February 7, 2012: It Is Inconsistent | Feb. 6 | Feb. 8 | 2011 | FOTD Home |
Fractal visionaries and enthusiasts:
NEW
FORMULA ALERT!
The astronomical 9.9 rating of today's image is no error. The
artistic value is up there with the best, and the mathematical interest
sets a new FOTD record. Put together, this raises the rating
to
the whopping 9.9. I did not rate the image a perfect 10
because I
wanted to leave a bit of room for a possible better fractal that might
eventually come.
The artistic value speaks for itself. The mathematical
interest
is the existence of an impossible minibrot. The perfect
Mandelbrot minibrot at the center of the image is impossible.
This impossibility led to today's name -- "It Is Inconsistent".
The image itself is an 'almost' Julia set of a minibrot in the
northwest outskirts of the cloud of debris surrounding a Mandelbrot set
corrupted by Z^(-12) energy. The orientation is double
rotated
only a tiny 0.15,0.15 degrees from the true Julia direction.
Because the size of Mandelbrot minibrots becomes infinite in the Julia
planes, they can never appear in Julia sets. But apparently,
someone forgot to tell the minibrot in today's image that it cannot be
there.
In addition to the minibrot itself being impossible, I have never
before seen a minibrot with a circular disk inside its main
bay.
This disk is the actual Julia set. Change the real(p2) and
real(p3) parameters to 90,90 and everything but this disk will vanish.
The calculation time of an incredible 7 seconds makes today's image the
best bargain in FOTD history. It will give the fractalist a
taste
of true fractal luxury.
Typical winter weather continued here at Fractal Central today, with a
mix of sun and clouds, (more clouds than sun), and a temperature of 45F
+7C. The fractal cats made the most of the sun while it was
shining, until their empty stomachs reminded them that it was time to
ask for food.
FL and I had another near eventless day, consisting of routine work,
which leaves almost nothing to write about. The next FOTD
will be
posted in 24 hours. Will it rate a very elusive perfect
10?
Probably not, but check back then to see. Until next time,
take
care, and we seem to be heading for another fractal hot streak.
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
It_Is_Inconsistent { ; time=0:00:07.50 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=JulibrotMulti2 function=recip
center-mag=-2.33382/-0.824264/0.03290941/1/-70/0
params=-12/2500/89.85/0/89.85/0/-1.517971789544359\
/0.8699445685140538/0/0 float=y maxiter=1500
inside=0 outside=tdis periodicity=6
colors=000zzzzzzzzzxzzqzzszzszzszzszzszzszzszzczzc\
zzczz4qYxzzpzzizsizXlzHpv6hq0`f0VX0OO0JI0MD0U83Y28\
_2De1Il0Op0Ur0_s6csAinIpfPv_QzPUtKUoESk9Sf4U_DR`MO\
`TMaUMcSPcQScPVaPX`PV_PSYPOXPMVPKUPCSP8QP8PPDOPHMM\
LMKPMHUOEYOCaOCfOCXXDK0KO2PQ3VV6`Y7_Y7_X7_X7YX7YV7\
YV7XV7XV7VU7VU7VU7US7US7US7SS7SQ7QQ7QQ7QQ7PP7PP7PP\
7OO7OO7MO7MO7MM7LM7LM7LL7KL7176KL7IL7IK7IK6HK6HK6H\
I6GI6GI6EH6EH60Vi1Ya7_XDaQKcLQeGYhAei6lj1je0i_0hV0\
fP0fL0_H1UD8O9GI6OD2X80e30m30Y34I38638628628627617\
6176zL4zK6zK6yK6xK6vI6tI6sI6qI6pH6mH6lH6jH6iH6hG6f\
G6eG6eG6cE6aE6`E6_E6YE6XD6VD6zzEzzEzzEyzGxzGvzGtzH\
szHqzHpzImzIlzIjzIlzLmzOmzPpzSpzVqxXqv_ssasqctmftl\
ivijvhmxeqxcsv`mt_isXesVaqSYpQUpOQmMMlKIlIGjGCiE8i\
D6VS7Hf74v80z80z90z81z87x7Cs7Im7Oi6Ve6``6hX4mS4tP4\
hOKXM`MLqMLqMLqLLpLLpEqyDqzGmzIjzLhzOeyQayS_xVXxYU\
v`QtcOteLshIsjGqmDqqAps8p }
frm:JulibrotMulti2 {; 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),
c=p+flip(q)+p4, z=r+flip(s)+p5:
z=(bb)*(z*z*fn1(z^(aa)+bb))+c
|z|< 6 }
END PARAMETER FILE=========================================