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 BTW, the DivideBrot4 formula will soon be superseded by the DivideBrot5 formula, which will be used for all future fractals of today's type.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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================