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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is an outzoom from yesterday's image. It's not exactly glorious, but I felt like exaggerating when I chose the name, so I named it "Glorious Outzoom". The rating of a 7-1/2 includes 1/2 point for my extra coloring effort. Coloring in GIF mode takes effort. It's not easy to get smooth colors with only 256 colors to choose from. The purplish spot just southwest of the minibrot at the center of today's image is the source of the break in the smooth sequence of bifurcating features surrounding the minibrot, which itself has been caught in the act of shifting from quadratic to cubic. This purplish spot is in fact yesterday's anti-minibrot image. Today's minibrot itself resembles one of order 2.718 but lacks the discontinuities that I always thought 'must' exist in such fractals. I have not yet figured out what is happening, but whatever it is, it sure is interesting. (And since the universe is a giant fractal, and keeps breaking the rules that seem so intuitive to us, why should it be surprising to see our small-scale fractals doing the same?) Since my 2000mhz fractal machine is still out of action, and will remain so until I find the time and energy to tackle it, today's image was run on the ancient but faithful 200mhz unit. On the old unit it takes 4-1/2 minutes to finish. On the ailing 2000mhz machine, it would finish in about 1-1/4 minutes. But why worry about calculation time when the completed image is or soon will be posted for instant enjoyment on the FOTD web site at: What a minor let down! Gerald D. has informed me that yesterday's 'anti-minibrot' is actually an example of 'reverse bifurcation', which I assume is relatively rare, but not totally unknown. And a further examination of yesterday's image has shown that in this image at least, the symmetry totally vanishes beyond the stage of 2-part symmetry. (Then again, what else could it do?) In yesterday's trivial closing comment, I speculated that everything is an illusion, and wondered what then is having the very convincing illusion that I myself exist. Alex Dukay replied that in his opinion it is the conscious mind that creates the illusion of an individual identity. Now I wonder what is having the illusion that the conscious mind exists. (The logic seems to be going in circles here, but the flaw is hard to pin down.) Chilly temperatures around 39F 4C, mostly cloudy skies, and occasional showers of cold rain and wet snow made Wednesday less than perfect here at Fractal Central. The fractal cats agreed and wasted little time hunched on their shelf by the drafty window, watching the TV show outside. My day was about average, which still leaves some things to be desired. The next FOTD will be posted in 24 hours. Until then, take care, and prosper. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Glorious_Outzoom { ; time=0:04:28.53--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot5 maxiter=2000 periodicity=10
center-mag=+29.20416308310227/-1.333596110856609/6\
355680/1/100/0 float=y inside=0 logmap=168
params=3/100
colors=000cUncUmcUlcUkcUjcUicUhcUgcUfcUecUdcUdcUcb\
VbaW``WaZX`YX_VXZUXYTWXTVWTUVTTUSRTSPSQNRNLQKJPGHO\
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GteGtfGtfHtfHsgHsgHsgHsgHzzzzzzzzHrvHrrHqiIqiIqjIq\
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moJmoJmoKmpKlpKlpKlqKlqKlqKkqKkrKkrKkrKksLjsLjsLjs\
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`YH`ZIa_Ia_Ia`IaaIbbIbbIbcIcdJceJceJdfJdgJdhJdhJei\
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YzkXziXzhWzfWzdVzcVzaUz_UzZVz`VzaVzbVzcVzdVzeVzfVz\
gWziWzjWzkWzlWzmWznWzoWzp }
frm:DivideBrot5 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1)+0.00000000000000000001:
z=sqr(z)/(z^(-a)+b)+c
|z| < 1000000 }
END PARAMETER FILE=========================================
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times.
