FOTD -- August 04, 2008 (Rating 9.5) Fractal visionaries and enthusiasts: I'm starting to discover the potential of the DivideJulibrot formula. Today's image is a Julia-set of East Valley of the large minibrot on the main stem of its parent fractal. This parent fractal came about when I divided Z^2 by (Z^(16)+10). On the surface it resembles an oversized Mandelbrot set, while deep inside it takes on Z^16 characteristics. The image is a splendid blending of quadratic East Valley elements with the more circular Z^16 elements. It rates a full 9.5, 1/2 point of which is due to my marginally expert coloring efforts. I named the image "Hexidecimal Quad" in recognition of the mixture of elements of two different orders. The calculation time of a superluminal, (which is possible in the world of fractals), 23 seconds, will make running the included parameter file a pleasure. An equal pleasure may be experienced by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the already-calculated image is posted for instant ecstasy. The Sunday weather here at Fractal Central was so good that the digital thermometer read 'comfort' from sunrise to sunset. Lots of sun, low humidity and a temperature of 82F 28C in the middle of the dog days must be considered near perfection. The fractal cats were more interested in a squirrel that was in the yard all morning, gathering nesting material. I did little but take it easy most of the day, though far busier days are in sight. The next FOTD will be posted in 24 hours. Until then, take care, and forget philosophy for a day -- a lack of philosophical pondering leads to less wisdom but more peace of mind. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Hexidecimal_Quad { ; time=0:00:23.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=0/0/0.891266\ /1/-90/0 params=90/90/90/90/-17.4231/0/0/0/16/10 float=y maxiter=1600 logmap=11 periodicity=10 colors=000FA2HA0LA0OA5S8CXAJaCQfEXkGcpIjuKqiJnYJkN\ JhKYLHk0Fd0DZ0BT09N08H0zh4zc8zECmCJcBOUAQK9QJAPKAK\ LBKMBKNCMOCSMKULRZKYaJeaIldHthKvmMurPxzRzzTzzXlz_`\ zdZqO_UNYTMWSLURKSQJQPJOOMZJWbFcfBci8mn4mu1zzCVXNb\ NYjDhlCbnBYoASq9Ns8Ht7CrAGpDKnFOmISkLWiN_gQcfSggcd\ hnaiyZhydgyjXqbMiWBaO0VH8TEFRCNQ9UO7`M4hL2oJ0vI0uJ\ 6uKFtLOtMWnbfhrqikojemjZkkTjlMhlGfm9dm3ch9YcESZKMV\ PGFcnJXnNRnRLnVFnZ9nY7cX5TW3JV18V00Y70`E1bK2TGHKDV\ BAhUsnNq`GoO9mA3l0LZ9bMLs9WtGRuMMuSHvYCvc7liMbo`Ut\ o_X4cR7gLAkFDoAGrMKuXNxhRzsUzzMzzEzz6zz0zz0cm1ar2`\ v3_z4WwCTtJQqRNnYKke4SV3PS2MP1KN4GV7Db8Ea8Ea9F`9F`\ AF_AG_BGZBGZ65h8Be9GbAL_BQYCWVD`SEePFjNPeLY`KgWJpS\ IeYEWbALg6Bl3FkAJjGNiMRhSVgYZfcbeifeo`hpWjqRlrLosG\ qtBsu8cf5OT29F3MI4ZK4kMDkRLkVUkZakbjkfrkjricrgXreQ\ rdKrbDr`6r_0jS4cL8XECQ7GJ0KNBGQMCUW9Xf5_p2XmCVjLSg\ UQdbObkTfiXihalgeofFZ6GR4 } 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)+0.00000000000000000001, 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=========================================