FOTD -- August 02, 2002 (Rating 6) Fractal visionaries and enthusiasts: At first glance, today's image looks like an exotic midget created by the MandelbrotMix4 formula, but it is not. The image, with it's almost-disconnected appearance, is actually a scene in our faithful old friend, the Mandelbrot set. The scene is located deep on a filament in the northeast suburbs of the large midget on the negative stem of the M-set. The exact location can be found in a few seconds by outzooming. As one backs out, the magnitude soon falls within the range of conventional math, so the trip back to the surface is a fast one. Today's scene almost appears disconnected, but it is not. All parts of the Mandelbrot set, including the midgets and the elements around them, are connected to the main body of the set. The shoreline of every midget and the main body as well is a single unit. True, the connection is often made by an infinitesimally thin filament, but the connection is there. By comparison, many fractals created by the MandelbrotMix4 formula are not connected. In these fractals, there frequently is no main body, but only a cloud of fractal debris scattered around the area like ejecta around an explosion. And like at the scene of an explosion, isolated bits of debris are often found far from the center, totally disconnected from the rest of the fractal. I named today's definitely connected fractal "Twirling Banners" when I was reminded of synchronized gymnasts twirling their banners. If it were not part of the M-set, today's image might have rated a 7. As it is, a rating of a slightly-above-average 6 will have to suffice. Since the image is in the magnitude range where arbitrary precision math is required, it takes over 22 minutes to render on my P200 machine. A download of the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will be considerably faster. The weather Thursday here at Fractal Central was of the typical high-summer variety -- a temperature of 97F 36C, blazing sun, high humidity, and light winds. In the evening, thunder clouds developed on the horizon, but never moved in. These conditions kept the fractal cats confined to the cool indoors through the afternoon. In the evening, when the sun sank low and they finally did venture outdoors, the local catbird began annoying them, apparently aware that their bird-catching days are nearly finished. And now it's Friday morning -- another hot day -- and I've got a pile of work to finish. It's time to reconfigure the fractal shoppe into a workroom and get busy. Until next FOTD on the 4th of August, take care, and fractals are too complex to be natural, yet they are not artifacts. So what are they? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Twirling_Banners { ; time=0:22:51.60--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.74644456175032895642/0.0051806197286\ 35784144/3.752443e+015/1/-122.5/3.8857805861880478\ 9e-016 params=0/0 float=y maxiter=6000 bailout=8 inside=0 symmetry=none periodicity=10 sound=off colors=000ho_eoXcoU`nQZnNZqNXnKWdHVVFUTFUSFURFUQFU\ PFUOFTNFTMFTKFTJFTIFTHFTGFSFFSEFSDFSCFSAFS9FR8FR7F\ R6FR5FR4FR3FR2FV5KY8O00000000000000000000000000000\ 0000000J0IJHFIEBIB8I84I51K66M7BN8GP8KQ9PSAUUBZVBdX\ CiYDn_Er`Et`Hr`Ko`Nl`Pj`Sg`Vd`Xa`__`bX`dU`gR`jP`lM\ `oJ`rG`tEVfDQTDKFDF2DH4CI6CJ8CKABLCBNEBOGBPIAQKARM\ ATO9UQ9VS9WU9XW8ZY8__8`a7ac7be7dj5cg7cd8cbAc_BcYDc\ VEbSGbQHbNJbLKbIMcENbGNaINaJN`LN`MN_ON_PNZRNZSNYUN\ YVNXXNXYNW_NW`NYbN_cNaeNcfNfhNiiNmkNplNpnNuoNzqNzr\ NzpMpoLjnKdmKalJajIbiIbhHcgGdfGfdFgcEibEjaDl`Cm_Cl\ aGkcKjdOifShhWhi_gkcfmgenkdpocrscswanp`iiZdcY_XWVR\ VQKXIBULESNGQQIOSLMUNKXPIZSGaUEcWCeZAh`8jb6ld8jcAi\ bChaDg`Ff_HeZIdYKcXMbWNaVP`UR_TSZSUYRWXQXWPZVO`UNb\ TMcSLeRKgQJhPIjOHlNGmMFoLEqKDrJCtIBvHAwG9vFBuFDtEE\ sEGrDHqDJpCLoCMnBOmBPlBRkATjAUi9Wh9Xg8Zf8`e7ad7cc7\ dd8cd9be9aeA`fA_fBZgBZgCY } END PARAMETER FILE=========================================