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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Can a fractal be used as a wallpaper design? Today's image shows that the answer is yes. The old formula I resurrected for today is named "Wallpaper", and the only thing it aparently does is create a wallpaper-like pattern. Since the formula is based on the Mandelbrot set, I named the image "Mandel Variation-5". Like is true of so many of these old forgotten formulas, I have no idea where it came from or what it was originally supposed to do, though with the way the functions are piled on in the iteration part, I doubt that I wrote it. The (p1) parameter is set to a point some distance north of Seahorse Valley. Bits and pieces of this valley form the smaller, more intricate parts of today's wallpaper sample. The larger flat diamond shapes are simply parts of the iteration bands in the area. Is there a market for wallpaper with a fractal design? Who knows. Maybe it has already been tried. I myself prefer the peaceful feeling a smoothly painted wall induces, expecially when the color is a pastel tint of blue. But some people enjoy the liveliness that a busy wallpaper pattern can create. There might be a place for fractals on the walls of our homes, but surprisingly enough, not here at Fractal Central. After giving today's image careful consideration, I rated it a below-average 4. This is no reflection on the worth of the formula. The formula might have far better images in it, but wallpaper is just not my thing, so I will not work with the formula long enough to find out. One very good point however is the speed of the image, which with its XY-axis symmetry, renders in an incredible 3 seconds. It will take several times as long to stop by the FOTD web site at: Lots of sun and a high temperature of 75F 24C here at Fractal Central on Saturday was just what the cats have been waiting for. Only a rather brisk wind kept the day from being absolutely perfect. Today is starting sunny but not quite as warm. The day will probably be good enough for the duo. For me things look peaceful. Hopefully they will stay that way until the next FOTD appears in 24 hours. Until then, take care, and spare no fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Mandel_Variation-5 { ; time=0:00:03.18--SF5 on a P200
reset=2004 type=formula formulafile=jim.frm
formulaname=Wallpaper center-mag=0/0/0.04266667
params=-0.75/0.49/16/0 maxiter=95 inside=255
float=y logmap=yes symmetry=xyaxis periodicity=0
colors=000qmmnibkdSSEKYMJcUIQXR1NTNUNrp3ol7mhAjdEb\
KIXr8_mBbiDedFjAciOSmrWjiONGXYRPim4hi8hfBhcEiqWhkR\
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ih6heAhbEhXThYQhZNh_KyYlp_XZM0cU9nholecjbSemF8eELy\
TXlNGUxQXi_ZVhEehMXhUPCczLbnTac``SWhEkpkOSFVVGaYHE\
xLPpJZhIvFWoQOj5DiGFhRGIr6Pm9WiCbdF6meJhXWdPRHa_RR\
RMo_UYy1usDgmPUJJJQOIWSIbXHjnligXbvXdpTekPgeLo2kkK\
Wv1YoJPNb6aeaccWebRgaMtry }
frm:Wallpaper { ;
; use fp math, no periodicity, XY symmetry
; p1=location in M-set
; p2=magnitude
z=c=p1+(1/p2)*(tan(cos(real(pixel)))\
+flip(tan(cos(imag(pixel))))):
z=z*z+c,
|z| <= 64 }
END PARAMETER FILE=========================================
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times.
