FOTD -- March 01, 2004 (Rating 6) Fractal visionaries and enthusiasts: Recently on the Fractint list I saw an image posted that shows disconnected features in the Julibrot. The image started me wondering. It is known that the classic Mandelbrot set is connected, but the perturbed M-sets are not. And it is known that Julia sets are either connected or disconnected, depending on whether their corresponding Mandelbrot points lie within the M-set itself. But, to my knowledge, has it ever been determined whether or not the four-dimensional Julibrot is connected? Does every apparently disconnected point have a filament leading through hyperspace back to the central hyperbay? I rather suspect that the Julibrot is connected, but this is based on intuition. I have not seen it proved and I could easily be wrong. . . . Now on to today's image . . . To find today's image, I took Z^(-1.2), combined it with 0.2 parts of Z^(2.1), then added (1/C). The resulting fractal consists of a large, distorted Mandeloid with a smaller, discon- nected Mandeloid some distance to the east. To locate the scene of today's action, I checked the East Valley of the larger Mandeloid, which in this case is on the north shore of the main bay. The scene of today's action lies in the interior of this valley, disconnected from the rest of the fractal. As is always the case, the disconnected nature of the general area is reflected in the disconnected nature of the features surrounding the central midget. The curving, feathery filaments add just enough artistic touch to qualify the image as FOTD for the first day of March. I had intended on naming the image "Fractal Interlude", but for some reason I wrote "Florida Interlude". The mistake seemed as good as my original intent, so I let it stand. Not much need to be said about the rating of 6, which is the most common FOTD rating. When adjusted for the render time of 4.07 minutes, the rating jumps to a 98. Those who choose to download the finished product from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will have little reason to concern themselves with the render time. The cats had a near perfect day in the Fractal Central yard on Sunday. With a temperature of 66F 19C and lots of sun to lounge in, the duo had nothing to do but nothing all day. And they do nothing very well. When evening arrived, they came indoors with their tails straight in the air, ready for their dinner. Today is starting in a similar manner. Hopefully, things will go just as well for the duo. I have a bit of work to clear away before I can declare my day a success. And the best way to finish a job is to start it. Until the next glorious or not-so-glorious fractal appears, take care, and watch for hit-and-run fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Florida_Interlude { ; time=0:04:04.09--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.59508887023064300/+0.219397667625330\ 00/40616.79/1/165/-7.78849103266754383e-009 params=1/-1.2/-0.2/2.1/1/0 float=y maxiter=620 inside=0 logmap=74 periodicity=10 colors=000FGQG8QHBSIDUKFWMHYOJ_RLaTNcVPeXRgZTi`Vkb\ XmcZoc`qc`tcbufaxgaxibxkbxmcwoewqhwskuumrwomvmhukc\ thZseUrbPq_KpXKoUKnRLmOLlLLkILjFLfJIbMG_PEWSBTV9PY\ 7M`4Ic2Ff0Ec2E`4EY6EV8ESADPCDMEDJGDGIDDKDAMBHJ9NHF\ TFKZCPdAUj8Zp6cq7hq7mrAqrKtsUwsczthztcruUmuKhvBcvB\ olAl_9pO9tD8x28zrOxsNvtMtuLrvKpvKmnHkgFi_CgTAeWCcY\ Eb_G`aI_dKYfMXhOVjQTlSSoUQqWPsYNu_Mw`PtYSrWUpUXnSZ\ lQajOdhMfeKicIkaGn_EqYCsWAvU8xS6uS7sS7qS8oS8mS8lcJ\ koUjmd_mdPmdEmdGmLIm1Km3Lm4Mm5Nk6Pj8Qi9RpASwBRuAQt\ 9Qs8Pr8Pq7Op6No5Nm5Ml4Mk3Lj2Ki2Kh1Jg0Jf0Kd4Kb8K`CL\ ZGLYKLWOMUSMSWMR_UZS`eLglDns6jp9fnCblFZiIVgLReONbR\ J`UFZXBXZDYXEYWGZVHZUGaUFdUEgUDjUCmUVqYlt`hpaelaai\ aZeaWcaScaPcaLcaIcaFcaBca8ca5ca8cZBeXDgVGiTIkRLmPN\ oNQqKSsIVuGXwE_xCazAdz8fz6gz7hz7iz7kz7mz7oz7qz7szT\ uzRwzPzzOzzMzzLzzJzzIzzPzzVzzazzUzzUzzUzzUzzUzzUzz\ UzzUzzSzzNzzIzzEzzBzz9zz7 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================