; Date: Thu, 24 May 2007 21:42:44 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 25-05-07 (Fractal Firestorm [7]) ; Id: <1.5.4.16.20070524214717.2b97d3fc@pop.mindspring.com> ; --------- ; ; FOTD -- May 25, 2007 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; After studying the "Something New" image of two days ago, I ; started wondering if the 4-D HyperMandelbrot set holds typical ; 2-D quadratic midgets. It certainly has many oddly-shaped ; holes, but these do not qualify as midgets. A bit of investiga- ; tion soon revealed the answer. ; ; Yes, the 4-D Mandelbrot set does have midgets, but these midgets ; are four-dimensional things the same as their parent fractal, ; and when they are sliced in a direction other than straight down ; the middle, they take all kinds of weird shapes. Thankfully, ; the midget in today's image *is* sliced down the middle and ; appears as a normal quadratic midget. In fact, the entire ; scene, with its ring of basins, could easily lie in the classic ; Mandelbrot set. ; ; But I have not forgotten the weird-shaped slices of the 4-D ; midgets found in other parts of today's parent fractal. These ; slices are also interesting. I'll choose one of these slices ; as tomorrow's FOTD. ; ; I named today's image "Fractal Firestorm", probably after the 8 ; orangish elements surrounding the midget. I rated it at a 7 ; because that's what I think it's worth. ; ; The calculation time of 5-1/4 minutes is true on the 2000mhz ; unit. The 200mhz machine would take 25 minutes to finish the ; job. But the fastest way of all to see the image is to view it ; on the FOTD web site at: ; ; ; ; The absolutely perfect days just keep coming here at New Fractal ; Central. The cloudless skies, light winds and a temperature of ; 84F 29C were near perfect for every outdoor activity except ; flying kites and growing crops. It's getting quite dry and the ; local farmers are starting to worry. The fractal cats don't ; worry about weather however. They reserve their concern for ; more practical things such as how long it will be before their ; evening treats are served. ; ; My worries are more numerous than the cats', and they will not ; be solved by a kind pet owner. But one near-certain way to ; forget the problems about which one can do nothing is to enter ; the world of fractals. Speaking of fractals, the next one will ; appear in 24 hours. Until then, take care, and I wonder whether ; fractals ever exhibit quantum non-locality. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Fractal_Firestorm { ; time=0:05:17.80-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 center-mag=-0.97586929974347690/-0.003732367487476\ 60/6.514006e+008/1/10/-5.09919721123075487e-005 params=0/0/-4/0/0.1/0 float=y maxiter=5000 inside=0 logmap=650 periodicity=0 colors=000PKhkMwiOtgQqeSncUkaWheYej_bna_sccwchncmf\ coZcjRcdJc_BcV3cQ9cREcSJcSOcTUcUZcUccVhcVgcSfcQecO\ ecLdcJccHbcFbcCacA`c8`c6ecJieVngfrirokblmNmoNnqNns\ NouNpwNpuNqsNrqNroNvmTylYxjXxhXxfXwdWwbWwaWw_VvYVv\ WVvUUuSUuRUuPTuNTtLTtJStHStGSpFTlEUiDUeDVbCWZBWVAX\ SAYO9YL8ZH7_D7_A6`65a35a47Z58X69V6AS7BQ8CO9DM9FJAG\ HBHFCIDCJADK8EL6EM4FL5FL5FL6GL6GL6GL7GL7HL7YJTHL8H\ L8IL8IK9IK9IK9JKAJKAJKBKKBKKBKKCKKCLKCLKDLJDMJDMJE\ MJEMJENJFNJFNJGOJGOJGOJHOJHPIHPIIPIIQIIQIJQIJQIJRI\ KRIKRILSILSHLSHMSHMTHMTHNTHNUHNUHOUHOUHOVHPVHPVGQW\ JQWMQWPRZSRaVRdYSg`SjcSmfTpiTslOvoFumGtlHskHriIqhI\ pgJoeJndKmcKlaLk`Lj_MiYMiXNhWOgUQfUSeWUdYWc_Yba_ac\ a`ec_geZigYkiYljYmiYnhYogYpgYqfYreYseYtdYucYvcYwbY\ xaYyaYz`Yz__zZazcczhezmgzrhzvizzjzzkzzlzzmzznzzozz\ pzzqzzrzzszzuzzwzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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========================================= ; ;