FOTD -- December 22, 2004 (Rating 7) Fractal visionaries and enthusiasts: In today's fractal we take a trip to the Z^(2.02)+C fractal. We check it 20 levels up the logarithmic hyper-spiral. (Actually the scene lies 16.858... levels up the spiral. The level 3.14159... or 'pi' is better considered ground level.) The formula is very close to that of the Mandelbrot set, and the fractal it produces is very similar. But there are significant differences. To start, the entire set appears rotated 30 degrees. The greatest change however has taken place at the north branch of Seahorse Valley, which has broadened into a plateau with a spire at its inner edge. Today's scene lies on the main-bay side of this spire. The midget I found there rates a lofty 7. I have never before seen a midget with such intricate decoration surrounding it unless it was produced by one of the fancy features of the program, which I feel are somewhat artificial. By contrast, today's scene, which was rendered with the outside set to the standard 'iter', shows what is 'actually there'. I named the image "Super Something", leaving it to the viewer to decide what that 'something' is. Since the exponent of Z is fractional, discontinuities must exist in the image, and indeed they are there. But with an exponent so close to integer value, the breaks are minor, and at first glance may go un-noticed. The rating of a 7 leaps to an overall worth of a rather disappointing 47 when the render time of almost 15 minutes is figured in. But the rendering may be eliminated entirely by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a peak temperature of 39F 3C, Tuesday was hardly balmy here at Fractal Central. But the dynamic cats, who had been confined indoors for almost two days, were willing to ignore the minor chill to enjoy an outing in the great outdoors of the holly thicket, where they passed the afternoon pretending they were stalking birds. Only a minor treat of tuna was needed to end their day on an up note. This morning is starting sunny and warmer, but rain is scheduled to move in before nightfall. I see a hint of trouble for the fractal duo. For me, the pile of real work waiting to be done is minor. This should assure another fine fractal in 24 hours, and maybe another outburst of philosophy. Until then, take care, and remember that, regardless of how much we learn, we will never know more than an infinitesimal part of all there is to know. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Super_Something { ; time=0:14:48.75--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 periodicity=10 center-mag=-0.61120335469249380/+0.436965672671546\ 70/6345769/1/-92.5/1.01919733624944e-008 logmap=215 params=2.02/0/20/0 float=y maxiter=4200 inside=0 colors=000W2RUE_SQhQaqPiyOhwNguMfsLeqKdoJcmIbkHaiG\ `gF_eEZcDYaCX_BWYAVW9UU8TS7SQ6RO5QM4PK3OI2NG1ME0LC\ 0KA0J80I60H40G25F0AE5EDAFCFGBKHAPI9UJ8WK7XgV9eUBcU\ CaUE`UFZUGXUIWUJUUKSUMRUNPUPNUQMURKUTIUUHUVHQRIMNI\ JKIFGIBCI78I45L58N6AP6DR7FT8HV8KX9MZAP`ARbBTdCWfCY\ hD`jEblEdnFgpGirGksLgsQcsV_s_WsdStiOtnKtsGtxCtz9sz\ 8sy8sw8su8ss8sr8sp8sm8sk8si8sg8se8sc8sa8sZ8sX8sV8s\ U8tQDtNHtKLuHQuEUuBYLoUNmVPkWRiXSgXUeYWcZXaZZ__`Y`\ aW`cUaeSbfRb_XdTaeMffFkg8ph2ui8vgEveKwdQwbWx`ax_gy\ YmyWryVsvTstStqQtoPumOujMvhLveJwcIwaHsUJpMKmELj7Mf\ 6Oc6P`6RY6SV5US5VP5XM5YJ5_G4`D4bA4c74e44f88eBBdEEc\ IHbLKbONaSQ`VU_YXZa_ZdbYgeXkhWnkVqcVic_bccWchPclIc\ qBcuCctDctEctFctGctHctIctIctJctKctLctMctNctOctOctP\ ctQctRctSctTctUctUctZcnbcifcckcZocTscOccYbcWbcVacU\ acT`cS`cR`cQjcDlcGmcIncLocNpcQqcSrcQrcOrcNrcLrcJgc\ CfcEdcGccHbcJ`cL_cMYcOXcQ } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================