; Date: Tue, 16 Mar 2004 11:06:58 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 16-03-04 (Paddles [6]) ; Id: <1.5.4.16.20040316110955.392fdf3e@pop.mindspring.com> ; --------- ; ; FOTD -- March 16, 2004 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; In a recent FOTD I wrote that almost all midgets in fractals ; created by the MandelbrotMix* series of formulas (formulae for ; the over-educated) are variations of the quadratic Mandelbrot ; set. Note that word 'almost'. Today's image shows a midget ; that most definitely is not quadratic, but cubic. And to top ; off the strangeness, the midget does not appear to be fully ; defined, almost as though it were cut in a non-critical plane. ; The pattern around the midget is perfectly defined however. ; ; This appearance of an imperfect cubic midget is far from the ; strangest scene I have stumbled upon in my adventures in fractal ; land. I have actually found perfect cubic midgets side-by-side ; in the same frame with midgets of the 6th order. A FOTD that ; appeared several years ago illustrates the scene. At the ; moment, the particular image is lost, but I would like to find ; it for further investigation. ; ; For some reason, the real(p2) parameter of today's image, which ; determines the amount of Z^5 to be subtracted from Z^3, is ; extremely critical, as it is in all fractals that I have so far ; found which contain higher-order midgets. ; ; I named the image "Paddles". The three prominent arms remind me ; of the paddle blades of an old-fashioned windmill. (Old-fash- ; ioned always seems to be more picturesque.) I rated the image ; at a 6, which is above average, but not outstanding. When the ; image's short render time is considered, its overall value comes ; in at a hefty 357. ; ; In a recent letter to the fractint list it was asked what I mean ; by a plane oriented halfway between the Mandelbrot and Julia ; orientations in the Z^2+C Julibrot. I am really not sure. The ; more I think about it, the less certain I become as to what I ; mean. I'll have more to say about this in the next FOTD that ; uses the Julibrot formula. ; ; I also recently was asked whether there is such a thing as twin ; fractals. I am not sure what the writer means by twin fractals, ; but there certainly are twin midgets. A pair of them will ; appear as tomorrow's FOTD. ; ; Though today's image is a fast one, the minor annoyance of ; running the included parameter file can be eliminated by ; downloading the completed image from Paul's web site at: ; ; ; ; The fractal cats, Thomas the lazy oversized orange and Tippy the ; thin wiry tabby, had one of their best days ever on Monday. It ; was one of those days when everything that could go right in the ; world of cats did go right. The weather was sunny, with a temp- ; erature of 63F 17C, but the big excitement came when a squirrel ; came too near Tippy, who appeared to be asleep. Tippy suddenly ; lunged and for a moment got his jaws on the squirrel's tail. ; Luckily for both the squirrel and Tippy, the squirrel pulled ; free and scampered up a holly tree, where he scolded loudly ; before going back to his hole. Thomas actually became alert ; during the scuffle. When they came indoors, I treated them to ; chicken, which they enjoy even more than tuna. ; ; But today is starting cold and rainy, and the two fractal cats ; are already turning sulky. We'll see how it goes. For me, it ; looks to be an average day. And if all goes well, the fractal I ; find will be above average. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Paddles { ; time=0:01:40.79--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.4615028914331138/0/9778.83/1/-90/3.8\ 857805861880479e-016 params=1/3/-0.21/5/0/0 float=y maxiter=2000 inside=0 logmap=25 periodicity=10 colors=000h0hh0hh0hh5hhAhhFhhKhhPggUffZeecddhc`k4V\ f9PbDJYIESMTLLZCKYHPYLTYPXXU`XYdXahWglWlpWqtYqrZrq\ _qoaznbulcpkdpj16l28m3An4Co5Ep5Gp6Iq7Kr8Ms9Ot9QtAS\ uBUvCWwCYwGTrKOnOJjREfV9bZ4Za0VZ5SWAPTFNQKKNPIKUFH\ YDFRNEKXCDeB6oA0xH6vNCtUIr_OpfUnl_lsejyjhvgiseiqci\ n`ilZiiXigViiWjjWjkWjlXkmXkoXkpYlqYlrYlsZmuZmvZmw_\ nx_ny_nz_nuakqbimcfiedefbag_YhYUjWQkTMlRImPEZRBKT8\ 6VAARBENCIJELGFPCGT8HW5G_4Fb4Ee3Dh3Cl2Bo2Ar19u1Ct2\ Fs3Ir4Lr5Oq6Rp7Uo8Wo8VmAVlCVlDVmFVnGUoIUpJUqLUrNUs\ OTtQTuRTvTTwUTxWTyXdzdpzlkzmgznczo_zpWzqSzrOzsKztG\ zuOzdWzOcz7bzAbzDbzGazJazMazP`zS`zU`zX_z__zb_zeZzh\ ZzkZzmPz5Pz7Pz9PzBPzDPzEPzGPzIPzKPzMPzNPzPPzRPzTPz\ VPzWSzXUzYXzZZz_az`cz``zZYzYVzWSzVPzUMzSJzRGzQWzaj\ zmhzhgzdez`dzWczSazO`zJZzFYzBXz7Uz6Sz5Pz5Nz4Lz4Iz3\ Gz3Ez2Bz29z17z17z17z17z16z16z16z16z16z16z16z15z0Zz\ hbzkeznizqlztpzwszzrzyqzx } 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 PARAMETER FILE================================== ;