FOTD -- June 02, 2003 (Rating 7) Fractal visionaries and enthusiasts: The FOTD for June 2 once again takes advantage of the multi- valued nature of the complex log function. The iterated expres- sion is a very simple Z^(1.5)+C. The trick in the MandelbrotBC1 formula is that an unlimited number of different images can be produced by the expression Z^(1.5), depending on which of the infinity of returned log values are chosen. The real(p2) parameter of the formula makes the choice. Today's image is part of the particular Z^(1.5) fractal that results when the real(p2) parameter of the MandelbrotBC1 formula is set to -31. The amorphous thing at the center is a midget of order 1.5. I have no idea what the jagged-edged colored disks surrounding the midget are. I have never seen anything quite like them. I have named the picture "Burbles". Those disks reminds me of something bubbling. The rating of a 7 seems correct for the image, which has more math interest than artistic worth. To see these truly unique fractal burbles, run the attached parameter file and wait 5 minutes, or download the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday started blustery and chilly here at Fractal Central, but by afternoon, the sun appeared, the wind slacked off, and the temperature rose to 66F 19C. The cats had a good day. This morning is starting much better. The cats will likely have another good day. For me, it's several hours work before my day will be good. Until next time, take care, and keep blowing those burbles. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Burbles { ; time=0:05:06.76--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.72523926124837650/+0.172183551614105\ 20/488923/1/-62.5/9.1405363139562823e-010 params=1.5/0/-31/0 float=y maxiter=12000 inside=0 logmap=105 symmetry=none periodicity=10 colors=000GstKptNmuQkuThvXev_cwb`weYxiWxlTyoQyrOyo\ NvmNskMpiMmgMjeLgcLdaLa_KZYKWWJTUJQSJNQIKOIHMIEOJG\ QJISJJUJLVJMXJOZJQ`KRbKTcKUeKWgKYiKZkK`lKajRdhYgfd\ jdkmbrp`xsYvrWtrUsqRqqPppNnpKmoIkoGjnDhnBgm9em6dl4\ bl2al3bk3cj3di3ei4fh4gg4hf4hf5ie5jd5kc5lc6mb6na6o`\ 6o`5la5ia5fa5ca5`a5Yb5Vb5Sb5Pb5Mb9PcDSdGVeKYfN`gRc\ hVfiYijalkdolhrmlunoxoszpvzpozahyNaw9aw9aw9aw9aw9b\ vAbuBbuBctCctDcsDcsEdrFdrFdqGdqHepHepIepIeoJeoJfnK\ fnLfmLfmMglNgkNgkOgjPhjPhiQhiQhhRihSigSigTifUjfUje\ VjeWjdWkdXkcYkcYkbZla_la_l``m`am_am_bmZcnZcnYdnYen\ XeoXfoWfoWgoVhpVhpUipUjpTjqSkqSlqRlqRmrQnrQnrPorPp\ sOpsOqsNrsNrtMstMttLttLuuKvuKvuJwuJwsJwqKwoLwmMwkN\ wiOwgPweQweRweSwfTwfTwgSwgSwgSwgSuhRwiRwiRwjQwjQwk\ QwkQwkPwlPwlPwmOwmOwnOwnNwnNwoNwoNwpMwpMwqMwqLwrLw\ rLwrLwsKwsKwtKwtJwuJwuJwvJxvJywJzwJzxJzxJzyJzyJzzJ\ zzJzzJzzJzzJzzJzzJzzJzzJz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 20.0 PAR-FORMULA FILE==================================