; Date: Tue, 02 Sep 2003 10:59:22 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 02-09-03 (Brave Little Midget [6]) ; Id: <1.5.4.16.20030902105951.298f3168@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; or: ; ; ; ; 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 PARAMETER 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|