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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The parent fractal of today's image is one to puzzle the fractal pundits. (If pundits can be puzzled, that is.) The puzzle lies not in today's image itself, which, with its eight arms ending in irregular holes, and well-defined areas, is pleasant enough, but in its location in relation to the entire parent fractal. The midget at the center of today's picture lies near an irregular hole, which lies just to the north of a quadratic midget, which in turn lies in the suburbs of a cubic midget, which lies in the basin of an order-6 midget, which lies in the center of a kind of unstable East Valley of the parent fractal. I'm not exaggerating all this variety. Set the logmap to 0, and do the outzooms to see for yourself. I call the valley unstable because it is very sensitive to changes in the real(p3) parameter. A string of midgets extends down the center line of this valley. Nothing unusual in a string of midgets, but no two midgets in this line are the same. Instead of the expected string of identical quadratic midgets, there are midgets of every shape and order, and some midgets that combine parts of midgets of different orders. Interesting exploration certainly waits in this valley, and I'll be wandering in it for the next several FOTD's. I might not find a lost civilization, but I'll find some interesting images for sure. I named today's image "8-Legged Weirdo". The picture itself, which rates a 6, is not that weird, but the area of the parent in which it lies is one of the most unusual I have ever ventured upon. The rating is conservative but honest. The render time of near 25 minutes on a classic P200 machine is on the slow side. A far more efficient way of seeing the scene is to download the completed GIF file from Paul's web site at: The fractal weather Saturday featured lots of clouds and temperatures on the cool side for this, the hottest time of the year. But the high of 81F 27C was mild enough for the dynamic duo to spend several comfortable hours in the yard, remembering the days when they could actually catch those birds and squirrels they now only watch and chatter at. As I write this, it's Sunday morning and the clouds have turned to light rain. It's a perfect day for doing nothing and enjoying it. As always, I'll return in 2 days with the next in the unending series of FOTD images. Until then, take care, and keep your powder dry, (whatever that means). Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
8-Legged_Weirdo { ; time=0:24:40.96--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+0.4106409957710013/+0.0021028911297467\
/4.29809e+012/1/-150/-0.0559633657765741532
params=1/3/-0.3/5/0.29/0 float=y mathtolerance=/1
maxiter=2700 inside=0 logmap=421 periodicity=10
colors=00035y6Bw8GvBMuDRtGXrIaqLgpNloPjlRiiTgfUfcW\
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GojDpjBqi9ri6sh4th2ug0vg6whBxhGyiLziQziWzj`zjezkjz\
kozkmzi6zu5zv5zw4zw4zx3zy }
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==================================
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