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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Fire and brimstone fill today's image, as an erupting fractal volcano on the left spews its fiery ejecta high into the atmosphere and over the cliff at the right edge of the frame. In the cloud of debris near the right edge lies a tiny object resembling a midget M-set. The resemblance is only superficial, for at the odd angle of today's image, no midgets are possible. The image is an odd slice of the open rectangle that appears in the C=-1.7435,0.0 Julia set of the Z^2.003+C fractal at Z coordinates 0.00019,0.07388. This unexpected and near perfect rectangle is one of my favorite fractal objects, one to which I often return. Its actual four-dimensional shape would appear to a 4-D person as a 2-D hole, with two extended dimensions and the remaining two dimensions very small, much as a sheet of paper in our 3-D world has two extended dimensions and one small dimension. Since two of its four dimensions are so small, this open area appears as a rectangle only when sliced in the Julia direction and at the exact C coordinates. The slightest rotation or imag(C) deviation totally destroys its straight edges and surrounding symmetry. At today's angle, the symmetry is totally destroyed. I named the image "Firefall" because, with a little imagination, it shows fire spewing from the ground and falling over a cliff. Others may see something else, but the falling fire is all I can see. The rating presented little problem. The slightly-above-average 6 seems just right. The image is a fast one, requiring only 2-1/4 minutes to render from the parameter file, on my worn-out machine. About the same time will be required to go online and download the completed GIF image from Paul's web site at: Freezing rain, followed by heavy rain and melting snow brought flooding, fallen trees, power outages, and a roof leak to the Fractal Central area Wednesday. By evening, the high temperature of 36F 2C had melted most of the ice that had built up on trees and sidewalks. Conditions were so bad outdoors that the intrepid cats were thankful to be permitted to remain indoors all day. The roof leak will require further investigation. Today is starting much improved, but I expect a lot of work before the day is finished, which might cut into my fractal time. To see how things work out, check back here in 24 hours, when the next FOTD will appear almost by magic. Until then, take care, and beware of fractal brimstone. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Ongoing_Eruption { ; time=0:02:17.75--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=multirot-XZ-YW-new center-mag=-0.01885\
870562667460/-0.00508405854824132/96.13768/0.1758/\
-180/-72.5978701069904417 params=98/-8/2.003/0/0.0\
0019/0.07388/-1.7435/0 passes=1 float=y
maxiter=2500 inside=atan periodicity=0
colors=000UGWTETWCSTCPSAORAMP8KO7JM6HK5HJ4HI4GH4GG\
4GE4FD4FC4FA4EA4E74D64D54D44C34C24C24A44A64A84AA4A\
D5AF6AG7CH8CIA7JADKCEMDENEFOFFPFGRFFSFFTFEUFEWFDXE\
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X4YX6XX7XX8XXAXXCWYDWYFWYGWYHUYIUYKUYMTYNTZPTZRTZS\
SZUS`KZ`KYZJYYIYXIXXHXWGX }
frm:multirot-XZ-YW-new {; 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)+p3, c=e*imag(pixel)+p4:
z=z^(p2)+c,
|z| <= 36 }
END 20.0 PAR-FORMULA FILE==================================
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