FOTD November 17, 1998 (The Omega Point) Fractal visionaries: The weather today was so dull that I can barely remember it. Oh yes, it was partly cloudy with a temperature of 60F 15.5C and a south wind at 12kph. Regardless, it was a perfect day for scrounging in fractal land for that one perfect fractal that might exist among the infinity of infinities of fractals that might exist. Unfortunately, tonight has become totally cloudy, and the meteor storm, if it happens, (which I doubt), will be invisible from fractal central. But I'll be up around 5am just in case a hole opens in the clouds and the meteors are there. The fractal I found was created by the next in my series of 12 MandNewt formulas, MandNewt10. This formula, as well as numbers 11 and 12, has six variable parameters. Since the six parameters are limited to real numbers, the resulting fractals always have X-axis symmetry. In some cases, the extra variable parameters are redundant, simply increasing or decreasing the values of other parameters, but overall the result is totally unpredictable, which is the way I like my fractals. I named the picture "The Omega Point" because as I studied it, I wondered if there could possibly be a last fractal. Actually, that's the way I name most of my fractal pictures -- I stare at them until a name comes into my head. The picture is a lot like my "Fractoland" picture of several days ago, though I'm not blaming this one on Dr. J. The picture has vague buds half obscured by bits and pieces of ectoplasmic fractal material, and areas of chaos offset by organized areas of quasi-order. But this image has at least a hint of order amid the most chaotic disorder. The spiral occupying most of the top third has no corresponding feature in the earlier picture. This spiral reminds me somewhat of the images produced by the Barnsley formulas. The GIF file has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> And now I suspect that the honorable thing to do would be to wrap this up and see if I can get it posted. Until next time, when I shall likely be a bit more settled, take care, and remember that no matter how far you search, you will never find the last fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com START 19.6 PARAMETER-FORMULA FILE============================ The_Omega_Point { ; 16 min on a P200, 640x480x256 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt10 passes=1 center-mag=-0.7352\ 27/1.28731/1.153329/1/-75/-2.50563458870090017e-014 params=3.524/1.979/-3.263/1.769/0.733/0.736 float=y maxiter=12000 inside=0 logmap=yes periodicity=0 colors=000HELHEMGDNGDOFDPHFRFDPE7ODANC9MB8LABPEATI\ 9XMCWLi_KmZJlYIjXHiWGhVFfUDeSCcRBbQAaP9_O8ZNAYODXP\ FWQHVQKVRMUSOTTQSUTRVVQWXPW_OXaNYcMZfM_hL`jK`lJaoI\ bqHcsHctIdtIdtJetJetJetJetKfuKfuKfuKfuLguLguLguMhu\ MhuMhuMhuNiuNivNivNivOjvOjvOjvOjvPkvPkvPkvQlvQlvQl\ wQlwRmwRmwRmwRmwSnwSnwSnxRmxRlxRlxRkxRkxRjxRjxRixR\ hxRhxRgxRgyRfyRfyReyRdyRdyRcyRcyRbyRbyRayR`yR`yR_y\ R_yRZyRYyRYyRXyRXyRWyRWyRVyRUyRUzRTzRTzRSzRSzRRzRQ\ zRQzRPzRPzROzROzRNzRMyQLyQLyRLyRLySMySMyTMyTMyTMyU\ MyUMyVNyVNyVNyWNyWNzXNzXNzYOzYOzYOzZOzZOz_Oz_Oz`Pz\ `Pz`PzaPzaPzbPzbPzcQzcQzcQzdQzdQzeQzeQzeQzfRzfRzgR\ zgRzhRzhRzhRziSziSzjSzjSzkSzkSzkSzlTzlTzmTzmTzmTzn\ TznTzoUzoUzpUzpUvqQqrNlsJfsFatCXu8Sv4Mu1Nu1Nu1Ov2P\ v2Pv3Qv3Rv4Rv5Sw5Tw6Tw6Uw7Vw8Vx8Wx9Xx9XxAYxAZyBZyC\ _yC_yD`yDayEazEbzFczGczGdzHezHezIfzJgzJgzKhzKizLiz\ LjzMjzMkzNlzOlzOmzPnzPozQ } frm:MandNewt10 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-g j=c*z^d+g z=z-e*h/j, f <= |h| } END 19.6 PARAMETER-FORMULA FILE==============================