; Date: Fri, 06 Feb 2009 22:40:09 -0500 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 07-02-09 (Julia More or Less [?]) ; ; Id: <1.5.4.16.20090206223945.2b177a3a@pop.mindspring.com> ; --------- ; ; FOTD -- February 07, 2009 (Rating ?) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is not a Mandelbrot set, nor is it a Julia set. ; It is an Oblate set, a hybrid mixture of Mandeloid and Julia ; stuff. The X-axis lies in the Julia direction, while the Y-axis ; lies in the Mandelbrot direction. ; ; I have not yet made up my mind about today's image, which is why ; I gave it a rating of a question mark. At times, these four- ; dimensional slices through the Julibrots can be spectacular, but ; at other times, they are just plain ugly. Today's image lies ; somewhere in between. ; ; The name "Julia More or Less" is absolutely true, but only as ; long as we consider the horizontal direction. When we turn to ; the vertical direction, we are moving through a Mandelbrot set. ; The other directions lie in the Julibrot, and are neither Julia ; nor Mandelbrot dimensions. ; ; The parallel blue stripes in the background are the 'bridges' ; that exist only in planes in which only one direction is perpen- ; dicular to the Mandelbrot orientation. When all directions are ; perpendicular to the Mandelbrot orientation, which is possible ; only in spaces of four or more dimensions, we have a Julia set. ; ; Maybe I'll continue this four-dimensional stuff in upcoming ; FOTD's, maybe not. I've gone over it several times in the past. ; ; Perhaps the best feature of today's image is its brief calcula- ; tion time of only 49 seconds. And even this minor effort may be ; totally avoided by surfing electronically out to the FOTD web ; site at: ; ; ; ; and viewing the finished image there. ; ; Not a single cloud marred the spectacularly blue sky here at ; Fractal Central on Friday, while the temperature of 36F 2C felt ; like spring. The fractal cats enjoyed the weather from their ; sunny shelf by the big southwest window, taking their breaks ; only when hunger called. My day was busy enough that one would ; never guess we are supposed to be in economic hard times. The ; next FOTD will be posted in 24 hours. Until then, take care, ; and it's all real, whatever that means. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Julia_More_or_Less { ; time=0:00:49.79-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot passes=1 maxiter=3600 center-mag=2.31005/0/9.197812/1.3049 params=0/0/90\ /0/-1.3243408/0/0/0/3/1.4 float=y inside=0 logmap=6 symmetry=xaxis periodicity=10 colors=000P9bL9fI9iE9mA9p69t39w6Br9CnBEjEFeGHaIIYL\ ITOIPNILNIGOICPI8QI9RI9SI9TI9UH9VGAXEAYDA_DA`CAbAB\ c9Be7Bg6Bi4Bi3Bm9GqFLuLQxQVuSYrT_oUalVciXefYgcZia_\ kZagWccUd_RfWOhSMiPJkLGmHEnDKp9Kq6Kq6Kp7mo7mo7mn7m\ n8zm8zz8zz8zl8mk9mj9mj9mi9Bi9BhABgABfABeACdACcBCcB\ CcBCcBCcBCcCCcCCcCDcCDcCDcDDcDDcDDcDDcDDcEDcEEcEEc\ EEcEEcFEcFEcFEcFEcFEcGFcGFcGFcGFcGFcHFcHFcHFcHFcHG\ cIHcJHcJIcKJcKJcLKcLLcMLcMMcNMcNNcOOcOOcPPczQczQcz\ RczSczSczTczTczUczVczVazW_zXYzXWzYUzZSzZQz_Qz_Qz`Q\ zaQzaQzbQzcQzcQzdQzeSzeUzfWzfYze_zdazdczcczcczbczb\ czaczacz`cz`cz_czVczZczZczYczYczXczXczWczWczVdzZez\ YdzYdzYdzYczYczYczYczYbzYbzYbzYazYazYazYazY`zX`zX`\ zX`zX_zX_zX_zXZzXZzXZzXZzXYzXYzXYzXYzXXzXXzWXzWWzW\ WzWWzWWzWVzWVzWVzWVzWUzWUzWUzWTzWTzWTzVTzVSzVSzVSz\ VSzVRzVRzVRzVQzVQzVQzVQzVPzVPzVPzTKzJ2zK3zK3zK3zK4\ zK4zK4zK4zL5zL5zL5zL5zL6z } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint