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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's scene is a zoom into the 'bof61' chaos that fills the distorted rectangle in yesterday's image. I was curious to see whether the chaos is as complete as it appears. Surprisingly, I found that some order is hidden in the apparent depths of the chaos. True, most of the chaos inside the rectangle simply goes on forever with no signs of order, but mixed in with the total chaos are tiny areas of order, such as those that prevent today's image from being just another screen full of sandy debris. The pyramid on the left side of the frame is mostly obscured by the chaotic haze, but enough of its triangular shape shows through to make the image worth being declared FOTD for September 23. The string of sparkling yellow-orange things curving up the right side adds to the interest. Most of the other apparent order in the chaos is an artifact of limited resolution. To add some width to the pyramid and to straighten it, I stretched the image by a factor of 13.7 in the horizontal direction and skewed it slightly to the right. The resulting shape reminds me of the bent pyramid in Egypt, as it might appear in a sandstorm. (The pyramid had to be bent to prevent it from collapsing.) I named the image accordingly. Since the scene lies inside the workhorse Z^(2.003)+C rectangle, and this is about the 20th FOTD trip to the rectangle, I did not give the picture a rating. If I had rated it, a rating of about 7 would have been appropriate. With a render time of 34 minutes, the image is a rather slow one. But those pangs of impatience may be eliminated by going to the FOTD web site and viewing the finished image there. The web site may be found at: Some sun, some clouds and warmer temperatures in the low 70's, around 22C, made conditions quite pleasant here at New Fractal Central on Friday. The fractal cats paid little attention to the weather however. They found enough excitement indoors to keep them fully occupied. My day was busier than yesterday but still slower than usual. All this means that the next FOTD will appear on schedule in 24 hours. Until then, take care, and what additional surprises could lurk in an innocent rectangle. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Sandstorm_Pyramid { ; time=0:34:01.75--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 passes=1 periodicity=0
center-mag=+0.00363659192954869/+0.001741560509220\
49/22401.94/13.698/87.5/0.446164143791587364
params=90/0/89/0/-1.7435/0/0.00019/0.07388/2.0031/\
0 float=y maxiter=1500 inside=bof61
colors=0000K70L80M90NA0OB0OC0PD0QE0RF0SG0SH0aQ0kZ0\
cP0WG0wz0RJ0PL0NM0KO0IP0GR0ES0BU09V07X05Y08_2B`5Da\
8GcAJdXefXfhXgi`daRcgLZdPSXAP_4KX0FV0AS05Q04P03O03\
N00BNTc0LU0LU0LT0WF0VF0VE0VE0VE0VE0VE0VD0VD0VD0VD0\
UC0UC0UC0UC0UC0UB0UB0UB0UBzh00aR0YM0OG0QB0M60J00G0\
0D00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E\
00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00\
E00E00E00E00E00E00E00E10E10E10E20E20E20E20F30F30F3\
0G40G40G40H40H50H50I50I50I60J60J60J70J70J70J70J80J\
80J80J90J90J90J90JA0JA0JA0JB0JB0JB0JB0KC0KC0KC0KC0\
KD0KD0KD0KE0KE0KE0KE0KF0KF0KF0KG0KG0KG0KG0KH0KH0KH\
0KI0KI0KI0KI0KJ0KJ0KJ0KJ0KK0KK0KK0KL0KL0KL0KL0KL0K\
M0KM0KN0KN0KN0KN0KO0KO0KO0KP0KP0KP0KP0KQ0KQ0KQ0KQ0\
KR0KR0KR0KS0KS0KS0KS0KT0KT0KT0KU0KU0KU0KU0KV0KV0KV\
0KW0KW0KW0KW0KX0KX0KX0JY0KX0KX0KX0KX0KW0KW0KW0KW0K\
W0KV0KV0KV0KV0KV0LU0LU0LU }
frm:SliceJulibrot4 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(p5)+c
|z| <= 9 }
END PARAMETER FILE=========================================
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times.
