FOTD -- February 19, 2005 (Rating 8) Fractal visionaries and enthusiasts: Today's image was created with the MandelbrotMix3a formula. This formula works much like the MandelbrotMix4 formula, with the exception that it combines four different powers of Z rather than two, and a critical starting point of Z must be calculated separately and entered as the real(p5) parameter. Since calculating critical points is too much like work, I rarely use the M-Mix3a formula. To produce today's image I combined various portions of Z^(2), Z^(-3), Z^(4), and Z^(5), and entered them as the first four parameters. The (p5) parameter is one of the formula's critical points. The parent fractal consists of two large Mandeloids surrounded by a horde of much smaller isolated and disconnected Mandelbrot midgets. Today's image shows one of these cut-off midgets. At first glance today's image appears to be a partially evaporated one. This is not the case. Fractals whose generating formulas contain positive powers of Z do not evaporate. Other than the brilliant white inside of the midget, the image consists totally of outside material. The skeletal effect was achieved entirely by rendering the scene with the outside set to 'tdis' and then creating a sharp discontinuity in the color palette, a fact which may easily be demonstrated by rotating the palette a few steps in either direction and observing how drastically the image changes. I named the image "Super Membranes". When I gave it this name I was thinking of 'M-theory' or 'membrane theory' the latest fad in the search for a theory of almost everything, which is augmenting and perhaps replacing 'superstring theory' just as superstring theory replaced the 'grand unified theory'. The rating of an 8 might be a bit overblown, but the image is one that makes the viewer take a second look, so a rating of 8 it will be. For maximum fractal convenience, the completely rendered image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Biting winds, snow flurries, and a high temperature of 28F -2C on Friday kept the fractal cats confined to the relative warmth of the porch, where they sat for no more than 15 minutes. Extra tuna was needed to keep their spirits up. This morning is starting sunny but cold. It looks like a questionable day in store for the duo. For me it looks like an average day coming up, which describes most all days here at Fractal Central. The next FOTD will appear in 24 hours, and if all goes well, it will have a bit of philosophy included in the philofractal version. Until then, take care, and be thoughtful. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Super_Membranes { ; time=0:01:36.88--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-2.30831927441704200/+0.742924861375744\ 90/963509.9/1/105/1.52394585894999324e-007 float=y params=1/2/0.5/-3/0.333/4/0.25/5/0.8364500249/0 maxiter=255 inside=255 outside=tdis periodicity=10 colors=000ppZpuXpzWrrVtjVvbVxVVpY_i`daciVfmNh`GjU9\ lc2nm4lr5kvJkzNlzSozWrz`rz`rz`rz`rz`rz`rzTG1XM2_S3\ cX4ea5hf6mk7rq8wv9zz9zwAzvBzuCn`CmdDluEktFknFjnGig\ HhfIifIkeJmeKofKqbQs_WuXawTguQmsMsqIyoLumNrkPoiRlg\ TheVecXbaZ__`XYaZWcaUdcSfeQghPijNjlOijOihPifPjdRkb\ SlaUm_VnYXoWYpU_qT`rRbsPctNeuLfvK_wSVxORyKMzGIzCCz\ 86z4KzKnzWgzSazOVzKPzGJzCCz86z4dz2Wz1Oz1Gz08z0AzY8\ zR6zK4zD2z6DzZ8zN4zBtzDjzAaz8Sz6Jz49z2izVkzX_zOOzG\ Cz8kzWezS_zOUzKOzGIzCCz86z4mzXPzG6zz5zq4zh3z_2zR1z\ I0z91zt0ze0zS0zE`z6Zz5Xz5Vz5Tz4Rz4Pz4Nz3Lz3Jz3Hz2F\ z2Dz2Bz19z18z1Bz5Ez9GzDJzHLzLOzORzSTzWWz_Yzc`zgbzj\ ezfhzbkzZnzVlzUkzTizShzRgzQezPdzObzNazM`zLZzKYzJWz\ IVzHUzGTzESzDRzCQzBPz9Oz8Nz7Mz6Lz4Kz3Jz2Jz1Mz6PzBS\ zGVzKMz3PzFRzRTzbVznXzzZzy`zybzxczxezwgzwhzvjzvlzv\ mzuozuqztrzttzsvzswzstztqztnzulzuizvfzvczwazwczrdz\ mezhfzcgzZhzUizPpzcpzazzz } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================