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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: At first glance, today's image appears hopelessly dull. It's another rendering of the Mandelbrot set, no big deal. But this Mandelbrot set is strange indeed, for it is the Mandelbrot set only on the surface. The deeper one delves into it, the more its elements change from the quadratic kind to the cubic kind. For a striking example of this strangeness, check one of the very small minibrots on the main stem, the smaller the better. You will find not a Z2+C minibrot but a Z3+C minibrot. The same is true throughout the entire parent fractal. And the most incredible thing about the formula is that by changing the imag(p2) parameter, the quadratic M-set can be made to have in its depths characteristics of any order whatever. The formula that does all this is pure serendipity. When I wrote it, I had nothing particular in mind. I simply wanted to see what the expression would do. And was I surprised! Today's image is not the last we will see of this formula. I have already found two outstanding cubic midgets, which will appear as the FOTD's for June 25 and 26. The name "Strangeness" is self-explanatory. The calculation time of 23 seconds makes running the included parameter file a breeze. And those who do not enjoy windy conditions may escape the breeze by viewing the finished image on the FOTD web site at: Fine weather prevailed here at Fractal Central on Monday until nightfall, when a heavy thunder-shower moved in, leading to a pleasantly cool night. The temperature of 84F 29C and the plentiful sunshine during the day suited the fractal cats just fine. My day was made more interesting by the discovery of today's image, which promises an abundance of goodies. The next in the endless line of FOTD images bearing goodies will appear in 24 hours. Until then, take care, and the best is yet to come from this formula. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Strangeness { ; time=0:00:23.22-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot2 passes=1 params=2/-1/5/1000
center-mag=-2.879/0/0.17468 inside=0 periodicity=10
float=y maxiter=1000 logmap=yes symmetry=xaxis
colors=000KB1JF8JJEIMKIQQHUXHXbG`hGcnSZpcVqoRrzNsp\
PrgQrZRrQTrHUr8VrEYpK`nPclVfj`ihekgXmhPnhHph9qh1rh\
5sd9s`CsYGtUJtRNtNQtKMuOIvSEvWBwZ7wb3xf0xi2yg3ye5y\
c6ya8y_9yYAyXBuYCrYDoZElZEiZRjbbkenlizllfkfOkaSdZV\
ZWZTTaNQYQTUTVQWXNZZJaaFdcBge8igIdfS_f`WfjRfsNfrPg\
qQgqSgpTgpUgnXbl_ZjbUieQghMekHcnDbp9YoETnIOmNJlREk\
VFlQGmLHmGInBJo6Jo2KhKLaaMWrJVqGVpDVoAVn7VnFalMgjU\
mh`sfethjujnvkswmwxntveruYptQmrIkqAip2hn3gz3fz4fz4\
ez4dz5cz5cz5WzIPzVIzgHzcHz`HzYHzVHzRHzOHzLHzIMzKRz\
MWzO`zQezSjzUozWszYozakzegzhhz`hzTizMizEiz7ozFuzMz\
zTrzUkzUczUXzVPzVIzVGzdEzm1zzAzhJzRJzF`zErzDjzEczE\
WzFPzFPzLPzRPzXPzbPzgSzfVzeYzd`zcbzbXzkRztRzrSzoSz\
lTzjTzgUzeVzbVz_WzYWzVXzSXzQYzNYzLczNlzLhzPJzoKzqM\
zrNztPzuNzzQzvTzrWznZzkazgdzcgz`dzWazRZzMWzHTzCRz8\
QzEQzJPzPPzUOz_OzdQzbSz`Uz_WzYYzW_zVazTbzS`zYZzbXz\
gVzmTzrRzwPzuNztLzsKzrIzq }
frm:DivideBrot2 { ; Jim Muth
z=0, c=pixel, aa=real(p1), bb=imag(p1),
dd=real(p2), ff=imag(p2)+64:
z=z^aa/(z^bb+dd)+c
|z| <= ff }
END PARAMETER FILE=========================================
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times.
