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Fractal of the Day
by Jim Muth
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Fractal enthusiasts, lurkers and visionaries: As I write this FOTD, I can look through the fractal shoppe window and see three separate fireworks displays in progress around the city. And the weather is also hot as a firecracker. Once again the predicted showers failed to appear, but the heat did not fail. It is getting ever more oppressive. The temperature of 99F (37C) was great for nothing but fractals. Tomorrow is due to be even hotter, so I suppose tomorrow will also be good for nothing. Today's picture is a new view of yesterday's cubic midget. It is actually the same scene of the Julibrot sliced in a different direction. The midget itself lies buried near the center of the frame. It's quite stretched and a bit hard to find. At this angle, which is close to halfway between the Parabolic and Oblate directions, the surrounding pattern undergoes a strange transformation. We can see the nine elements converging on the midget, but before they can trifurcate into 27 elements, they get cut off, and form some rather interesting configurations. (The 27-element convergence never appears.) I named the picture "A New Angle" to bring out the fact that it is a different aspect of yesterday's image. Yes, I did give the image a boost in a graphics program, but not enough to damage its purity. It's a very fast fractal, so it might be quicker to run the parameter file than to download the JPEG image file from: Since I've already exceeded my speculative philosophical quota for the day in earlier letters, I'll add nothing at this time. But I will be here again tomorrow with another fractal, which easily could be another view of the same scene. I also could easily erupt into more philosophy, (if my ramblings qualify as such). Check then to see what happens. Until then, take care, and I've yet to see the first fractal fireworks display. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START FORMULA==============================================
multirot03-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=z*z*z+c,
|z| <= 36 }
END FORMULA================================================
START PARAMETER FILE=======================================
A_New_Angle { ; 0:00:33.06 on a p233, 640x480
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formulaname=multirot03-XZ-YW passes=1
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}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
A_New_Angle { ; 0:00:33.06 on a p233, 640x480
reset=1960 type=formula formulafile=multmult.frm
formulaname=multirot03-XZ-YW passes=1
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}
frm:multirot03-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=z*z*z+c,
|z| <= 36 }
END 19.6 PAR-FORMULA FILE==================================
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times.
