March 11, 2012: No Discontinuities | March 10 | March 12 | 2011 | FOTD Home |
Fractal visionaries and enthusiasts:
Today's
fractal is
an outzoom of yesterday's image, which lies in the fractal debris on
the northeast side of today's minibrot.
Today's FOTD is a close-up of a minibrot halfway through the process of
morphing from quadratic to cubic, and doing so without
discontinuities. The iterated expression is not the expected
Z^(2.5)+C, it is sqr(Z)*(recip(Z^(3)+30))+C. And since no
fractional exponents are involved, no discontinuities will appear in
the fractals it creates.
I have never understood exactly how the JulibrotMulti or similar
formulas work, but today's image shows a perfect minibrot of order 2.5
without the frustrating broken-up bits and pieces that spoil so many
otherwise good fractals.
The name "No Discontinuities" simply describes the minibrot.
I could give the image a rating no higher than a 5, which indicates its
mathematical worth. I put almost no effort into the coloring,
so
the artistic worth is near zero.
The calculation time of 45 seconds is blessedly brief, but viewing the
finished image on one of the FOTD web sites is more convenient.
Lots of sunshine and much warmer temperatures arrived at Fractal
Central today. The fractal cats heartily approved of the high
temperature of 57F 14C and showed their approval by sharing the sunny
shelf without quarreling. The humans, FL and I, had an
everyday
day, whatever that might be.
The next FOTD will be posted in 24 hours. Until then, take
care,
and when someone survives a tornado that destroys his town and kills
his friends, why does he claim to have been blessed? If that
person were realistic, he would think rationally. Before he
assumed his survival was a blessing, he would wonder whether he would
welcome a similar blessing next year.
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
No_Discontinuities { ; time=0:00:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=JulibrotMulti function=recip
center-mag=-0.872575097/+29.735974572/5146/1/100/0
params=3/30/0/0/0/0/0/0/0/0 float=y
maxiter=1500 inside=0 periodicity=6
colors=000UZYWaXZcX`fXchWejWhmWjoWmqVotVrvVtxVruXp\
sYnqZlo_jm`hjafhbdfccddabe_`fYYgWWhUUiSSjQQkIJsPOl\
VTeaYZgbSngLvkCtlEslGrlIpmKomMnmNlnPknRjnThnVgoXfo\
Ydo_cpabpc`pe_pgZqhXqjWqlVrnTrpSrrKArKBsKCtKDtKEuK\
FuKGvKHwKIwKJxKKzKLxKMwKNuKOtKQrKRqLSoLTnLVlLWkLXj\
LYhL_gM`eMadMbbMdaMe_MfZOfaMgYKgVIhRGhOEiLCiHAjE8j\
A6k70j05k59lADmFHnKLoPPpUTqZXrc`shdtmhurlvvmwzmxzm\
yzmwzmuvmtrmrmpqhnocmnaklZjjXhiUggSefPddNbcLaaI__G\
ZZDXXBWW8UU6ZN1TT4OZ6Id9y4ADiBJaEPVHiBEUOJF`O0mT5l\
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McFKeFJfHKdILbKMaLN_NNZOOXQPWRQUTRTURRWSQXTOZUN_UL\
aVKbWIdXHeYFgYEhZCj_Bk`9mb7l`8l_8lZ8kY8kX8kW9kV9jU\
9jT9jS9jR9iQAiPAiOAiNAhMAhLAhKBhJBgIBgHBgGBgFBhEEi\
DHjDJjCMkBOlBRlATm9Wn9Yn8`o8bp7ep6gq6jr5lr4os4qt3t\
t3vrCjpK_nSOm_DlXDkVEkTEFPFFRIETLDVNDXQCZTC`WBbZBd\
aAfcCJZFLZHOZKQZMSYPVYRXY }
frm:JulibrotMulti {; draws all slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p2*0.0055555555555556),
b=pi*imag(p2*0.0055555555555556),
g=pi*real(p3*0.0055555555555556),
d=pi*imag(p3*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a), aa=-(real(p1)-2),
bb=imag(p1)-0.0000000000000000001,
c=p+flip(q)+p4, z=r+flip(s)+p5:
z=z*z*fn1(z^(aa)+bb)+c
|z|< 100000000 }
END PARAMETER FILE=========================================