FOTD -- May 08, 2008 (Rating 6.5)
Fractal visionaries and enthusiasts:
I am often puzzled by dimensions. What are they? Are they
merely the number of mutually perpendicular lines that can be
erected through a single point in a given space? Or are the
lines a mere indicator of dimension? Where do dimensions come
from? Why is our universe limited to three spatial dimensions
when a higher number would allow for far more varied phenomena?
Since stable planetary orbits are impossible in spaces of
dimensions greater than three, maybe intelligent life is
possible only in our familiar 3-D space. But then why is it so
easy for computers to work with higher dimensions, and so easy
for humans to write about higher-dimensional phenomena, yet
impossible for humans to visualize the things they write about?
Before the 20th Century our universe was obviously three-
dimensional. All we had to do was look at it. Then along came
relativity, which made the universe four-dimensional. Next up
was Kaluza Klein theory, which required a five-dimensional
universe. When string theory burst upon the scene, it needed 26
dimensions, which were somehow compressed into ten dimensions,
with six of them rolled up into infinitesimal hyper-loops. The
last I heard, M-theory has upped this number to eleven
dimensions, with seven of them curled-up invisibly, and who
knows where we will go from here.
It is beginning to appear, at least to me, (not at all the
rational skeptic,) that the concept of dimensions is a human-
invented mental construct, and what we know as visualized
dimensions are actually manifested levels of consciousness.
Humanity is at the three-dimensional level of consciousness.
Yes, I know this sounds mystical, but I am no apologist for the
hopelessly inadequate, common-sense Newtonian view of the
universe, which I now see as a sub-set of a far broader reality,
which is probably a sub-set of a still broader reality, and so
on to infinity.
But why worry about theoretical infinities when we have actual
infinities in the world of fractals. Today's image came about
when I subtracted 1/2 part of Z^4 from one part of Z^3 and added
C to produce a parent fractal that resembles nothing as much as
an angel lying on its side with its head facing east and a
tongue of fire over its head. (This Sunday is Pentecost.)
Today's image is located on the southern shore of this tongue of
fire, and indeed has eight tongues of fire circling the central
minibrot. I named the finished work "Tongues of Fire" and rated
it at a 6-1/2.
The calculation time of 3-1/2 minutes is bordering on slowness,
but still brief enough to make running the included parameter
file almost a joy. For those with over-qualified computers, the
finished image is posted for viewing on the FOTD web site at:
<
http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Perfect spring weather prevailed all day Wednesday here at
Fractal Central. The sky was clear, the wind was light, the
humidity was low and the temperature reached 81F 27C. The
fractal cats were more concerned with the pigeons pecking for
scraps on the sidewalk.
My day was slow enough to leave time for both a fractal and a
philosophical discussion. And better yet, it looks like
tomorrow will be the same. Until next time, take care and you
can't get a universe from absolutely nothing, which means there
always was something rather than nothing. (Don't ask why that
something has always been there.)
Jim Muth
jamth@???
jimmuth@???
START PARAMETER FILE=======================================
Tongues_of_Fire { ; time=0:03:32.62-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident passes=1
center-mag=+1.396812017323909/-0.0389524851568373/\
3.840418e+011/1/-27.5/0 params=1/3/-0.5/4/0/0/0/0
float=y maxiter=3200 inside=0 logmap=400
periodicity=10 mathtolerance=0.05/1
colors=000FARGARHAQIAPJAOKANKAMKALKAKKAKKBKKCKKDLK\
ENKFNKGOKHPKIRKJSMKTOLUQMUSNVUOWWPXYQX_RYaSZbT_bU_\
cV`cTabRbaQbbP_dOXeOUgNRhNOf`BfYAfU9fQ8AA7pS6zm5zd\
4zY3yS2tL1p66_BBXGFTLKQQONUTKZXGcaDheAmj7qn`qZ_o__\
m`ZlaZjbZhcYgdYeeYcfXbgX`hX_iWWmVTpUQsTNvWQuYSu_Vu\
aXtc_teathcsjfslhsnkrpmrrorqmoqklqijphgpfepdboc_oa\
Yo_VoZTnXRmVQmTOlRNlPLkNKjLJjJHiHGiFEhDDhBCQFW8Io9\
KmALkBMjCNhDOgEPeFQcGRbHS`IT_JUYKVWLWVMXTNYSSWQXTO\
aRMfOKTvTbcNTzlVwhXseZob`l_bhXdbUfXRCRSBVUBYXA`_Ac\
aAfd9jg9mi8pl8so8vqWierYUTNfVMdWMbYM`ZMZ_MYaMWaMUa\
MSaMX`Mc_Mc_Mc`Mc1Wm5Vm8UmBUmETmHSmKSmNRRRQQUQPXPO\
_OMbOLeNKhMJJn8Mk9PhASeBVbCY_D`XEcUFfRGiOHkRskQnkP\
ikPdkO`kNWkNRkMMGchJceMccOcaRd_UeXWfVZgTahRciOfjMi\
kKRlQamM8nvCqrFtoIwkMzhPzdSzazzZzzVzzSzzOzzLzzTzzN\
zz2zz8zzDzzQzzOzzNzzMzzLzzKhzzizzjzzjzzjzzjzzjzzjz\
zjzzkzzkzzkzzUzzSzzQzeLzz }
frm:MandAutoCritInZ {; 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)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
