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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's image, we sink all the way down to an exponent of Z^(1.015) and the hard-to-find chaos that lies in the resulting fractals. We examine this lowly fractal at a point 275 levels down the logarithmic spiral, though from the degree of disorder in the image, I assume the spiral has long since ceased to resemble the spiral shape we are familiar with. Not only is the image filled with discontinuities, but the discontinuities are discontinuous. The whole thing vaguely reminds me of an undersea scene, and I named it "Undersea Fantasy" accordingly. It's a spectacularly colored image, with colors perhaps a bit too gaudy, so I held the rating to a 7. As I warned earlier, the chaos in these very low fractals is of a very high maxiter and quite hard to bring out. The render time of 1 hour and 5 minutes for today's image demonstrates this fact. This slowness will grow only worse as we continue our descent toward our ultimate but perhaps unreachable goal of Z^(1.009). Luckily for fractalists with other things to do, the finished image of today's fractal will soon be available on the FOTD web sites at: With the temperature hovering around 66F 19C, heavy rain fell all day here at Fractal Central on Saturday. It came to an end shortly before sunset, but by that time the cats' day had been totally spoiled. Their moods were sour, and the tuna treat only partially restored their spirits. Today is starting cloudy, but at least it is dry. If all goes well, and the forecasted showers hold off, the dynamic duo will have a better day. The fractal basement took on water in the rain, so my task for today will be to dry things out down there. Until next FOTD, take care, and how low can you go? Stay tuned to see. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Undersea_Fantasy { ; time=1:05:47.33--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=-4.41217/0.0769257/4.96124/1/12.5/1.784\
961067841095e-013 params=1.015/0/-275/10000 float=y
maxiter=12000 inside=255 logmap=202 periodicity=10
colors=050LJYNJXNSXPHVPHV_HTQGTSGSSGQTGQTEPVEPVENS\
ENXDLXDKeDKYDI_BI_BH`BH`BFb9Eb9Ed9CY9Ce7AV79g79`77\
h67h65j65j64k52k52m51m51o50o50p50h50r50r50s50s50k5\
0s50s50s50s50s50s50s50s60m60s70s70s90s90hB0sB0uD0u\
D0uE0uE0uG0uG0uH0uH0jJ0uJ0uK1uK1jM1uM1uO1wO2wP2wP2\
wR2wR2wS4wS4wU4wU4wV4wV5jX5wX5wY5wY5x_7x_7xa7xa7xc\
7xc9xd9xd9xf9xf9xgAxgAxiAxiAxjAzl9xjAxjAwjAwjAuiAu\
iAuiAsiAsgArgArgArgApgApfAofAofAofCmdCmdCkdCkdCkcC\
jcCjcChcChcChaCgaCgaCeaCe_Ce_Cd_Cd_Eb_EbYE`YE`YE`Y\
E_XE_XEYXEYXFYVGXVHXVIVVJVVKVULTUMTUNSUOSSPSSQQSRQ\
SSPSTPRUPRVNRWNRXLPYLPZLP_KP`KOaIObIOcHOdHOeHMfFMg\
FMhEMiEKjEKkCKlCKmAKmAJmAJm9Jm9Jm7Hm7Hm7Hm5Hm5Gm4G\
m4Gm4Gm2Gm2Em1Em1Em1Em0Dm0Dm0Dm0Dm0Bm0Dm0Dm0Em0Em0\
Gm0Gm0Hm0Hm0Jm0Jm0Km0Km0Mm0Mm0Om0Om0Pm0Pm0Rm0Rm0Sm\
0Sm0Um0Um0Vm0Vm0Xm0Xm0Xm0Ym0Ym0_m0_m0am0am0cm0cm0d\
o0do0fp0fr0gr0gs0is0iu0ju }
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(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 20.0 PAR-FORMULA FILE==================================
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