FOTD -- April 15, 2011 (Rating 8) Fractal visionaries and enthusiasts: For today's image I took a trip back in time to 1996 or so, when I was involved with the MandNewt series of formulas (formulae for the over-educated). I brought up formula number 6 in the series of 12 and entered the parameters 3,2,1,1,2,2. I had intended on making the final parameter a 3, but struck the 2 by mistake. I didn't notice the error until I had already found the image, and I was certainly not going to correct it then. Serendipity strikes again! The image is a most unusual one -- not a solid image but more a series of clouds of vapor filled with vague patterns. To keep things from turning too ghostly, a few areas of solid interest are scattered through the scene, with the large dumb-bell shape being most obvious. I have long since forgotten what I was trying to accomplish with the MandNewt formulas, but they do make some very interesting images, so they are now a permanent part of my formula collec- tion, always ready to produce a surprise or two. The name "Something from Nothing" is true of fractals in gen- eral. Fractals are made of numbers, and numbers are pure abstractions. And from what I am able to gather from the popularized quantum books, the sub-atomic world is also made of numbers -- numbers that do not solidify into particles until we look for them. The universe is made of numbers -- what a coinci- dence. The universe might be the world's greatest fractal. The rating of an 8 would also be an 8 on the old scale. I was considering a rating of a 9, but at the last minute decided to turn conservative. An image like today's always looks best when viewed in high definition, so calculate it at the highest definition available. The finished image may be viewed on Hal's web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> or on my web site at: <http://www.crosscanpuzzles.com/Archives.html> The last I checked, Paul's original web site was still up at: <http://www.Nahee.com/FOTD/> Though I have almost given up hope that Paul will ever be able to bring it up to date. Spring arrived in full force here at Fractal Central on Thurs- day, with sunny skies, light winds and a temperature of 70F 21C. This was ideal for the fractal cats, who purred their approval as they were served their regularly scheduled treats. FL, who has been eager to get to work on the 2011 version of the fractal garden, took full advantage of the ideal conditions and raked like crazy. My day was busy. I guess most every day will be busy until my web site is up to date, which at the present rate will take a year or so. For now, the next FOTD will be posted in 24 hours, give or take a few. Until then, take care, and be happy in your play. Jim Muth jamth@mindspring.com START PARAMETER FILE======================================= SomethinFromNothin { ; time=0:01:34.80-SF5 on P4-2000 reset=2004 type=formula formulafile=mandnewt.frm formulaname=MandNewt06 passes=1 periodicity=0 center-mag=-1.06865/5.81989/0.0461874/1/60/0 params=3/2/1/1/2/2 float=y maxiter=256 inside=atan colors=000KKUgUqrhzuuzeYMf_LhaKjcIkeHmgGniFogEoeDo\ cDoaCo_BoYBpWApUApS9pQ8pO8pM7pK7lI8hG8dF9`D9XCATAA\ P8BL7BH5CmcCC5FC5HC6JC6LC6NC7PC7RC7TB8VB8XB9ZB9`B9\ bBAdBAfBAhGDeKFcOIaSK_WMY_PVcRTgTRkWPoYNs_LmYLgWLb\ ULXSLSRLT_AUg0Vd5WaAX_EYXJZUO_SS`PXaMabKecHjdEoeCs\ gEphGmiIjkKglMdmOaoQZpSXqUUsWRtYOu_LwaIxcFydDwcEuc\ EtcFrbFqbGobGnaHlaHkaHjWNiQShLXgFagAfjDdmFcpIarK`u\ NZxPYzRXuPYqOYmNYhMYdKZ`JZWIZSHZOF_JE_FD_BC_7B_I9U\ T7Oc6Jn4Dx38gIOSWcCirEelFbgGZbIWYJSTKPOLMJMPJMSJMU\ JNXJN_JNbJOdIOgIOjIPmIPoIPrIQuIQxIQzIOwLMtOKqQInTG\ kVFhYDe`Bbb9_e7Xg5Uj4Rl5Qm6Qm7Qm8Qn9QnAQnBQoBPoCPo\ DPpEPpFPpGPqHPqHOqIOrJOrKOrLOsMOsNOsNOsOPpOQnPRlPS\ jQShQTfQUcRVaRW_SWYSXWSYUTZRT_PU_NU`LVaJVbHVcEWcCW\ dAXe8Xf6Xf4Sh6Oi8KkAGlCCnE8oG4qI0rJ2pK4oL5mM7lM9kN\ AiOChPEgPFeQHdRJcRKaSM`TO_UPYURXVTWWUUWWTXYSYZQZ`P\ ZbO_cM`eL`gKahIbjHclGcYNT } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END PARAMETER FILE=========================================