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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I named today's highly-rated image "FMOD Fantasy". I gave it the name because the scene is an evaporated all-inside one that consists entirely of <fmod> inside fill. Without the fill, the scene would be a total blank. I do not know exactly how the <fmod> fill works. I assume it measures some distance, but however it works, it works quite well with today's screen-full of trapped points. (The <bof61> fill also produces a fractal rather than a blank screen, though the image produced by the <fmod> fill is by far the better. The parent fractal, which adds Z^(-0.25) to Z^(0.25), can hardly be called a fractal, for it also consists entirely of trapped inside points. With the <fmod> fill applied to it, the parent consists of a large crescent with the horns pointing east, the edges of the crescent lined with buds. Today's scene is located in the valley area of one of the second-order buds. When coloring the image, I used a little more care than usual. It shows in the result. One of the reasons I consider my FOTD images to be mathematical curiosities rather than works of art is that I so often lack the time to find and refine the best color palette for the images. I cannot consider something on which I do less than my best to be a work of art. But as mathematical curiosities, some FOTD images are truly unique. This is not surprising, since fractals themselves are unique. They come from nowhere, exist for a few brief moments, and unless recorded, return to whence they came. Though the appearance of today's image departs from that of my typical images, I rated it at an exceptional 8. The parameter file takes 14 minutes to run on my tired old machine. The GIF file of the completed image takes only a minute to download from: Running the parameter file is more fun; downloading the image is more convenient. The near ideal weather here at Fractal Central on Sunday resulted in reasonably happy cats. They approved of the few patches of sunlight that filtered through the holly trees, and they approved of the light winds. They would have preferred the temperature to have been a few degrees higher than 52F 11C, but they held their complaints to a minimum. Their moods remained adequate well beyond their evening meal time. Today's weather will be similar, though with a few more clouds. The cats' day will likely be similar also. Until tomorrow, when the next glorious FOTD will appear, take care and be mod but not fmod. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
FMOD_Fantasy { ; time=0:14:01.30--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.50885461141383900/+0.003097982086237\
17/2179214/1/-155/5.94581836543817133e-009
params=1/0.25/1/-0.25/0/0 float=y maxiter=1800
inside=fmod proximity=0.011 periodicity=10
colors=000iLJjMKkIGlFDmC9n96o32p53q63r74s84t95uA5v\
C6wD6xE6yF7zG7zH8zI8zK9zL9zM9zNAzOAzPBzRBzSCzTCzUD\
zVDzWDzXEzZEz_Fz`FzaGzbGzcGzeHzfHzgIzhIzhJziJyjKxj\
JwkJvjJukItkIsjIrkIrkHrkHqjHqjHpjGpjGojGojGojFnjFn\
jFmjFmiEliEliEliEkiDkiDjiDjiCiiCiiChhChhBhhBghBghB\
fhAfhAehAehAeh9dg9dg9cg9cg8bg8bg8bg8ag7ag7`g7`f6_f\
6_f6Zf6Zf5Zf5Yf5Yf5Xf4Xf4We4We4We3Ve3Ve3Ue3Ud2Td2T\
d2Ud1Td2Td2Sd2Sd2Sb2Rc2Rc3Rb3Qb3Qb3Qa3Pa3P`3O`4O`4\
O_4N_4NZ4NZ4MZ4MY5MY5LX5LX5KX5KW5KW6JV6JVUJVUIUUIU\
UITUHTUHTUGSUGSUGRUFRUFRUFQUEQUEPUEPUDPUDOUCOUCNUC\
NUBNUBMUBMUALUALUALU9KU9KU8JU8JU8JU7IU7IU7HU6HU6HU\
6GU5GU5FU4FU4FU4EU3EU3DU3DU2DU2CU2CU1BU1BU1BU2AU2A\
U3AU3AU4AU4AU5AU5AU69U69U79U79U89U89U99U99UA8UA8UA\
8UB8UB8UC8UC8UD8UD7UE7UE7UF7UF7UG7UG7UH7UH6UI6UI6U\
RsmRsmStmStmTtmTtmUtmUumVumVumWumWumWumQtmIwmLwmNw\
mQwmSwmUwmXwmZwm`wmcwmewm }
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END 20.0 PAR-FORMULA FILE==================================
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