FOTD -- December 01, 2003 (Rating 8) Fractal visionaries and enthusiasts: Like so much of our current view of reality, fractals are non- intuitive. Before the theory of relativity, who could have thought that matter is a different form of energy, that electro- magnetic waves are transmitted by nothing, or that the present moment of time is not universal but unique to the individual observer? Before the quantum theory, who could have guessed that photons and electrons are incomprehensible things that can be seen as either waves or particles; or that, with a proper experimental set-up, it is apparently possible to change the past; or that the closest we can come to reality at the quantum level is the mathematical equations which describe it? Before fractals were discovered, who could have guessed that an expres- sion as simple as Z^2+C could lead to infinity? The world extends far beyond the part of it comprehended by an ant. It extends far beyond the part of it comprehended by the fractal cats. These lower forms of life (the cats would dis- agree here) lack the intelligence to grasp the vastness of exis- tence. But then there is man. Is our intelligence the highest form of intelligence possible? Is it sufficient to grasp the totality of existence? Apparently not. One-hundred years ago, we assumed that our local galaxy com- prised the entire universe. Then the telescope at the Mount Wilson observatory showed that we were hugely underestimating the vastness of the universe. In recent years we have been pon- dering an infinity of parallel universes combined into an infi- nitely more vast multiverse. Next, we might be thinking of an infinity of multiverses. And there are those 11 dimensions (up from 10) required for M-theory to make sense. How can we find a 'theory of everything' when our concept of 'everything' keeps growing? I sometimes feel that, due to the limitations of out intellectual apparatus, we are even today unaware of as much of existence as an ant going mechanically about its programmed chores. And artificial intelligence can be of little help, for we will design our computers to 'think' as much like ourselves as possible. If a computer actually were to start thinking in a truly new and original manner, we would likely fail to comprehend its unfamiliar logic, and assume it was malfunctioning. We would re-program it to 'think' more like ourselves. It is kind of discouraging. We are nearing the limits, and the limits are ourselves. 120 years ago, we thought we had discov- ered almost all there was to know; today it looks like we don't even know what we don't know, and even worse, because of our limited minds, we never will know. Oh, before I forget -- we have a fractal today. It is an 'evap- orated' scene in the fractal created by a whimsical formula of 1's and 4's based on the square root of 2. I named it "Seasonal Wreath" because it reminds me of the wreaths that decorate so many doors and windows at this time of year. I rated the image at an exceptional 8, which might be a bit liberal. But after almost three weeks of Mandelbrot images, it seems like a refreshing change. The render time of two minutes is well within reason, even though a download of the completed image might be a bit faster. That download may be found on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday turned out to be another near-average day here at Fractal Central, a bland day, slightly chilly, with little to tell about. The partly cloudy skies and temperature of 48F 14C were barely acceptable to the cats, who were outdoors only an hour. Their spirits were lightened, however, by the last of the left- over turkey. This morning is starting mild with promises of a pleasant day. But a cold front with high winds is due around midday. The cats dislike wind and cold, so we'll have to hope for the best for them. Until tomorrow, take care, and take life one fractal at a time. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Seasonal_Wreath { ; time=0:02:17.81--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.32911156705464600/-0.065564664774447\ 56/15547.06/1/-67.5/1.6424422933e-010 params=14/-1\ .414/1/-14.14/-1.4/1e+100 float=y maxiter=1800 inside=bof61 periodicity=10 colors=000ZO`SUbL`dFffMd`TbV_aPf_JlZEmcDnhCnmBorAo\ w9r`VuEoqFlnFjkFghFedFbaF`ZFYWFWSFUPFRMFPJFMAAACFH\ 9FF6FD9JFBMGEQIGTJJWLL_MObOQfPTjRcnSmsUrwVzzWrxYhv\ Zbt_bsabrbbrcbqecpfcpgcoicnjcnkcmmclncloeinfgngenh\ cnianj_mkYmlWmnTmoRmpPlqNlrLlsJltHluFlrEfoEalEXiER\ fEMcEH`EBYE6VE1UI3TM4SQ5RT6QX8P`9OcANgBMkDLnEKrFJv\ GIyHJtNKpTLlYMhcNdhO`nPXs72lB3jF3iJ3hN3gQ4eU4dY4ca\ 4be4ah5_l5Zp5Yt5Xw5Wu6Vt6Ur6Uq7To7Tn7Sl8Sk8Rj8Qh9Q\ g9Pe9PdAObAOaAN`ANcEMeIMgLMiPLkSLnWLpZLrbKteKviKxl\ KZ4fa7dc9beB`gDZiFXkHWmKUoMSqOQsQOuSMwULrSKnRJjQIf\ PIkHaeFU_DMVBETCHSCKRCNQCQPCTOCWNCYMD`LDcKDfJDiIDl\ HDoGDqMLnRSkW_h`feenbju`etW`sSWrNSqJNpEIoAEn6Hl8Jj\ 9MhAOgBReCTcDWbEY`F`ZGbXHeWIgUJjSKlRLiPMgNNeLOcJP`\ HQZFRXDSVBTS9UQ7VO5WM3XK2XI3VH3TG4RF4QE5OD5MC6KB6J\ A7H97F88D78C87E87F87G96H96I96JA5KA5LA5MB4NB4OB4PA4\ QA4RA4SA4TA4TmCPs4UlBXeHZ } frm:MandelbrotMix4 {; 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=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================