FOTD -- November 14, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal is unusual in that it contains flat, nearly featureless areas surrounded by areas of total chaos. The flat areas are of more interest, since many hold midgets at their centers. Today's image shows one of these flat areas, with its midget sitting proudly at its center. To emphasize the difference between the chaotic and flat areas, I have given the scene a color palette that highlights the flat areas. The largest flat area, which surrounds the midget at the center, has four well-defined spirals at its corners, thus the name "Four Corners". The other obvious flat areas in the image appear to also have midgets at their centers, but I have not yet checked these. The parent fractal was created by combining some Z^(-2.1) with a lesser amount of Z^(-8.9), and adding (1/C). The exact portions were chosen at random with the program's evolver feature. The parent's shape resembles a clover-leaf, with no immediately apparent critical areas. But sometimes things can be critical where least expected, and today's parent is a fine example of this always-enjoyable phenomenon. A trip back up to the surface of the parent fractal will reveal how unlikely the existence of today's midget would seem to be when seen from the surface. And some other interesting things will be seen on the way, including a tiny, most unlikely bud, in the valley of which today's scene is located. Not wanting to under-rate myself, I rated today's image at an above-average 7. Yes, I realize that if every image is rated at a 6 or 7, then the standard for an average image will increase until the typical image once again rates a perfectly average 5. But that is a consideration for the future. The render time of 24 minutes is slow. The download of the completed GIF image file is fast. The download can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather here at F.C. on Wednesday was cloudy, breezy and chilly, with light rain in the morning. The wet grass and temperature of 50F 10C kept the fractal cats pretty much house bound, but they accepted their confinement with only a modicum of displeasure. Today is starting sunny, and it is due to be warmer. The cats should have a better day. My day will improve when the work is finished and I have had time to settle down to read the latest issue of "Skeptical Inquirer" magazine, which I picked up last evening. In it I see an article which, at first glance, appears to state that psychokinesis (mind-over-matter) has been con- firmed by the rational scientific method that skeptics place so much faith in. The article then tries to escape the rational conclusion by stating that something must be wrong with the standard scientific method of doing statistics. I haven't read the entire article yet, but if it in fact claims what it appeared to claim when I skimmed it, I'll have much to philosophize and be cynical about in the near future. If the standard statistical method could lead to a wrong conclusion about psychokinesis, how many other currently accepted statisti- cal proofs could also be in error? On the other hand, if psycho- kinesis is true, how many other 'paranormal' things could also be true? Things could be getting interesting. (Or perhaps I got the wrong impression when I skimmed the article.) Until next time and next FOTD, take care, and though skeptics doubt the existence of a non-material world beyond the senses, why do they still fear that it might exist? (One thing for certain is that the non-material world of fractals does exist.) Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Four_Corners { ; time=0:24:20.96--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.300621681407275/-0.6277892275393613/\ 2140275/1/7.5/-1.3143590944786343e-008 params=4.64\ /-2.1/0.77/-8.9/0/525 float=y maxiter=3600 inside=0 logmap=362 periodicity=10 colors=000TAGVBFYBE_CDbDCdEBfFBiGAkH9nI8pJ7sK6uL5w\ L5xM7xN8xO9xPAxQBxRCxSDyTFyUGyVHyWIyXJyYKyZLy_Mz`O\ zaPzbQzcRzdSzeTzfUzfVyc`xdfwelvfrugnthjsigrjcqk_pl\ XorTnpQmyfgmvkulmlbmnTnkJnh9mf8le8ld8kc8kb8j`8i_8i\ Z7hY7hX7gW7fU7fT7eS7eR6dQ6cO6cN6bM6bL6aK6aJ6`I8`HA\ `GB_FD_EE_DG_CHZBJZAKZ9MZ8NY7PY6QY5SY4TX3VX2WX1YX1\ ZW2_W3_V4_V5_V6_U7_U8_U9`TA`TB`TC`SD`SE`SF`RF`QE`P\ E`OE`ND`ND_MC_LC_KC_JB_IB_HAZGAZFAZE9ZD9ZD9ZH8WK7U\ N6UR5UU4UU3UU3UU3UU3UU3UU5UU6UU7UU9SUPOUBLSPIQEFOF\ CPHDQRDRJERTESLFTMFUNGUTGVPHWUHXRIXSIYUJZVJ_WK_WK`\ XLaYLbZMb_MdaLfdLhgLjiLllKnnKmmKmkKigUihcfcmc`t`Yy\ YVvVStVPqWMoXNlYQjZTg_We`Zbaa`bdYcgWdjTemRfpOgsMhv\ JiyHfiIcUJ`EKYHNVKQSNTPQWMTZKWaHZdEagBdj8gm5jp3mrI\ fnW`kiVhwPerSanVYjYVf`RbbO_dQYeSWfUUgWShYQi_OjaLkc\ JleHmgFmiDmkBmm9moBmqDmsFmuHmvImwKmxMmyOmzPmzOmzNm\ zMmzLmzLmzKmzJmzMmzOmzQmz } 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==================================