; Date: Sat, 11 Dec 2004 11:32:33 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 11-12-04 (Brot Rising [8]) ; Id: <1.5.4.16.20041211113418.0d874130@pop.mindspring.com> ; --------- ; ; FOTD -- December 11, 2004 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; I have always enjoyed pictures that show imaginary but possible ; scenes on other planets circling other stars. Today, thanks to ; the HyperMandelbrot formula, we have a star-like 'brot' rising ; above the floor of an imaginary valley on an imaginary planet in ; Fractal Land. After a bit of consideration, I named the image ; "Brot Rising". ; ; The word 'brot' does not refer to food. It is a word I invented ; to describe a fractal feature that shows the typical Mandelbrot- ; type buds and is likely to hold intact midgets. True, the bud ; in today's image is partly concealed by exotic alien clouds, and ; I doubt that it holds any intact midgets, but it comes close ; enough to the shape of a Mandel bud to earn its name. ; ; The scene itself exists in the four-dimensional hypercomplex ; Mandelbrot set, which itself is a single four-dimensional slice ; of an eight-dimensional monstrosity known as the hypercomplex ; Julibrot figure. Unlike the more familiar four-dimensional ; Julibrot, parts of which I can visualize, this Julibrot is ; totally beyond my woefully limited power of visualization. But ; a bit of rather simple math will show that through any of its ; points there passes: ; ; 1 stand-alone 0-dimensional point ; 8 mutually perpendicular 1-dimensional lines ; 28 mutually perpendicular 2-dimensional planes ; 56 mutually perpendicular 3-dimensional spaces ; 70 mutually perpendicular 4-dimensional spaces ; 56 mutually perpendicular 5-dimensional spaces ; 28 mutually perpendicular 6-dimensional spaces ; 8 mutually perpendicular 7-dimensional spaces ; and 1 stand-alone 8-dimensional space ; ; The series reminds me of Pascal's triangle. ; ; The image rates an 8, mostly because I like other-worldly ; scenes. It renders in 2 minutes, which is fast enough to earn ; it an overall worth of 393. It may be donwloaded in somewhat ; less time from the FOTD web site at: ; ; ; ; The temperature reached 50F 10C, but persistent light rain fell ; all day Friday here at Fractal Central. The cats passed the day ; alternating between sleeping on the couch and sitting on their ; shelf by the window, watching the rain. Extra tuna kept them ; happy. This morning is starting cloudy with more rain. The day ; probably will go no better for the dynamic duo. ; ; For me, the day appears as though it will be slow, which only ; increases the chances of a great fractal for tomorrow's FOTD. ; Check then to see how great. Until next time, take care, and ; rise with the buds. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Brot_Rising { ; time=0:02:01.99--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=t periodicity=0 center-mag=-0.166657/0/5.940446/1.1211/-90/3.88578\ 058618804789e-016 params=1.03/0/5/0/1e-008/0 float=y maxiter=2500 inside=255 logmap=yes colors=000FJHHGHJEHKBHL9HPHHRJHULHWOHZRHaVHdZHfaHi\ eIlhJolJqoJ9NcAMcBLcCKcDJcEIcFHcGGdHFeIEfJDgKChLBi\ LAjL9jK8jL9jMAjMAjNBjNCjOCjPDjPDjQEjQFjRFjSGjSGjTH\ jTIjUIjUJjVJjWKjWLjXLjXMjYMjZNjZOj_Oj_Pj`PjaQjaRjb\ RjbSjcSjcTjdUjeUjeVjfVjfWjgXjhXjhYjiYjiZjj_jk_jk`j\ l`jlajmbjmbjncjocjodjpejpejqfjrfjrgjshjshjtijuijuj\ jvkjvkjwljwmjwljwljwljwliwkiwkhwkgwkgwkfwjfwjewjdw\ jdwjcwicwibwiawiawi`wh`wh_whZwhZwhYwgYwgXwhXwhWwiV\ whVwhUwiUwiTwiSwiSwiRwiRwiQwiPwiPwiOwiOwiNwiMwhMwh\ LwhLwhKwhKwiLwiMwiMwiNwiOwiOwjPwjPwjQwiRwiRwiSwhSw\ iTwiUwiUwhVwhVwhWwiXwiXwhYwhYwhZwh_wh_wi`wi`wiawib\ whbwhcwhcwidwiewiewifwifwigwjhwjhwjiwjiwjjwjkwjkwk\ lwklwkmwknwknwkowkowkowlowlowlowmpwmpwmqwnqwnrwnrw\ oswoswotwptwpuwpuwqvwqvwqwwrwwrxwrxwsywsywszwszwsz\ wszwszwszwszwtzwtzwtzwtzwuzwuzwuzwuzwuzwuzwuzwuzwu\ zwuzwuzwuzwuzwuzwuzwuzzz` } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } ; END PARAMETER FILE========================================= ; ;