Dec. 4, 2013: Pseudo-Quadratic | Dec. 3 | Dec. 5 | 2013 | FOTD Home |
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.
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\
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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=========================================