FOTD -- August 31, 2013 (Rating A-6,M-6) Fractal visionaries and enthusiasts: Today's image has a curious appearance, which is actually the beginning of definition breakdown. In today's case however, the breakdown produces a soft, rather pleasant fuzzy effect that raises the image's artistic worth to a 6, making it worthy of being declared FOTD for today. The name "Zexpe of the North" points out that the exponent of Z is the number epsilon, and that the scene lies at the northern extremity of the parent fractal. The parent fractal is actually the 'zexpe' fractal, or more accurately, one of the 'zexpe' fractals. Due to the multi- valued nature of the complex logarithmic function, there are an infinity of 'zexpe' fractals. Today's 'zexpe' fractal resulted when I iterated Z^(epsilon) nine levels up the complex hyperladder with no function applied. It is shaped much like the classic 'zexpe' fractal, with two large period-2 buds. There is no X-axis symmetry however, and the northern bud more closely resembles a quadratic bud, with a single nearly straight main spike pointing northwest. Today's scene lies near the tip of this spike. Since there is nothing really outstanding about the image and the breakdown of definition could be considered detrimental as easily as beneficial, I could rate the artistic worth no higher than a 6. The complex-log math trick is so shopworn that I could rate the math value also no higher than a 6. The calculation time of 1-1/2 minutes is fast enough to keep boredom and ultimate disappointment at bay. And the web sites can always remove the wait entirely. Save some time by checking the web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> More clouds than sun marked the first day of the three-day Labor Day holiday weekend here at Fractal Central today. As of post time, the threat of rain never materialized, but there is still no guarantee the rest of the day will be dry. The fractal cat was a bit cranky, probably due to the humidity, but the fractal humans simply took things in stride. The next FOTD, a FMOD specialty, will not be posted until next month, which luckily is only one day away. Until it actually appears, take care, and when we elected our president, we were so enthusiastic about how he would "save the nation". It now looks like we made a big (but predictable) mistake. Jim (I never make mistakes.) Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Zexpe_of_the_North { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.6026507393347338/+1.366413693704379/\ 3.395445e+012/1/-25.5/0 params=2.71828182845905/0/\ 9/0 float=y maxiter=5500 inside=0 logmap=97 periodicity=6 colors=00000K00K00K00K00K00K00K00K00K00K00K00K00K0\ 0K00K00K00K11K22K33K44K55K66K77K88K99KAAKBBLCCMDDN\ EEOFFOGGOHHNIINJJNKJMIKMHKMFKLEKLCKLAKIBKKBKLCKMCL\ NCMODOPDQQDSREUTEXUE_VFbWFeXFhYGkZGn_Gq`HtaIraIpaJ\ nbJlbKjbKhcLfcLdcMbdM`dNZdOWeOUePSePQfQOfQMfRKgRIg\ SGgSEhTChTAhWHbZNXaTRdZLgdFjj9km4lp3lp3lp3mp3mpAmo\ AnoAnoAnoKnoKooKonKonUpnUpnUpnUpncqocqocqocqomrpmr\ pmrpmsqzrpzqnzpkzoivofrndmmahl_ckXZkVUjSPiQMhNJgLJ\ gIKfGKeDKdBLc8Lf91d7Bc6La5V`4d_3n`6l`8k`Aj`Ch`Eg`G\ f`Id`Kc`Nb`Pa`R_`TZ`VY`XW`ZV``UbcS`bT_aTZ`TY_TX_TW\ ZUVYUcXUcWUcWUcVUcUVcTVcTVcSVcRVcQVhPWhPWhOWhNWhMW\ mLZmKamIWmGQmDNmBKmCLmDMmEOmFPmFQzGSzHUzIWzJYzJ_zK\ azLczMezNgzOizOkzPmzQozRqzSszSvzTzzTzzUzzUzzUzzVzz\ VzzVzzWzzWzzWzzXzzXzzYzzYzzYzzZzzZzzZzz_zz_zzdzzaz\ z_zzYzzVzzTzzRzzOzzMzzKzzIzzFzzDzzBzz8zz6zz4zzlzzj\ zzhzzfzzczzazz_zzYzzVzzTz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================