|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Since September is a month with no minibrots, I have decided to spend a few days manipulating the mysterious rectangle in the Z^(2.003)+C Julia set. To see the rectangle in its pure form, bring up the julzpower formula, set the value of C to -1.7435,0 and the exponent of Z to 2.003. Then go to the F6 screen and set the center point to 0.00019,0.07388, set the magnitude to 125 and strike the 'enter' key twice. A few minutes later a most unusual fractal will fill the screen. This empty rectangle and its incredible variations will be the subject of the next few FOTD's. Don't be deceived by the emptiness inside the rectangle. The empty area is paper thin and lies exactly in the Julia orientation. Even the slightest variation of the imaginary part of C totally destroys the perfect rectangular shape and fills the empty area with detail. In today's image I have added a tiny imaginary part to the exponent of Z rather than to initial C. This tiny change has not only broken up the rectangle and filled it with intricate detail, it has rotated the rectangle. I named today's image "Starring a Rectangle", and why not? The rectangle certainly is the star of the show. I have featured this same fractal object so many times that I could not give today's version a rating, but the image certainly is worth the 2-1/2 minutes required to render the scene from the included parameter file. Rendering can be a nuisance on over-qualified machines. Those with such units may view the rendered and dismembered rectangle on the FOTD web site at: Mostly cloudy skies, gusty northwest winds, and a temperature of 66F 19C here at New Fractal Central on Wednesday made conditions a bit brisk for the fractal cats -- not that it worried them. They spent the afternoon inside, getting into trouble. The mischief peaked when Cassie tried to climb the living room curtains to catch a fly on the ceiling and ended up on the floor with the drapes on top of her. Oh well, it's a cat's duty to get into trouble. In my department, the work remained on the slow side, which means the fractals were on the fast side. More of the same is expected tomorrow, so I can see no reason the FOTD will not appear on schedule. Until then, take care, and who knows what might come next? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Starring_Rectangle { ; time=0:02:29.46--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 passes=1 periodicity=10
center-mag=+0.00020125342561368/-0.000100679231968\
01/92.98646 params=90/90/90/90/-1.7435/0/0.00019/\
0.07388/2.003/3e-005 float=y maxiter=1500 inside=0
logmap=51
colors=0002Qk2Qj2Qi2Qh2Qg2Pf2Oe2Nd2Mc2Lb2Ka2J`2I_2\
HZ2GY2GX2GX2FW2FW2FV2EV2EU2DU2DT2DT2CS1CS1BR1BR1BQ\
1AQ1AP1AP1AO1AO1AN1AN1AM1AM1AL1AL1AK1AK1AJ1AJ1AI1A\
I1AH1AH1AG1AG1AF1AF1AE1AE0AD0AD0AC09C09B08B08A08A0\
79079078068067057056056045045034034033023022012000\
000000000000000000000000000000000000000000c`Ab_9cZ\
9cZ9cY9cY9cX9cX9cW8cW8cV8cV8cU8cU8cT8cT7cS7cS7rR7r\
R7rQ7rQ7rP6rP6rO6rO6rN6rN6rM6rM6rL5rL5rK5wK5zJ5zJ5\
zI5zc4zc4zc4zc4zc4zc4zc4zc3zc3zc3zc3zc3zc3zc3zc3zc\
2zc2zc2zc2zc2zc2zc2zc1zc1zc1zc1zc1zc1z41z30z30z20z\
20z10z10z00zF4zE3zE3zE3zE3zE3zE3zD3zD3HmzHmzGmzGmz\
GmzGmzGmzFmzFmzFmzFmzFmzEmzEmzEmzEmzEmzDmzDmzDmzDm\
zDmzCmzCzzCzzCzzCzzCzzBzzBzzBzzBzzBzzAzzAzzAzzAzzA\
zz9zz9zz9zz9zz9zz8zz8zz8zz8zz8zz7zz7zz7zz7zz7zz7zz\
6zz6zz6zz6zz6zz5zz5zz5zz5zz5zz4zz4zz4zz4zz4zz3zz3z\
z3zz3zz3zz3zz2zz2zz2zz2zz }
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=========================================
|
times.
