FOTD -- March 13, 2010 (Rating ?) Fractal visionaries and enthusiasts: Today's image holds not only the promised surprise but a mystery as well. I named it "Misplaced Surprise" because the minibrot in the upper right seems strangely out of place. Yesterday's image is an East-Valley-type Julia set. This is evident by its appearance. Today's image shows the same scene from a viewpoint double-rotated only 0.001,0.001 degree from the Julia direction. (Double rotation is another story.) Despite such a tiny rotation, the resulting image has lost all resem- blance to a Julia set, and more closely resembles a non-critical Mandelbrot scene. But wait! This is impossible! What is a near-perfect Mandelbrot minibrot doing in a fractal that is so close to being a Julia set? Actually, the minibrot is far from perfect. A closer examina- tion will reveal that it is perturbed, but the fact that it is there at all makes the image so exceptional. When I began rotating the scene toward the Mandelbrot orienta- tion, I had one of the biggest surprises of my fractal career. A near-perfect Mandelbrot midget unexpectedly appeared amidst the degenerating Julia features. This is striking because, due to the four-dimensional shape of Mandelbrot elements in the Julibrot, with 2 infinitely extended dimensions and 2 compact dimensions, Mandelbrot features supposedly cannot appear in a Julia set. Another thing I notice in the image is the missing elements. In the pure Julia version, 32 striped red elements surround the cen- ter. In today's almost-Julia version I see only 24. I have no idea what happened to the missing elements, though I suspect a second radiant center lies off the screen some distance to the left. I have no answers to these fractal paradoxes, nor do I expect to think of any. I guess it will forever remain one of those unex- pected things that make fractals so interesting. Since the image is of purely mathematical interest, and would have little artistic worth to the 'look ma I'm an artist' type of fractalist, I rated it at a question mark. The calculation time of 1-2/3 minutes for all this surprise and mystery is quite a bargain. Those who are not bargain hunters may view the image on the new FOTD web site at: <http://www.Nahee.com/FOTD/> The weather here at Fractal Central took a turn for the worse Thursday night, and Friday dawned with cloudy skies and light rain. Friday brought continued clouds, intermittent rain and a temperature of 50F 10C. These conditions did not please the fractal cats, who wanted more sun. Unfortunately, with rain forecast for at least 3 more days, the cats will remain unhappy. My day was fair enough. If all goes well and no antiquing expedition arises on Saturday, the next FOTD will be posted in 24 hours. Until then, take care, and be with the fractal elite. P.S. My almost-useless AOL e-mail address may be discontinued in a month or so. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Misplaced_Surprise { ; time=0:01:39.89-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t float=y center-mag=-0.00021870072691744/-0.000080784627994\ 88/3194.472/1/-7.5/0 params=89.999/0/89.999/0/0.27\ 58107881858941/-0.006746958379780152/0/0/2.003/0 maxiter=6000 inside=255 logmap=310 periodicity=0 colors=000000XJaMCPB6CvGeFMQ7BDz82S51E20zEPS9GE48T\ UqJK_9AIaFgPATC5E8maeqz2`q1Rc1IR09DrtxdehRSUDUzVKz\ F6Sry4di3RV2DF1kisWU`GFIlxG_hCOU8CF4ixpNUQdz0zO0KG\ 0A80Ah06U03F0WvEGT7e08BrglGwZVoLih8xaGmRObGWT5faAz\ zFzzKe_DMj7LI6qU`_KOIACoqTQREURYKIMA9BdIQUDJK9DA46\ tZoqHX_BMI5B`xpvuDgf9TT6EE3aRzJDVBmg7XT3GE1Ul0M_0F\ O07CkPQWGHG88pONbIHQCBD65UuzaT1SL0JE0970EyqAic7VR3\ FDaQxSJhJDU96FwXTUGEhnyNwFFcA7K5peXQLGDB08704304Db\ 8z94V4LjGEVA7F5EVK9KD4A6jZRCZq9Qc6HR38D`8qI4R6_gtH\ FS87pD9Z86H43fYHWPCLH8A842Ly1AVig6UT4FE2q4M9Ib6DT4\ 9J2499vL6gF4TA2E5NTBHL8BE5572Q82J61D41620tg4SM2L2H\ E1B705gtaMSJte1eV0SL0EA02Rg1IT09ECMO6BCEOMp_BZO7HC\ 3itOYeINSCBE6upGfbCTQ8ED41g9hzz0MUzr2jqK0fFzOABC57\ bdUEQhAJU7Dc36_RLOIEC970`50O30C1Da_8PO4CCZG6NA4B52\ _MgRGXIBM95Bk7oW4YG2HhheSDDI88944vlOi_RNIDt2fa1SJ0\ Es78e56S34E12ZunAgH7XCzzz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================