FOTD -- June 20, 2003 (Rating 6) Fractal visionaries and enthusiasts: When a discontinuous function is iterated, a discontinuous fractal results. Most of the FOTD fractals that are generated by the MandelbrotMix4 (or 2) formula are discontinuous, and indeed, the discontinuities often create the image. Today's image however is continuous. It combines 0.3 parts of Z^(-2) with 0.3 negative parts of Z^4 before it adds (1/C). The resulting parent fractal is an oversized area of chaos, rotated 45 degrees, which needs two outzooms before it totally fits on the screen. Near the center are two symmetrical and completely outrageous mutant Mandeloids, with no relation at all to the proper Mandel shape. But these Mandeloids have no discontinui- ties, and that alone makes them interesting. Today's scene is located rather deep in one of the less-likely valleys of the eastern Mandeloid. (In this Mandel-figure, all valleys are unlikely.) One of my taken-for-granted midgets is located as usual at the center, though it is too small to occupy more than a few pixels. But the midget is not the center of attention. That honor goes to the elements that fill the image, and delineate a kind of cogwheel. These elements are almost totally disconnected, but they are unbroken. Not a single discontinuity mars the wholeness of the image. This is how the fractals with fractional negative exponents would appear if a way could be found to eliminate the discontinuities, a task that is impossible but still fun to speculate about. I named today's image "Pure Wholeness" because that's what it is. Too bad I could rate it no higher than a 6, but even a 6 is at least slightly above average. Running the parameter file, with its render time of almost 9 minutes, is one way of admiring the wholeness of today's image. A second way is to download the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Clouds were plentiful here at Fractal Central on Thursday, but the temperature reached 81F 27C and the rain held off until nightfall. These pleasant conditions enabled the cats to enjoy several hours in the yard and enabled me to save a can of tuna. Today should be a wetter repeat. If I get the routine work done early enough, and if the rain does hold off, it might turn out to be another good day for both cats and humans. But to finish I must start, so until the next FOTD in 24 hours, take care, and study them as we might, we will never understand all there is to know about fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Pure_Wholeness { ; time=0:08:37.50--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+2.486158315330713/-0.00021229147922154\ /3.847846e+009 params=-0.3/4/0.3/-2/0/525/0/0 float=y maxiter=3600 inside=0 periodicity=10 colors=000cyVbzPbzKVqHNfGGXE8MC0CBEJ9SP9cT8q_8ze6z\ i6zcPz_eyVvx`pveiuicsp_quTpyNpzJupByc4zQ0zE0z10z40\ x80sB0mC0fG0bJ0XM0SN1XK8_HEbEJeBPi8Vm4_p1es0im0kf0\ n`0pV0sP0uGzuSzxcvzpnzzfzxcvsbmn`ci_VeYM`XCXV3ST0J\ _qXfvhnzvvzzzz0QH0VM8_QGbVPf_XiccnhkqkcpfYnbSm_MkV\ EiQ8hN1fJ0fG1cC8`9EY6KX3QT0XQ0bN0hM0s8Mz0p0zz8xzNk\ zbYzqMzkJueGm_CeVB_xmYmqScuMVyGMz9Cz33z00z00z00z0C\ z0Pz0bz0pz0zz0zk8yXExHMx1ScKKM`E3s60z00z93zJCzSMz`\ VzicyskxzfssbnkYicTeXP`PKXHGT9JXCM_EPbGScHVfJYiK`k\ MVQCQ44T18X09_0B`0Cc0Ef0Gh0He0Jc1Kb9M_HNYPPXXPQ0cT\ 4hV6p0Qy4GsB6mH0f`TnVNhPJcJE_C9V84QHG_PPhXYpcfykpz\ syzmnzfczbTzXKzS9zM0zH0zf0`z440pu6qiHq_SsPbsEmu3xu\ 0ui0s_0pQ0nG0m60iE8hKEeQMcXSbc__ieYpmXvsPpkJicCcX4\ YP0SH0M90H30Q40Y60e80m90uB0zC0vE0qG1kH3fJ6bK8XMBSN\ CNPHHYMBeQ4nT0vN0uH1sB3q44p06p9cmG`TKY9PX00J0ihqme\ snbup_vqXvuTxvQyxNzyKzev` } frm:MandelbrotMix2 {; 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)+(p4)), 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==================================