; Date: Mon, 06 Dec 2004 10:04:32 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 06-12-04 (Un-Unity [5]) ; Id: <1.5.4.16.20041206100614.29c7c6da@pop.mindspring.com> ; --------- ; ; FOTD -- December 06, 2004 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Today's formula is not strictly an escape-time formula, but the ; type of image it draws (it draws only one image) is close enough ; to escape-time images to be included in the Fractint tour. ; ; We learned in high school that the graph of X^2+Y^2 is a circle, ; but we never learned that it could be a fractal. (At least I ; didn't) As today's image shows, X^2+Y^2 makes a striking ; fractal. All that is necessary to bring out the latent fractal ; is to make the journey to unity a bit difficult, as has been ; done in the 'unity' formula. (An interested fractalist is also ; a help.) ; ; The fractal is a strange one. Features that are clear on the ; surface vanish mysteriously as we zoom in on them. When today's ; image is rendered at a resolution of 640x480, there is an ; obvious but very narrow circle of radius 1 around the origin. ; At a resolution of 800x600 only a few scattered traces of this ; circle are visible. And when we try to zoom in on the circle, ; it vanishes completely. It is not only this delicate circle ; that vanishes when it is enlarged; nearly every feature in the ; interior of the circular fractal itself is unstable, almost as ; though the entire fractal were a moire pattern. ; ; Today's image shows the entire unity fractal rotated -135 ; degrees. By setting the outside to 'atan' and turning on the ; 'decomp' feature, I was able to divide the fractal into two ; contrasting semi-circles and come up with an image worthy of ; FOTD status. The name "Un-Unity" implies that the two halves of ; the image are so different as to be separate entities. ; ; The image is extremely fast, rendering in less than 6 seconds on ; my 7-year-old machine. Since the 'unity' formula has no parame- ; ters to tweak, and the fractal is unstable when it is zoomed ; into, I could take no credit for finding a great image. But ; today's FOTD is a fine rendering of the basic fractal, well ; worth the rating of an average 5 that I gave it. And when the ; hyper-fast render time is considered, the overall worth measures ; an astounding 5102. ; ; Of course, such numbers are meaningless. All fractals that ; complete in less that a minute should be considered 'instant' ; fractals. ; ; Today's fractal can be seen by running the included parameter ; file or by downloading it from the FOTD web site at: ; ; ; ; The warm sun continued all afternoon here at Fractal Central on ; Sunday, while the temperature reached a mild 54F 12C, giving the ; fractal cats all the time they wanted in the yard. It was one ; of the best days in the past several weeks. The day was so good ; in fact that no special treat was needed to keep the duo happy ; in the evening. This morning is starting cloudy however, and it ; is colder. Rain is also threatening, so I doubt that the good ; day will be repeated. ; ; For me it will be just another workday. When I finish, I will ; have to decide what kind of fractal theme to tackle next. Check ; back tomorrow to see what I dream up. Until then, take care, ; and be at unity with both yourself and the cosmos. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Un-Unity { ; time=0:00:05.88--SF5 on a P200 reset=2004 type=unity passes=1 periodicity=none center-mag=0/0/0.6915629/1/135/-5.050126983261e-014 float=y maxiter=256 inside=0 outside=atan logmap=yes decomp=256 colors=0000004NG5LG5KH5JI5IJ5HK5FL5EM6DM6CN6BO69P6\ 8Q67R66S65SAAVEEYII_MMbQReUVgYZjablegoikrmotqswtwz\ szzszzszzszzswzstzstzsszsszsrysrxsrwsqvrqvrpvrpvrp\ urourournurnurntrmtrmtrltrltrltshrsepsbns_lsXjsUht\ RgtOetLctIatF_tCYt9Xt8Zu7av6cv6ew8fwAfwCfwEgwFgxHg\ xJgxLhxMhxOhyQiySiyTiyViyXjzZjz_jzakzckzekzfkyehye\ execxe`weYweWvdTvdRudOudLtdJtdGtdEleFdeFXfFPfFYLyY\ JyZIyZHy_Fy_Ey`Cy`Bya9ya8yb7yb5yc4yc2yd1yd0yc1vb2s\ a2pa3m`3j_4g_4dZ5aY6ZX6WX7UW7RV8OV8LU9ITAFSACSB9RB\ 6QC3QC1RE3SF4TG5UH7VI8VK9WLBXMCYNDZOE_PG_RH`SIaTKb\ ULcVMcWNeTOfQPhNQiKRkHSlFTnCUo9Vq6Wr3Xt0Yu0Ys1Wq3V\ o5Un7Tl9SjBRhDPgFOeHNcJMaML`OKZQJXSHVUGUWFSYEQ_DOa\ CNcBGIH90NB2OC6PEBQFFRGJSIOTJSULXVM`WNdWMeVLeVLfUK\ fUKgTJgTIgSIhSHhRHiRGiRFiQFjQEjPEkPDkOCkOClNBlNBmM\ AmMAmM9mL9mK9mJ9mI9mH9mG9mF9mE9mDBgBDa9EW8GQ6HL5HK\ 7HK9HKAHKCHKDHKFHKGHKIHKJ } ; END PARAMETER FILE========================================= ; ;