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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: A little bit of 3i can make a great difference to the appearance of the classic Mandelbrot set. In today's fractal we add only 1/10000 part of 3i to the M-set, but that tiny part of the imaginary number wreaks almost total havoc. Today's scene is located in an area that would lie near a small bud on the southwest shore line of the M-set -- that is if the parent fractal were the undistorted M-set. But though there is a resemblance, the parent fractal is not the M-set, it is little more than a parody of that mighty fractal. When 1/10000 part of 3i is added, to the Mandelbrot set, the set looks like someone took a knife to it and tried to slice it into quarters. I am not sure whether the result is a true fractal or an artifact of the formula, but whatever it is, it holds some interesting places to explore. Since I put next to no effort into today's image, I did not name or rate it. The calculation time of 2-2/3 minutes on my P133 machine equals about 1-1/2 minutes on the standard P200 machine. This is brief enough so that little effort will have been wasted if the image fails to please. And if all else fails, the already-calculated image is available for viewing on the FOTD web site at: It's been another spectacular day for me and the fractal cats here at Old Fractal Central -- lots of sun and a temperature of 75F 24C. While I spent the day enjoying the weather, the cats spent the day lurking in the holly thicket. Unlike the new fractal cats, who can only look outside, the old guys get to go there. The next FOTD will appear by technological magic in 24 hours. Until then, take care, and if no FOTD appears in 24 hours, it will be because the ancient machine I am working on has finally come to its last iteration. (Every time I turn on the old P133, it's a battle getting it to start up as it should.) Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
FOTD_for_May-02_07 { ; time=0:02:41.75--SF5 on a P133
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMixImag function=ident float=y
center-mag=-0.64917647027/-0.388846347602/31162.79
params=1/2/0.0001/3/0/0 maxiter=2500 periodicity=10
passes=1 inside=255
colors=000zW8zSCzQExMIrKKlIMhFQbDSYAXSAZMA`IAdDAf9\
AhQAnfIsxUxzdzz_urWphSmXOhMKdDH`8DX8AS8AP8AK8AG8AE\
8DC8H88K88O88S88W88_88d88h8Kl8Up8ct8Un8Kh88aK8WX8Q\
h8Mb8IZ9FVABPAAKAAGAACAA8AA8DA8GA8KA8UA8cA8mA8zA8z\
KEz_PznZvZQ_IKFAFDAKDAPBAU9AZ8Ae8Ah8Af8Dd8K`8SZ8ZX\
8fV8nQ8tP8zM8zK8zI8zS8zb8zj8zu8zz8xz8rx8ls8dpBZmGS\
jKKfQFdXA`bAZhAVnASrAQlAffAxjAslApnAmrAjuAfvBdxDbz\
HZzIXzKSzOQzQMzSKzUIuQb_OudMphKmlIhpHduF`xDXzBSzAP\
zAKzAGzACzA8zA8zA8zA8zA8zA8zA8xB8uD8nF8hH8dI8XS8Q_\
8Ij8Dr88z88zC8zK8zS8zVDOAIIIOAGUAPYAXOAZFE`8Ve8ei8\
tl8zp8zp8zu8wzBlzOazbSzpIzzAzzAzzAzzAzzAzzAzzAzzAz\
xAzvAzrAzpAznAzlAzjAzlAzlAznAunAmnAdpAVpAMrAErB8rB\
8uI8vO8xU8z_CzhGznIztMzzQzzSzwEzl8za8zS8zK8zI8zI8z\
I8zIAzHMzHXzHhzHuzHzzIzzIzzIzzIzuIznKzhKzbKzXKzQKz\
KMzFMz9Mz8Mz8Mz8Iu8Hp8Dn8Bj8Ah8Ad8A`8AZ8AV8AS8AQDA\
PIAMQAKYDIdFGlIEuMCzQAzzz }
frm:MandelbrotMixImag {; Jim Muth
z=p3, c=fn1(pixel),
a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2):
z=a*(z^b)+d*(z^flip(f))+c,
|z| <= 100 }
END PARAMETER FILE=========================================
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times.
