; Date: Thu, 03 Jul 2008 23:49:47 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 04-07-08 (Perfectly Cubic [8]) ; ; Id: <1.5.4.16.20080703235000.2bd78740@pop.mindspring.com> ; --------- ; ; FOTD -- July 04, 2008 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; In a recent letter to the Fractint list, JoTz noticed that the ; parent fractal of the "Order Septemdecem" FOTD image, which ; resembles a Mandelbrot set and was posted on June 27, has a bit ; of unexpected detail in its interior. I have known about this ; extra stuff since I started working on the DivideBrot formulas. ; The extra detail in the parent of the septemdecem fractal is ; actually the fragmentary remains of a Z^17+C Mandeloid, which ; appears when the imag(p1) parameter is set very close to but not ; exactly at zero. (I usually use the number 0.0000000001 instead ; of zero. In this case, the exponential form [1e-010] inserted ; in the formula does not work. This will be corrected in version ; number 5.) ; ; When imag(p1) is set to virtually zero, the resulting fractal is ; the normal Z^17+C Mandeloid. But as imag(p1) is increased, this ; Mandeloid gradually grows in size and morphs into the tradition- ; al Mandelbrot set, leaving order-17 debris to dissolve in the ; interior of the forming M-set. Some of the intermediate steps ; are quite interesting, but due to the size change, an animation ; with consistently sized elements would be difficult. ; ; The basic rule is: the smaller the value of imag(p1) the smaller ; the size of the resulting fractal and the more prominent the ; higher order shape, while at the same time, the greater the ; value of imag(p1) the larger the size of the resulting fractal ; and the more prominent the classic Mandelbrot-set shape. ; ; Today's scene takes advantage of the dissolving high-order ; debris in the center of the main bay of the parent 'almost-a- ; Mandelbrot set'. The scene is located in what first appears as ; a tiny dot, but when blown up reveals itself as an entire ; fractal universe. ; ; Due to the unusually large magnitude of the image, an outzoom ; to the parent fractal is quite a trip, but very interesting. ; But be sure to turn off the logmap feature before taking the ; backwards trip. ; ; BTW, the DivideBrot4 formula will soon be superseded by the ; DivideBrot5 formula, which will be used for all future fractals ; of today's type. ; ; I rated today's image, which shows an unusually well-defined ; cubic minibrot, at an 8. It's worth it. I named it "Perfectly ; Cubic" for the same reason. ; ; The calculation time of 47 seconds will cause no pain to those ; with computers that are not over-qualified. Those with machines ; that can surf the web in a flash but cannot run Fractint may ; still see the image by visiting the FOTD web site at: ; ; ; ; and enjoying there the image that Paul calculated. ; ; Lots of clouds, only a little sunshine, high humidity, a tempera- ; ture of 84F 29C, and a threat of rain followed by actual rain, ; made Thursday less than ideal here at Fractal Central. Not ; concerned with weather, the fractal cats spent a good part of ; the day trying to catch a fly. When one of them eventually ; caught it, the exhausted duo settled down to sleep. ; ; My day was busy, mostly because tomorrow is a holiday. The FOTD ; does not take time off for holidays however, and will be posted ; on schedule in 24 hours. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Perfectly_Cubic { ; time=0:00:47.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=-0.606\ 3981173832952/+0.006169462807566/5.040456e+012/1/\ -83.80/0 params=3/3/3/0 maxiter=1000 logmap=58 float=y inside=0 periodicity=9 mathtolerance=0.05/1 colors=00097UAAWBDYCG_DJaEMcFPeGSgHViIZkKbmMfoOkqQ\ rsroumpsllqkhnjfliejgcheaec`caZa_Y_XWXUUVRSTOQROO_\ JMXUKVdKSoUQzcOymQxmRwmTvmUumVuzXtzYsmZrc`qUaqWcpY\ do_znazmczmdzq_ztVzwQzzLzzIzzFzzDzzAzz7bz5azHazTaz\ dazleztizzlzlbzZTzLJzlEzpGztIzxKzzMzvOzqPzlQzfRzaS\ zXTzRUzMVzHWzGRzGMzFHzFCzE7zE2zSGzdUzqfztPzw8zqGzk\ OzeWz_bzUjzOrzIyzHtzHozGjzGezF`zFXzESzENzDIzDDzD9z\ EFzELzERzEXzEazLZzRWzXUzbRzhOwnMumOsmPqmQolRmlSklT\ ikUgkWekXcjYajZ_j_Yi`WiaUibVf`Y`_`WZcSYfOXhPWiPWkP\ WlPWmPWoPWpPWrPWsPWtPWvPWwPWxPWuSVsUUqXUoZTm`SkcSi\ eRggRkhQnhPqhOtiNwiMziMtjPokRikUdlW_mZUm`PncKoeEoh\ 9pj4pl6qk8rkAsjBtjDujFviHwiIxiKyhMzhOzgPzgRzgzzfzz\ fzzfzzhzzjzzkzzmzzozzpzzrzzszzdJzQIz4Cz36z21z2Lz3d\ z4zz5zz6zz7zz7zz8zz8zz9zz9zzAVzASzBPzBMzCJzCGzBDzA\ BzA8z96z93z81z87zEDzJJzOPzTVzY`zbfzglzlqzqrzsszttz\ vuzwvzywzzrztnzniziezcQzk } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint