Fractal of the Day
by Jim Muth
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FOTD -- March 20, 2009 (Rating in Doubt)
Fractal visionaries and enthusiasts:
Today's strange image is a scene in an almost-Julia set of the northeast shore line of the main bay of the Mandelbrot set. It is not part of a Julia set, nor is it part of a perturbed Mandelbrot set. It is an oblique slice through the Z2+C Julibrot figure oriented within a degree or so of the Julia direction.
The straight bright bar across the lower part of the scene is what I call a bridge. It appears straight because regardless of where Z is initialized in a perturbed M-set, the points will always settle into the same orbits unless they escape first.
I had no idea how to rate such an image, so I left the rating in doubt. The name "Looping Bridges" describes the many loops and spirals dancing around the bridge.
The calculation time of 2 minutes is thankfully fast, though the trip to see the completed image on the FOTD web site at:could be even faster.
A cloudy start gave way to a partly cloudy afternoon here at Fractal Central on Thursday. The fractal cats enjoyed the times when the sun was shining and made the best of things when it was not. The temperature hovered around 52F 11C most all afternoon.
My day continued busy. The next FOTD will be posted in about 24 hours. Until then, take care, and look for light.
Jim Muth
jamth@mindspring.com
jimmuth@aol.com
START PARAMETER FILE=======================================
Looping_Bridges { ; time=0:02:08.44-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 passes=t float=y inside=0
params=90/90.07/92.48/89.01/0.2438/0.5139/-0.0081/0\
.5024/2/0 logmap=-3 periodicity=9 maxiter=18000
center-mag=0.00665081/0.170958/3.138989/1/-90/0
colors=000jRhh0efVbd0_bYX`AVZaSXKPVdMTKKRgHPKENkBK\
N4Ml9OMDQcHRLLTWQVKUXVYW0cYQaZ0`_NZ`0YaNXb0VcNUe0S\
fURg0QhVOi0NjSMk0KmTJn0HoVGphlqijrnCsXBtYDtYEzzFtz\
GtzHtZJtZKCzxCzxCzxDzxDzxDzxDzxEzxEzxEzxEzxFzxFzxF\
zxFzxGzwGzwGzwGzwHzwHzwHzwHzwIzwIzwIzwIzwJzwJzwJzw\
JzwKzwKzwKzwKzwLzxLzxLzxLzvMzxMzxMzxMzxNzxNzxNzyNz\
yOzyOzyOzyOzyPzyPzyPzyPzyQzyQzyQzyRzyRzyRzyRzzSzzS\
zzSzzSzzTzzTzzTzzTzzUzzUzzUzzUzzVzzVzzVzzVzzWzzWzz\
WzzWzzXzzXzzXzzXzzYzzYzzYzzYzzZzzZzzZzzZzz_zz_zz_z\
z_zz`zz`zz`zz`zzazzazzazzazzbzzbzzbzzbzzczzczzczzc\
zzdzzdzzdzzezzezzezzezzfzzfzzfzzfzzgzzgzzgzzgzzhzz\
hzzhzzhzzizzizzizzizzjzzjzzjzzjzzkzzkzzkzzkzzlzzlz\
zlzzlzzmzzmzzmzzmzznzznzznzznzzozzozzozzozzpzzpzzp\
zzpzzqzzqzzqzzqzzXzzXzzXzzYzzYzzYzzYzzYzzYzzYzzYzz\
YzzYzzYzzYzzYzzYzzZzzZzzZzzZzzZzzZzzZzzZzzZzzZzzZz\
zZzzZzz_zz_zz_zz_zz_zz_zz }
frm:SliceJulibrot4 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*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),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(p5)+c
|z| <= 9 }
END PARAMETER FILE=========================================
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