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@mindspring.com jimmuth@aol.com 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=========================================