; Date: Fri, 10 Apr 2009 16:54:01 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 11-04-09 (The Magic Rectangle [7]) ; ; Id: <1.5.4.16.20090410165430.2bcf7200@pop.mindspring.com> ; --------- ; ; FOTD -- April 11, 2009 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Today's image shows one of the strange rectangles that exist in ; a Julia set of the Z^(2.003)+C Mandeloid. (To see one of the ; actual rectangles check the Z^(2.003)+C Julia set with a C-value ; of -1.7435+0.0i at the Z coordinates of 0.00019+0.07388i, with ; the magnitude set to 100. It's not a perfect rectangle, but ; it's close enough to be quite surprising.) ; ; When we check today's image however, we wonder what has happened ; to the rectangle. The rectangle, or at least one slice of it, ; actually is in the image. It appears as the dark bluish area in ; the lower right corner, with the narrow white line across its ; center. ; ; The rectangle has been reduced to a single narrow line because ; today's image is not a Julia set. It is what I call an Oblate ; set, a slice through the four-dimensional Julibrot figure that ; is defined by the imaginary C-axis and the real Z-axis. It is ; actually a fractal hybrid -- half Julia, half Mandelbrot. ; ; Even though no full rectangle appears in the image, I named it ; "The Magic Rectangle". The missing rectangle is made up for by ; the image's unusually strong impression of a three dimensional ; scene. I have no idea what the quite solid looking things might ; represent however. ; ; I rated the image at a 7, which means I consider it to be an ; average FOTD image. The calculation time of 1-1/4 minutes is ; unusually fast, which will be good news for those who prefer ; more than a single slice of their rectangles. ; ; Another way of viewing the image is to surf out to the FOTD web ; site at: ; ; ; ; and view it in completed form there. ; ; Totally miserable conditions prevailed both with the weather and ; the fractal cats here at Fractal Central in central Pennsylvania ; on Friday. The spitting rain and temperature of 46F 8C kept the ; cat duo glued to the warmest radiator, glaring at the outdoors ; in full sulk. ; ; My problem was not the weather -- I had no time to worry about ; that -- but with the rush that won't go away. I still managed ; to find time for the fractal however. And I would not be sur- ; prised in the least if another fractal were to show up in about ; 24 hours. Until next time, take care, and never question the ; fractal truth. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= The_MagicRectangle { ; time=0:01:14.91-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=OblateN passes=1 center-mag=-0.0106678\ 7037571017/+0.00398419476438538/231.7069/0.202/\ 4.105/63.193 params=2.003/0/0.000185/0.0739678/\ -1.7434/0 float=y maxiter=15000 inside=253 logmap=32 periodicity=10 sound=off colors=030mzzmyzmxzmxzmxzmxzmxzmxzmxzlwzkwzjwzivzh\ vzgvzftzetzdrzcrycrxcqwcqvcqucntcntclsclsclrcirciq\ ciocgocfmcemcelcejccjcbhcbfc`fc`ec_ecZccZacWacW_cW\ YbUYaUX`SX_SVZSSYQSXQRWQPVOPUONTMNSMLRLJQJJOIIMJGK\ GGIGEGHCFHEEIGDHICGJBGLBHNAGPAFR9FS9FV8FX8DX7DY7D_\ 6Da5Bc4Bd3Be2Bg19h09j09k09j07l07n07n05o05o05o05n03\ n03n03n03n01n01n01n01n01n01n00n00n00n00n00n00n00n0\ 1n13n33n55n77n97nB9nDBnFBnHDnJFnLFnNHnNJnPJoQLoSNp\ UNpWPqYQqZQraSrcUsdUsfWshYsjYrjZqlaqmaoocmqdmsdltf\ lvhjxhhyjhzlfzlezmezoczsazqczoczoezmezmfylfxlhvjhv\ hjthjsflqflodmmdmlcojcojaqhZqfZrdYrcYsaWsZWsYUsWWs\ YUsZUsZUsaUsaUscUsdUsdUsfUsfUshUsjUsjUslUslUsmUsoU\ soUsqUsqUssUstUstUsvUsvUsxUsyUsyUszUszUszUszUszUsz\ UszUszUszUszUszUszUszSszQszQszPszNszNszLszJszJszHs\ zFszFszDszBszBsz9sz7sz7sz5sz3sy3sy1sy1sx0sx0sx0sv0\ sv0sv0st0st0sv0szzzzzszzs } frm:OblateN {; Jim Muth b=p1, z=real(pixel)+p2, c=flip(imag(pixel))+p3: z=z^(b)+c, |z| <= 16 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint