; Date: Sat, 31 Aug 2013 14:47:19 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 31-08-13 (Zexpe of the North [A-6,M-6]) ; Id: <1.5.4.16.20130831144820.21cffb9c@earthlink.net> ; --------- ; ; 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: ; ; ; ; ; ; ; ; ; ; 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|