= 36 }
END FORMULA==================================================
START PARAMETER FILE=========================================
Tree_from_the_Side { ; 10min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=multirot.frm
formulaname=mult1-5-XZ-YW passes=1 center-mag=0.400\
405/-0.00715304/62.99038/0.1064/-3.028/-50.419
params=24/73/-0.195/0/-0.195/0 float=y maxiter=3000
bailout=25 inside=0 logmap=13 symmetry=none
periodicity=10 colors=0000J42H42H44H44G46G26G28E2AE2\
AE2CC2CC2EA2EA2GA0G80H80H80J60J60L60L40N40L22N40P60P\
80R80RA0TC0TC0VE0VG0XG0XH0ZJ0ZJ0`L0bN0bN0dP0dR0eR0eT\
0gV0gV0iX0iZ0kZ0k`0mb0mb0od0qe0qe0sg0si0ui0uk0vm0vm0\
xo0xq0zq0zs0zu0zu0vq0<2>kk0ei0bg0Ze0Vb2R`6LZAHXCEVGA\
TJ6RL8TN8VN8VP8XP8XP8ZR8ZR8`R8`T8bT8bT8dV8eV8eXAgXAg\
XAiZAiZAkZAk`Am`Am`AobAqbAqdAsdAsdAueAueCveCvgCxgCxg\
CziCziCzkCzkCzkCzmCzmCzmCzoCzoCzoEzmEzkEzkEziGzgGzgG\
zeGzeGzdHzbHzbHx`HxZJvZJvXJvXJuVJuTLsTLsRLqPLqPNoNNo\
NNoLNmJNmJPkHPkGPiGPiEPiEXgEbdGibPo``vXkzVuzTzzRzzPz\
<8>zPzzPzzNz<2>zNzzNzxNzxNzvNz<2>uNzuNzsLzsLzqLzqLzo\
LzoLzmLzmLzkLzkLziLziJzgJzgJzeJzeJzdJzdJzbJzbJz`Jz`J\
z`JzZLzZLzZNzZNzZNzZPzZPzZRzZRzZRzZTzZTzZVzZVzZVzXXz\
XXzXXzXZzXZzX`zX`zX`zXbzXbzXdz<2>XezXezVdzXezXgzZgzZ\
izZkz`kz`mz`mzbozbqzbqzdszduz
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Tree_from_the_Side { ; 10min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=multirot.frm
formulaname=mult1-5-XZ-YW passes=1 center-mag=0.400\
405/-0.00715304/62.99038/0.1064/-3.028/-50.419
params=24/73/-0.195/0/-0.195/0 float=y maxiter=3000
bailout=25 inside=0 logmap=13 symmetry=none
periodicity=10 colors=0000J42H42H44H44G46G26G28E2AE2\
AE2CC2CC2EA2EA2GA0G80H80H80J60J60L60L40N40L22N40P60P\
80R80RA0TC0TC0VE0VG0XG0XH0ZJ0ZJ0`L0bN0bN0dP0dR0eR0eT\
0gV0gV0iX0iZ0kZ0k`0mb0mb0od0qe0qe0sg0si0ui0uk0vm0vm0\
xo0xq0zq0zs0zu0zu0vq0<2>kk0ei0bg0Ze0Vb2R`6LZAHXCEVGA\
TJ6RL8TN8VN8VP8XP8XP8ZR8ZR8`R8`T8bT8bT8dV8eV8eXAgXAg\
XAiZAiZAkZAk`Am`Am`AobAqbAqdAsdAsdAueAueCveCvgCxgCxg\
CziCziCzkCzkCzkCzmCzmCzmCzoCzoCzoEzmEzkEzkEziGzgGzgG\
zeGzeGzdHzbHzbHx`HxZJvZJvXJvXJuVJuTLsTLsRLqPLqPNoNNo\
NNoLNmJNmJPkHPkGPiGPiEPiEXgEbdGibPo``vXkzVuzTzzRzzPz\
<8>zPzzPzzNz<2>zNzzNzxNzxNzvNz<2>uNzuNzsLzsLzqLzqLzo\
LzoLzmLzmLzkLzkLziLziJzgJzgJzeJzeJzdJzdJzbJzbJz`Jz`J\
z`JzZLzZLzZNzZNzZNzZPzZPzZRzZRzZRzZTzZTzZVzZVzZVzXXz\
XXzXXzXZzXZzX`zX`zX`zXbzXbzXdz<2>XezXezVdzXezXgzZgzZ\
izZkz`kz`mz`mzbozbqzbqzdszduz
}
frm:mult1-5-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=z^1.5+c,
|z| <= 36 }
END 19.6 PARAMETER-FORMULA FILE==============================
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