Fractal of the Day (FotD) by Jim Muth

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 perpendicular 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 calculation time of only 49 seconds. And even this minor effort may be totally avoided by surfing electronically out to the FOTD web site at:

http://home.att.net/~Paul.N.Lee/FotD/FotD.html

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 periodicity=10 center-mag=2.31005/0/9.197812/1.3049 symmetry=xaxis params=0/0/90/0/-1.3243408/0/0/0/3/1.4 maxiter=3600 float=y inside=0 logmap=6 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=========================================