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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: To start, I must admit that today's Julia-like image is abysmally slow. And that is not all. It is merely close to being a Julia set. In fact, it is within 1/2 degree of arc of actually being a Julia set. But it is not a Julia set; it is "Close but no Cigar". If the image were a Julia set, it would consist of nothing but the spider-like arms in the foreground. The brilliant, straight-edged, horizontal bar in the background, partially showing through the spider arms, is actually a grossly enlarged and infinitely stretched view of the area of the Mandelbrot set associated with this particular Julia set. The pure Julia version may be seen by changing the imag(p1) parameter from 90.5 to 90. One benefit of this change is that the Julia set renders in 1/10 the time of the 'almost' Julia set. The spidery arms in the pure Julia set are thicker and not nearly as intricate as those of the 'almost' set, especially in the lower part of the image. And unless I am mistaken, there are fewer arms in the pure Julia set. Of course, in the Julia set the straight-edged feature in the background, which adds most of the interest, is totally missing. The very slow render time of today's image is a bit misleading. When I first rendered the image, I used the old version of the multXYZWcompjb-min formula. Since then, I have moved the term (c^(p3-1)) to the initialization part of the formula, which lets it be calculated only once for each point rather than recalculated at every iteration. This cuts the render time almost in half. All previous versions of the multXYZWcompjb-min formula should be replaced with the version that is included in today's parameter file. The 'frm:' that precedes the formula name must be removed before the formula can be included in a formula file. I have rated the image at an 8. This might be a bit overblown, but I rather like the image, and feel that it is worth the 8. But even with the new version of the formula, the image is a slow one that is much more convenient to download. I have sent the image on ahead to Paul, so it should be posted to the FOTD web site, ready for download, shortly after you read this. The web site may be accessed at: Wednesday turned out not too bad here at Fractal Central. The sun was visible about half the time and the temperature reached 43F 6C, which is about where it should be at this time of year. The cats spent about an hour in the yard, which is a little below their normal time outdoors. Their evening tuna was near average. But this morning I see light snow falling, with heavy snow forecast for later today. The duo might not have a good day. I expect an average day, but then, even an average day is filled with things of interest. The next FOTD will appear in 24 hours. Until then, take care, and look beneath the surface of the everyday things of life. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Close_but_no_Cigar { ; time=2:26:36.40--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multXYZWcompjb-min function=ident/flip
passes=1 center-mag=-0.419308/3.33067e-016/1.62121\
2/1/90/3.88578058618804789e-016 params=90/90.5/1.2\
/0/1.1/0/0/0/-0.818/0 float=y maxiter=100000
inside=0 logmap=15 periodicity=10
colors=000PIVPIWOIXOJYNJZNK_MK`MKaLLbLLcKMdKMeJMfJ\
NgINhINiHOjHOkGPlGPmFPnFQoEQpEQqDQrDQsCQtCQuCQvDQw\
DQwDQwEPwEPwEOwENwFNwFMwFMwFLwGLwGKwGJwGJwHIwHIwHH\
wHHwIGwIFwIFwJEwJEwJDwJCwKCwKBwKBwKAwLAwL9wL8wL8wM\
7wM7wM6wM6wL8wL9wKAwKAwKAwJAwJAwIAwIAwIAwHAwHAwGAw\
GAwGAwFAwFAwEAwEAwEAwDAwDAwCAwCAwBAwCAwDAwEAwFAwGA\
wHAwIAwJAwKAwLAuMAsMAqNAoOAmPAkQAiRAgSAeTCcUEaVG_W\
IYXKWXMUYOSZQQ_QO`QMaQKbQIcQGdQEeQCfQAfQ8fQ6gP5gP5\
hO5hO5hO5iN5iN5iN5jN5jO5kP5kQ5kR5lS5lT5kU4lV5lW6lX\
6lY8mZAm_Cm`EmaGnbIncKndMneOofQogSohUoiWpjYpk_plap\
mcpneqogqpipqkormnsomtqluskvujwwixyjwzjwzjwzkwzkwz\
kvzkvzlvzlvzlvzluzmuzmuzmuzmuzntzntzntzntzotzoszos\
zoszpszpszprzprzqrzqrzqrzqqzrqzrqzsrztszutzvuzwvzx\
wzyxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:multXYZWcompjb-min {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5,
q=(c^(p3-1)):
z=(-z)^(p2)*(q)+c,
|z| < 400 }
END PARAMETER FILE=========================================
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times.
