FOTD -- September 02, 2003 (Rating 6) Fractal visionaries and enthusiasts: When I wrote yesterday's discussion, I was in a mood of disap- pointment over the things that might have been accomplished in outer space in my lifetime, but were never even tried. Last evening, to remind myself of what might have been, I played an old video tape I recorded almost 20 years ago of a TV presenta- tion of Ray Bradbury's collection of short stories known as "The Martian Chronicles". These stories, which were written mostly in the late 1940's and early 1950's tell the story of the human colonization of Mars and the inadvertent destruction of the already-dying race that had inhabited Mars for apparently millions of years. I'll not go into the plot, which is well known, but I must comment on the time frame in which the Martian Chronicle stories are supposed to take place. Apparently, in 1950, Ray Bradbury, who mellows his fantasy with healthy skepticism, considered it quite believable to write about men from Earth walking on Mars in the year 2003. Well, it is now the year 2003. Where are the men walking on Mars? And what does this failure bode for all the future achievements, which according to sci-tech enthusiasts, science and technology are supposed to bring us? One thing that will certainly be with us in the future is fractals. Today's image is but the smallest example. The parent of today's fractal is an almost-perfect classic M-set rotated about 10 degrees. The set is almost perfect because the exponent of Z is 2.01 rather than 2. The true M-set, with its whole-number exponent, would not rotate when calculated with the MandelbrotBC1 formula. Mandeloids in this range hold interesting new features along the negative X-axis, where a prominent split develops. The MandelbrotBC1 formula rotates these near-whole-number Mandeloids in a controlled manner, so that the split can intersect any desired part of the almost-perfect set. In today's case, which uses the default values and rotation, the split intersects the southern branch of Seahorse Valley, and wreaks its havoc there. The character of the Valley has totally changed. The familiar features are gone. All the features in the vicinity of the great split have split again and again into tiny fragments, until little remains of the original appearance of the area. Yet despite the overall chaos, many midgets remain virtually intact, acting as centers of attraction for the new features emerging from the chaos. Today's image shows one of these brave little midgets holding its place even while the world around it is falling apart. In honor of its valor, I have named the image "Brave Little Midget". The circular holes surrounding the midget are permanent features that do not fill in with higher iterations. Nothing at all like them appears in the classic Seahorse Valley. And look closely at the arrangement of features around the midget. You will notice that it is not quite symmetrical, and does not quite fall into the 2-4-8... series of the classic M-set. The midget in today's image may be brave, but its effort has cost its appearance. I could rate the image no higher than a 6, which is not bad, but still only the slightest above average. The render time of 15 minutes can be avoided as always by down- loading the completed GIF image from the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> As I expected, it never rained here at Fractal Central during the day on Monday, and the dynamic cats had another happy afternoon in the yard. True, a thunder-storm did arise at 9pm, but that was after dark, when the day had ended. The tempera- ture of 88F 31C was uncomfortable for people, but within the comfort range of fractal cats. Today brings another forecast of thunder. It remains to be seen what will actually happen. One thing certain to happen is that the work which needs to be done will be done by day's end. And when the work is out of the way, I will try to find a fractal worthy of a rating of at least a 7. To see if I succeed, check back here in 24 hours. Until then, take care, and see what lies beyond the next iteration. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ BraveLittleMidget { ; time=0:15:10.06--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-0.79333921686891930/+0.011042202099867\ 17/3.308758e+007/1/-60/7.13843934817270931e-007 params=2.01/0/0/0 float=y maxiter=2100 inside=0 logmap=276 periodicity=10 colors=000ThmSglRfkQejPdiOccNaXM`RLZKKYEJW7JV1PZ6V\ bB`fGeiLkmQqqVyuZvt_st`ptamsbksbhscerdbre_rfYqfVqg\ SqhPpiMpjKpjLlfLicLf_LcXL`TLYQMUNMRJMOGMLCMI9MF6TO\ 5ZX5ee4km4jk7ij9hiCggEgfHfeJecMdbOcaRc`TbZVaYY`X__\ Vb_UdZTgYRiXQlWPnWOp_NobNoeNohNnlMnoMnrMmuMmzKrxMm\ vNitOerPapRYnSUlTPjULhWHfXDdY9bZ5a_1bZ3bZ4cY5cY6cX\ 7dX8dW9dWAeVBeVDfUEfUFfTGgTHgSIgSJhRKhRLkSLhRMfRNd\ RObRO`RPZRQXRRVRRTRSRRTPRTNRULRVJRWHRWFRXDRYBRZ9RZ\ 7R_5R`1Nc3R`4UY6XV7`T8cQAfNBiKCmIEpFFsCGvAIs9Jp9Kn\ 9Lk8Ni8Of8Pd8Qa7S_7TX7UV7VS6WP6YN6ZK5_I5`F5cD5hA4m\ 84r54w34z53r63m83h93cB3_C3_D3ZF3YG3XI3WJ3VK3UM3TN3\ SP3RQ3TP2RR3QS4PT4OU5MW5LX6KY6JZ7H`7Ga8Fb8Ec9Dd9Eb\ CFaEF`HGZJHYMHXOIWRJUTJUWKUYKU_LUbMUdMUgNUiOUlOUnP\ UqQUsQUvRUxRUzSUuTUqUWlVYhV_dWa_XcWYeRYgNZiJ_kE`mA\ Zo7`q6bs6du5fv5hw5ix4ky4mz4oz3qz3rz3dzRSzmTznUzoVz\ oWzpXzqYzqZzr_zsezKazRZzY } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================