FOTD -- December 04, 2013 (Rating A-9,M-9)
Fractal visionaries and enthusiasts:
Today's superior image shows a minibrot in the parent fractal
that results when the expression Z^(1.333)+C is iterated one
level up the hyperladder with no function applied. This parent
fractal rather resembles the eastern half of the main bay of the
Mandelbrot set, complete with a quite convincing large quadratic
bud on its northern side. Today's unusually brilliant scene
features a minibrot lying on a tiny disconnected filament
fragment near this almost-quadratic bud.
>From a distance, the minibrot in today's image is shaped
strikingly like the countless Minibrots found in the M-set,
though a closer check reveals huge differences. The name
"Pseudo Quadratic" refers to this false resemblance.
In my opinion, both the art and the math aspects are worth the
rating of a 9. The art rating reflects the extra effort
required to achieve the brilliancy. The math rating is so high
because I have never seen a minibrot so closely resembling a
quadratic minibrot in a fractal with an exponent of Z as low as
1.333.
The calculation time of 4-3/4 minutes is admittedly slow, but at
least in today's case, the result is well worth the wait.
The finished image is or soon will be available on the following
FOTD web sites:
<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>
Fine early winter weather prevailed here at Fractal Central
today. The day began with heavy fog, but the fog lifted in the
morning and revealed a mostly sunny sky that remained that way
through the afternoon. The ample sun raised the temperature to
a high of 48F +9C. The fractal cats appeared too interested in
each other to pay much attention to the sun on the window shelf.
The fractal humans had other things to do.
The next FOTD will be posted in the proper time. Until
whenever, take care, and which is worse -- conservatives who
want to pass laws to force everyone to obey the rules of
behavior set down in their Bible or liberals who want to pass
laws to eliminate the natural inequalities inherent in humanity?
As I see it, neither of these goals is ever going to be
achieved, but it sure is a lot of fun watching the two sides
continue their futile squabbling.
Jim (neither right nor left) Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
Pseudo-Quadratic { ; time=0:04:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=1
center-mag=-0.3243347326496687/+1.081261598206034/\
3.441011e+009/1/172.5/0 params=1.333/0/1/0 float=y
maxiter=5000 inside=0 logmap=-305 periodicity=6
colors=00000B00C00D00E00F10G20H30I40J50K60L70M80N9\
0OA0P50G50H50I50J50K50L50M50N50O50P50Q50R50S60T70U\
80T80T71S72S63S64Q53P53O42M40J30H30D208204100zQKtJ\
KqAKn8Hj8Dh46g60hB0iH0jL0kP0lT0mX0ma0ne0oi0pm0qq0z\
zFzzcVbB7HL6KK6MJ6OI6RH5TG5VF5YE5_D5aC6eD7iD8lD9pE\
AsEBwEBzEIyKPyQWyWbyaiygoylmvjkthjrfhpdfnbel`ciZbg\
X`eVZcTYaRW_PVYNTWOSVORTOQSPPQPOPPNNQLMQKKQJJRIHRH\
GRGESFDSECSJJWOQ_TXcYcgbjk`il_hmZhmYgnXgoWfoVfpUeq\
TeqSdrRdrOZzMTzJOzHIzECzC7zDCzDGzEKzEOzFSzFXzG`zGd\
zHhzHlzHpzIqzJqzKqzLqzMrzMrzNrzOrzPszQsXQsVRsSStPT\
tNUtKctImmKzmMzmOzmQzmSzmUzmWzmYzmZzmZzmZzmZzmZzmZ\
zmZxmZymZtmWomTjzRezOczMczJczHczEmzCmzJmzQmzXmzcfz\
jmzgmzemzbmz`mzYozWqzUszRuzPwzMzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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=========================================
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