; Date: Tue, 19 Aug 2008 22:33:20 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 20-08-08 (Blue Mandeloid [8]) ; ; Id: <1.5.4.16.20080819223409.2bd7d8f4@pop.mindspring.com> ; --------- ; ; FOTD -- August 20, 2008 (Rating 8) ; ; 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 Z^2 is ; divided by (Z^(2)+1.5). Yes, I realize that the value of ; real(p5) is 4, but dividing Z^2 by Z^2 creates a fractal with ; Z^4 attributes just as multiplying Z^2 by Z^2 creates Z^4 attri- ; butes. The 1.5 value of imag(p5) merely enlarges the parent ; fractal and moves the switchover to Z^4 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 center-mag=0/-0.457742/0.9418072/0.819/90/0 params=45/0/0/90/-1.25/0/0/0/4/1.5 float=y maxiter=1500 inside=0 periodicity=10 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========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint