|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: For some reason, I named today's fractal "Otherworldly Image". I forget the reason, but fractals are truly not of this world. How could they be when even the simple fractals I work with exist in four dimensions, and this 'real' world of ours is endowed with only three spatial dimensions? So the name is justified after all. The formula that created today's fractal adds together 8 parts of Z^(-1.3), 2 parts of Z^(-8.3), and one part of (1/C). The location of the image is in a Seahorse-Valley-like area of its multi-bayed parent. In this valley, the filaments extending from buds end in ring-shaped loops with various decorations and open areas along the loops. These ring-like features are very common in fractals that combine two negative powers of Z with the reciprocal of C. In the image, we are looking deep into one of the decorations in the interior of a ring. The ring theme infests the image, which is filled with rings and parts of rings. There are tiny rings at the peaks of the hills, and gigantic rings out beyond the borders of the image. I might have named the image "Ringworld" had that name not already been taken. After a bit of critical consideration, (I CAN think critically), I rated the image at an above-average 7. The coloring at least has somewhat of a theme, and the image is actually rather pleasant to look at. The 9-minute render time from the parameter file is a bit slow, but not beyond reason on a Sunday, the day set aside for fun and rest. The minor task of rendering may be escaped by downloading the completed GIF image from: The Saturday weather here at Fractal Central turned out to be even warmer than Friday's. The temperature reached 88F 31C, but drier air and a fresh breeze kept things within comfort. Approving of the conditions, the fractal cats spent several hours in the yard, behaving like the angels which they most certainly are not. It is now Sunday morning, and I've got to think of something to do this afternoon that will make the day at least slightly memorable. If I were to find the world's best fractal, that would do it, but if I did find the best fractal, how would I know it? What makes some fractals good and others not as good? If fractals had never been discovered (or invented?) would there still be good and less-good fractals? While I'm pondering these not-quite-monumental questions, I just might go out and have a bit of a good time. Until next time, which will arrive in about 24 hours, take care, and continue the search for eternal, if not universal truth, which, like fractal worth, might also be a by-product of the human way of thinking. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Otherworldly_Image { ; time=0:09:10.03--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+3.01903798379545600/+0.189182678822770\
60/9.653445e+008/1/-130/-3.14957595125980871e-006
params=8/-1.3/2/-8.3/0/525 float=y maxiter=1600
inside=0 logmap=132 periodicity=10
colors=000LBaLBcJ9gJ9eI9fI9gLDgNEiOIiRJkRNkVOlXRnY\
Tn_XpaYpbaqfbsgfsigtkktllwppxqqxstztwzwzzxzzaLsG0l\
E0kE0iD0iD0gD0gB0fB0s90d91l92b86e88a6Ba6D_6EV5GW4I\
X4JX2NV2OV2QT1TT1VRgY0fX0dX0bX1aX1_X2YX4XX4VX6TX8R\
X8QX9OXBNXBNXDLXEJXEIXGGXIEXIDXJBXL9XL8XN6XO4XO2XQ\
1XRzzzzzzzxzztzwszqpzknwfls_inTgkOdfIbbD_Y6YVlkifg\
f_fdVdaOb_IaYD_V6YT0Ik0Ji0Lg0Lf0Nd0Ob0Oa0Qa0R_0RY0\
TX0VV0VT1XR2lz1iz1gz1fs1dn1ag1_b1YXzY0zX0xX0wX0sX0\
qX1pX1lX2kX4iX4gX6dX8bX8aX9YXBXXBVXDRXEQXEOXGNXIJX\
IIXJGXLDXLBXN9XO6XO4XQ2XRzf0aa6J00I00I00G00G10G21E\
22E42D64D86D98BB8BB99DB9EB9GD8IE8IG6JG6LI6NJ4OJ4QL\
2QN2RO2TO1VQ1XRzRTzTRzTRxTRsTRnVRgVRbVRYVRRVRNXRIX\
RBXR6XRz0nq0ki0gb2dV8bNE_GLX8RTziGkdLO_Ofz0bz0az0Y\
z0Xz0Vz0Rz0Qw0Nt2Lq4Jp8GlBEkDBgG9fI8bL4aN2YQ0az0_z\
1Yg6s04q04p04n24l42k82i92gB2fE2dG1bJ1aL1_O1YQ6QI4R\
J4RJREpQEpQEnODnODlNDkNBk }
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END 20.0 PAR-FORMULA FILE==================================
|
times.
