FOTD -- June 01, 2003 (Rating 5) Fractal visionaries and enthusiasts: We've been talking about multi-valued functions a lot lately, so here's a formula and an image that takes advantage of multiple values. It's not a new formula; I have posted many FOTD images created by it in the past. But it gives an example that good things can sometimes come from fractured fractals. The formula being iterated is Z^(1.06)+C, a formula that normally would produce nothing but a tiny featureless dot in the center of the screen. (Change the real (p2) parameter to pi to see this dot.) But thanks to those multiple values and today's formula, which takes advantage of them, the tiny dot has been transformed into an immense cigar with many fields of chaos around its edges. Today's scene is a blow-up of the edge of one of those fields of chaos. I have named the image "Curlers" because of the many loops that fill it. Not really impressed with the image, I have rated it at only a 5. The render time of 1/2 hour is almost entirely expended on the top inch or so of the image, so don't be concerned when nothing much happens for a while. Those who prefer not to wait the 1/2 hour can download the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Rain fell off and on all day Saturday here at Fractal Central, while the temperature reached 73F 23C. A thunder-shower at 6pm climaxed the day's events as well as the cats' dis-satisfaction. Needless to say, a good treat of tuna was needed. Today is starting cloudy, windy and chilly, with occasional bursts of light rain -- not a good sign for fractal cats. For me, it's a sign I might not be able to trim the grass, but may have to go along on a shopping trip. Until next time, take care, and don't get broken up over fractured fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Curlers { ; time=0:38:53.19--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-6.07363/12.6745/0.4719481/1/72.5/-1.23\ 3735336114705e-014 params=1.06/0/121.2/3000 float=y maxiter=4200 inside=0 symmetry=none periodicity=10 colors=0007EXCCZHB`M9bR7dW6f`4hd3je7feAceE`eHYfLVf\ OSfSPfVLfZIgaFgeCgh9gl6go3dl5bi6`f8Zc9W`BUYCSVEQSF\ NPHLMIJJKHGLFDMHHPJKSLNVMQXOT_QWbRZdTagVdjWglXgmYf\ mxSuxRvsSsoSpjTmfTjaUhYUeTVbPV_KWXGWVFYQF_ME`IEbDD\ c9De5Df1Fc5Ga9H_DIXHJVLKTPLRTMOXNM`OKdPHhQFlRDpSBs\ PAnM9iJ8dH7_E6VB5Q94L63G32B116D3NP5c`7tZ8qY9oXAmWB\ kVCiUDgTEeSFcRGaQH_PIYOJWNJUPMTQPSSRSTURUWRWZQX`QZ\ cP_eP`hObjOcmNdoNbmMalL`jKZiJYhIXfHWeGUcFTbESaDR_C\ PZBOXANW9MV9OXBPZDQ`ERaGScIUeJVgLWhNXjOYlQZmR_kP`i\ OagNbeMccLdaKd_JeZLeYNfXPfWRgVThUVhTXiSZiR`jQbkPdk\ OflNhlMj`VqQcxSerUflWgfYi`ZjW`kQbmKdnEeo9`n8Wn7Sn6\ Nn5In4En39n24n10n09j4Ig8QdCOeAMf9Kg7Ig6Gh5Ei3Cj2Bj\ 1bl6hn9moCrqFwrItnJrkKphKmdLkaLiZMfVNdSNbPO_LOYIPW\ FQTBQR8RP5RKGPFRNBaL6lJ2wI4wJ6wJ7wK9wKBwKCwLEwLFwL\ EvNEuOEtPDsRDrSDqTCpVCoWCnXBmZBl_Bk`AjbAicAhdAheDk\ cGmbJoaMq_PsZSuYVwX4IT2GU } 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==================================