FOTD -- January 06, 2004 (Rating 8) Fractal visionaries and enthusiasts: Way back when I was a curious young boy, (I'm now a curious old boy!), I wanted more than anything else, a telescope. I wanted to see with my own eyes all those stars and nebulae of outer space that I had seen only in pictures in the popular astronomy books I was reading at the time. So I began worrying my father to give me the most powerful telescope available. I wanted something like a 2000 power telescope. I thought that the higher the magnification, the more stars and nebulae it would show. When I finally got my telescope, I was a bit disappointed. Instead of the 2000 power monster that I wanted, my father gave me a 40 power rich-field telescope. But he explained how telescopes work, how empty magnification is helpful when observing the planets, but basically useless when one wants to observe fields of stars and faintly glowing clouds of interstellar gas. He told me that those brilliant pictures in my books were time exposures on sensitive photographic plates, and that I would never see the nebulae with my eyes as clearly and brilliantly as they were illustrated in the books. A bit disappointed at first, I overcame my disappointment the first dark night in the yard, when my father directed the telescope toward the Beehive cluster. I used my telescope every clear moonless night after that for several years. I named today's image "Rich Field Fractal". It fills the screen with such detail that I can almost see myself at the eyepiece of that old telescope, which BTW is still packed away in a closet. The image itself is an 'evaporated' one, as ephemeral as those deep-space nebulae I gazed at in wonder those many years ago. The generating formula continues the theme of the past few days by combining various portions of Z^(-1.3) and Z^(-3.1). I then added (1/C) instead of plain C because (1/C) turns a fractal inside out, and fractals with negative exponents are already inside out. Turning them inside out a second time makes normal fractals out of them. And we all like things to be normal. As I said above, the image has been 'evaporated'. Evaporation works only on fractals with negative exponents of Z. When I find an interesting 'normal' scene in such a fractal, I usually 'evaporate' it by raising the escape radius to 10^100, (or one- googol). Sometimes the evaporated version is better, sometimes not. In today's case, it is a close call, but the 'evaporated' version is a bit better. I rated the scene at an 8, a rating that helps make up for the half-hour wait while it renders from the included parameter file. But a half-hour is still a half-hour, and those with more important things to do can save time by downloading the completed GIF image from paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It rained most all day Monday here at Fractal Central, and the temperature never rose above 45F 7C. The cats did not like it, but, compared to some of their past bad moods, their moods were acceptable. I gave them a treat of tuna just as a reward. The sun has appeared this morning, but a cold wind has sprung up. We'll see what the dynamic duo thinks of this. I have about the normal amount of obligatory work to finish before I engage in fun. The next FOTD will appear in 24 hours. Until then, take care, and live a peaceful life. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Rich_Field_Fractal { ; time=0:28:56.14--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+2.13380830806844900/+0.950227584052971\ 10/2264450/1/-12.5/1.19070429488443708e-008 params=-1.3/-3.1/-3.1/-1.3/0/1e+100/0/0 float=y maxiter=2500 inside=bof61 periodicity=10 colors=000a4k`5jZ5iX6hW7gU8fS8eR9dPAcNAbMBaKC`ID_H\ DZFEYDFXCFWFKUIPSLUQOYORbMUgKXkI_pGbuEdyCftFgoHhkK\ ifMjbOlYRmTTnPWoKYpG_mWcjZjW`lXefYj`YoVZtPZyJ`uIbq\ IcnIejIffHhcHi_HkWHlTHhQKdON`MPXJSUHUQFXMC_IAaE8dB\ 6fGA`LEVPIPUMJYPE_NG`MHaLIcKJdJKeHLgGMhFOiEPkDQlBR\ mASo9Tp8Uq7VoF_nMdmUil`nkgrghpdin`ilYjjVjhRkfOkdKl\ bHl`EmZAmX7nV4nTRnkQojQpjQpjQqjQrjQrjPsjPtjPtjPuiP\ uiPviOwiOwiOxiOyiOyiOziOziTwdYt`aqXfnTjkPohLsfHuiH\ vlHtjGsiFrgFqfEpdDocDmaCl`BkZBjYAiX9hV9gU8fS7eR7dP\ 6cO5bM5aL4`K4_J6ZJ8YJAXJCWJDVJFUJHTJJSJKRJMPJOMJQL\ JSKJTJJVIJXHJZGJ_FL`FN`EP`ER`DT`DU`CW`CY`B_`Ba`Ac`\ Ada9fa9ha8ja8la7na7oa6qa6sa5ua5wa5xa5zmUzzczzezzgz\ zmzzmzzTjXOkbJkgHn`FqVDsPBvJ9xDAuFAsGAqHAoIAmJAkKA\ iMAgNAeOAcPA`QAZRAXSAVUATVARWAPXANYALZAJ_BMYBOXCQW\ CTVCVUDXTD_SEaQEcPEfOFhNFjMGmLGoKGqJHrIHrIHrIIrIIr\ HIrHJrHj2oj0qh1of2ne3mc3l } 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==================================