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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: I really had no chance to find a proper fractal today. I used the little bit of free time I did have by writing the philosophy which appeared earlier on the Philofractal list. Pressed for time, I went to the Julibrot and got a new angle on the East Valley area of the largest Minibrot, the one at -1.75(realC). The angle of today's slice is turned 8-1/2 degrees from the Rectangular direction toward the Oblate direction. That certainly is a new angle. What I found is a feature which at first glance appears to be a mini-Julia set. But it can't be a Julia set because it's in the wrong orientation. This wrongness shows up as a lack of symmetry. I named the picture "Almost Symmetrical" because though it appears to have origin symmetry, a close examination will reveal subtle differences between the two halves. In fact, there is actually a bit of open area that appears in the lower right part of the image. The parameter file is not too slow, but it's slow enough that a download will make life a bit easier. That downloadable image file that will make life easier can be found on Usenet at: The weather today was surprisingly chilly. The temperature of 55F (13C) was great for fractals -- too bad I didn't take full advantage of it. The day's philosophy was posted several hours ago, so though I've got nothing to add at this time, I feel that my duty has been fulfilled. And of course I'll return as usual tomorrow in this exact spot. Until then, take care, and be at one with the world. Jim Muth jamth@mindspring.com |
START FORMULA==============================================
multirot-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=sqr(z)+c,
|z| <= 36 }
END FORMULA================================================
START PARAMETER FILE=======================================
Nearly_Symmetrical { ; time=0:04:24.00 on a p233, SF5
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XZ-YW passes=1
center-mag=-0.13405166828134080/+0.004569752847568\
19/5311.397/0.7724/24.127/28.611
params=90/81.5/0/0/-1.747/0 float=y maxiter=12500
bailout=25 inside=0 logmap=22
symmetry=yaxis periodicity=10
colors=0004A41A2<6>E`TGdXIh`<2>NskPwoQxrPvoPsleoie\
lfeic<2>g`VhZSiYQ<3>mUMnTLoSKoRK<6>dFfcEiaCl<3>X6x\
LVw9sw<4>4`Z4XV3TQ<2>0IB0F71H9<6>8TG9VHAXI<2>DaLDb\
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LBoO<3>5yZ<3>RUWXMWaEVf6V<11>7A6
}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Nearly_Symmetrical { ; time=0:04:24.00 on a p233, SF5
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XZ-YW passes=1
center-mag=-0.13405166828134080/+0.004569752847568\
19/5311.397/0.7724/24.127/28.611
params=90/81.5/0/0/-1.747/0 float=y maxiter=12500
bailout=25 inside=0 logmap=22
symmetry=yaxis periodicity=10
colors=0004A41A2<6>E`TGdXIh`<2>NskPwoQxrPvoPsleoie\
lfeic<2>g`VhZSiYQ<3>mUMnTLoSKoRK<6>dFfcEiaCl<3>X6x\
LVw9sw<4>4`Z4XV3TQ<2>0IB0F71H9<6>8TG9VHAXI<2>DaLDb\
MC_P<3>BRXBPZAN`ALbAJd<3>WNMaOHfPCkQ8<4>hENgBPg9S<\
3>e0b<3>Q4PM5MI6JE7G<5>CYcCbgCfk<3>BxzLvE<3>EpLCnN\
BmP9kR8jS<9>WUPYSP_QP<3>hKO_VHReA<3>daFg`Gj_HmZI<3\
>`KXXH_UDc<2>L3m<3>ipK`YVTFdTAUT6K<3>i9`mAeqAiuBmy\
BqyI`yPLrWYkai<6>bmfaoe`qe<3>Xwd<3>juQmuNpuJsuG<3>\
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LBoO<3>5yZ<3>RUWXMWaEVf6V<11>7A6
}
frm:multirot-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=sqr(z)+c,
|z| <= 36 }
END 19.6 PAR-FORMULA FILE==================================
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times.
