|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Today's strange image is a picture of a tiny midget located at -1.7496 on the negative stem of the Mandelbrot set, a point deep in the East Valley of the largest midget of all -- the one centered at -1.75. I named the picture "Midget Distortion" because it is distorted to the point where it resembles a leering face more than a Mandelbrot midget. The distortion is caused by slicing the midget in a new direction -- one of those orientations that produces neither Mandelbrot sets nor Julia sets, but something in between. Since the Julibrot is four-dimensional, there are more in-between orientations than can be imagined. The orientation of today's slice is totally skew -- 45 degrees from all six of the mutually perpendicular planes of the Julibrot, and one of six such totally skew orientations in the Julibrot. I actually chose a perturbed version of the midget to examine in this new direction. I did so because the 'true' version of Mandelbrot objects stretches to a near impossible degree when viewed in some of the odd directions. The degree of this stretching can be demonstrated by changing the real(p3) parameter of today's image to zero and re-calculating the image. The parallel stripes that result are quite uninteresting, though with enough outzooming and stretching in the vertical direction, the original true midget can be brought entirely into view. Today's image gave me a rating problem. Unable to decide on a rating of 5, 6, or 7, I finally decided on a compromise of 6, which is a little above average. The render time of 2 minutes from the parameter file is about equal to the time required to visit Paul's web site at: Bright sunny weather prevailed today here at Fractal Central. The temperature of 59F 15C felt warmer than it actually was, due to the light winds and warm sunshine. The fractal cats, who approved heartily, enjoyed several hours of outdoor activity. Of course, to the cats, outdoor activity means sitting in the grass, watching birds and squirrels, or lying on one of the porch chairs, sleeping. When I last checked, the Philofractal list, among others, was still down. With no outlet, the fractal philosophy is still backing up. But it's not being lost. Stay tuned for the re-activation of the list and the imminent eruption of controversial wisdom. The clock over the desk tells that it's time to be getting busy on non-fractal things. So until next time, take care, and be at one with something. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Midget_Distortion { ; time=0:01:57.20--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=multirot-XZ-YW-new passes=1
center-mag=+0.00000113718053904/-0.000000033119188\
92/5169577/0.115/-180/-88.3303584561142259
params=45/45/2/0/-1.749615506433/0/-1.749615507433\
/0 float=y maxiter=2400 inside=0 logmap=205
colors=000ACWADYAE_AFaAGdBHgCIjDJmEKpYQuzzznmzlazj\
PzhDzf1zi8tlFnnMhqTcs_YvfSxmNplUhl`akgUknNkuLmkJoa\
HpSPkQWfPbaOiXNpSMEOrMWtTcv`kxgry`jpVbgDABPVZINQCF\
H678zeljV_VLOFACtswlloeehZZ`SSULLMEEF777GPZCKS9FL6\
AE357DAmA8c76U5KX2U7zoP8QKz__sNVeHNSBFE57OrUJgOEXI\
9MC4B6r0eh0Z_0SR0LI0E9079zL7mG5`C3P81C4C8wA6n85e64\
Y53P32H118WdfSZ`OUWKPQGKLCFG8AA455ZAkkWzOGVugaaTPJ\
EC6bC4T93J6193KL_FFRAAI559uYKmTHfPF_LCTHALC7E85742\
h55_44R33I22z1zE5E727sVk`KWIAGFjXDdSBZO9TK7NG5HC3B\
8154cGHXDEQABK88D55622wZZhQQUHHF88xYTcMJKB90r`0hU0\
_O0RI0IC096TxaNkUH_MBOF5C7bVxJFUj4bV2QF1DZbbTWWNQQ\
HNJBOD5P65Q`3RO1SCKTXAUL8VG6WC4X82Y4X_Kta5kc4ce3Wg\
2Oi2Gk18m0Do6Bq59s47u35w23y11z0PzKLzHHzEEzBAz87z53\
z2QzGMzDIzBEz9Bz67z43z28zh6z_4zR3zI1z9sz`SzI6zC5zA\
4z83z62z41z2nzJezFYzCPz9Hz68z3JzuKzuKzuNzpQzkTzfVz\
aYzX`zSczNezIazQZzXWzcWzc
}
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==================================
|
times.
