Aug. 31, 2013: Zexpe of the North | Aug. 29 | Sept. 1 | 2013 | FOTD Home |
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.
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\
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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=========================================