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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is undoubtedly the bluest of all time. But it's not really a melancholy blue, it's a dynamic artistic blue, a deep royal blue that brings out the incredible energies flowing within the number fields that make up the world of fractals. Actually, it's a slice of the Julibrot that results when Z2 is divided by (Z^(2)+1.5). Yes, I realize that the value of real(p5) is 4, but dividing Z2 by Z2 creates a fractal with Z4 attributes just as multiplying Z2 by Z2 creates Z4 attributes. The 1.5 value of imag(p5) merely enlarges the parent fractal and moves the switchover to Z4 stuff to a deeper level. To add to the confusion, the orientation of the image slice lies halfway between the Mandelbrot and Rectangular directions. And actually, the Mandelbrot attributes are more apparent in this halfway direction than in the straight Mandelbrot direction. (To see the straight Mandelbrot direction change the value of real(p1) from 45 to zero.) Since blue is one of my favorite colors, and there is so much of it in today's image, I rated the image at an 8. The name "Blue Mandeloid" is a bit of a misnomer however, since the image is as much a Seahorse Valley Rectangleoid as a Mandelbrot fractal. One thing not in doubt is the speed of the calculation. It takes all of 13-1/2 seconds for the included parameter file to run on a S.O.T.A. machine capable of digesting ancient DOS programs such as Fractint. The finished image, in all its deep blueness, is or soon will be posted for instant viewing enjoyment on the FOTD web site at: There were a few more clouds than the fractal cats would have preferred here at Fractal Central on Tuesday, but there could be no complaining about the temperature of 77F 25C. The cats did not complain. With the real work finished early, my day was a bit slow. After browsing an hour or so in the philosophical section of the local library, I returned and settled down for my daily contest with the world of numbers. As today's image shows, the results of the battle were rather good. The next FOTD will be posted in 24 hours. Until then, take care, and think in higher dimensions. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Blue_Mandeloid { ; time=0:00:13.34-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot passes=t periodicity=10
center-mag=0/-0.457742/0.9418072/0.819/90/0 float=y
params=45/0/0/90/-1.25/0/0/0/4/1.5 maxiter=1500
inside=0
colors=000D3AD3DD3GE3JE3ME3PF7SFBVGFYGI`HMcHQfIUiI\
XlH_oGbrFeuEhwFkxKnyPqzUtzZwzczzhxzmvzrszvpzzmzzjz\
zgzznzzpzzqzzrzzpzwozwmzwizwgzwfzwgzwfzVlzUmzTmzSm\
zRmzZgzfbznXzvSzrQznPzjOzgNzcLz_KzWJzTIzUGzVEzWCzX\
AzX8zP7zH6z95zJVzTszKczCPzDPzDOzEOzENzFNzFMzGMzGLz\
HLzHKzIKzIJzIJzHMzGPzGRzFUzEWzEZzD`zCczCfzBhzAkzAm\
zDjz9pzIBzFQzCdz6szl7zTVzVOzNZzGhzfPzcSzaUzZWzXYzU\
_zSazQczNfzLhzIjzGlzDnzBpzxJzfVzQfza5zXDzTKzPRzLYz\
HdzDkz9Yz9hz9wz9vz9uz9uz9tz9tz9sz9sz9rzSAzPFzNKzLP\
zJUzHZzFczDhzBmzx9zsDzoHzkLzfPzbTzZWzU_zQczMgzHkzD\
ozVKzTNzRPzQSzOUzNXzLZzKazIczGfzFhzDkzCmzApzSIzLVz\
Ffz49z6Lz7Wz8gz0Wz5gzn3zUTz6Yz8hzMqzKrzIrzHrzFrzDr\
zCrzArzdDzaHz_KzXNzVQzSUzQXzN_zLbzIfzGizDlzBozKFzJ\
JzINzHQzGUzFYzE`zDdzChzBkzAozLlzFoziGzdLz_QzWVzR_z\
MdzIizDnzNXzIdzDkz8uz9tz9tz9tz9sz9sz9sz9sz9rz9rz9r\
ztUzh`zEGzDBzC6zB2zC3zC3z }
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=========================================
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times.
