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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Due to an unexpected small but rushed job, which needs to be delivered by this afternoon, today's discussion will be brief. Starting with today's image we will begin a series of FOTD's that explore scenes in the fractals created by the formula Z^(sqrt(2))+C. These fractals are infinite in number, and all are broken by discontinuities, but the midgets in them are relatively easy to find, and though not as varied as those in the classic Mandelbrot set, the midgets still have much variety. The names will merely indicate the number of each image in the series. The name of today's image is "Square Root of 2-1", which indicates it is the first in the series of images based on the square root of 2. Today's parent fractal is the one at ground level of the MandelbrotBC2 formula. In future FOTD's we will investigate other levels reached by this formula. The rating of a 7 is the seventh consecutive such rating. The render time of 1-1/2 minutes is blessedly brief. The finished image is posted on the FOTD web site at: With lots of sun, reasonable humidity, and a high temperature of 86F 30C, Thursday turned out virtually perfect here at Fractal Central, especially for the cats, who spent the afternoon hiding in the holly thicket, making sure the cat from two doors down the hill kept his distance. With only a moderately heavy load of work to finish, my day was not quite perfect, but it came close. Today is starting with some clouds and quite warm. Possible showers are forecast for later. We'll see how it goes. The next FOTD will appear in 24 hours. Until then, take care, and dream of fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
SquareRoot_of_2-1 { ; time=0:01:30.66--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2
center-mag=+0.56788044566820710/+1.699692341050198\
00/884217.7/1/-10/4.03226944195589354e-009
params=1.414213562373/0/0/0 float=y maxiter=4200
inside=255 logmap=67 periodicity=10
colors=000G5CC6DE7EG8FI9GJAHKBILCIMDJNEK9FMAGNBHOC\
IODIQFMVHQ`JUgLYjNaoPeuRhzMjwHltCmq7on2plvI1wVLwgd\
NkPPiVQh_SgeTfjVepWduXczW`oVYeUVWTSMSPCRTJRXQQ`WQd\
bPhiPkoLmqHorDps9rt6suEgbMXKUMmfFzr9zmFzhKzcQzZVzU\
``PeXRiRSlLToFQhENaEKVEHODEHDBAD94DEASIGeMMsf1RcFJ\
`TCZe5hdDqcLkbIfaF``CW`ATbDQcGOdJLeMIfPGgRDhTAhU7h\
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52gH3hT3id3g_8fWCdRHcNLH70JC2KG4LK6MO7NS9OWBP_DQcE\
TeKWgPYiV`k_cmdeojhqojrtdso_tjVueQv`LwWGwRHsTIpUJl\
VKiWKfXOcURaRVZPYXMaUJdSHhPEkNCcJOXGZPCiI9tUQZefDh\
YLkQTnI`qAhHXPGXPGXPGXPGXOFWOFWOFXOFYOE_OEaOEcOEeO\
EgODiNDkNDmNDoN0qICsNCuNCwNCxNByNBzNBzMBzMBzMAzMAz\
MAzMAzM9zM9zM9zM9zL8zL8zL8zL8zL8zL7zL7zL7zL7zL6zK6\
zK6zK6zK5zK5zK5zK5zK5zK4zK4zJ4zJ4zJ3zJ3zJ3zJ3zJ2zJ\
2zJ2zJ2zI2zI1zI1zI1zI1zI0zI0zI0zI0zI7zn6zm6zm6zm6z\
m6zm6zm6zl6zl6zl6zlgzWszs }
frm:MandelbrotBC2 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*floor(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END PARAMETER FILE=========================================
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times.
