Fractal of the Day
by Jim Muth
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FOTD -- May 26, 2009 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is filled with things that look like spider webs. This is why I named it "World-Wide Webs". The parent fractal is what happens when the formula Z^(1.83)+C is calculated 18 levels up the logarithmic hyper-ladder, (or hyper-spiral). This parent resembles a partially-eroded Mandelbrot set rotated about 180 degrees, with a very large disconnected minibrot just inland on the northwest shore line of the main bay. Today's scene is located in what I take to be East Valley of this minibrot.
The rating is limited to a 7, mostly due to the colors, which have an annoying muddiness that I couldn't get rid of. But the image is still an example of some of the unexpected scenes in the fractals with exponents of Z between 1 and 2.
The calculation time of 1-2/3 minutes is blessedly brief. Equally brief is the trip out to the FOTD web site at:where the already-calculated image may be viewed at leisure.
Tons of sunlight prevailed here at Fractal Central on Monday, and the fractal cats made the most of every photon of it. Nicholas got a bit testy when a wandering tomcat made a litter box of the side walkway, but Cassie calmed him in a hurry when she started playing with the catnip rat.
My day was slow and lazy, which is the way I prefer days to be . . . up to a certain point, that is. The next FOTD will be posted in 24 hours. Until then, take care, and how do we know for sure that anything is real, or even if such a thing as reality actually exists, for that matter? (My guess is that it's a leap of faith necessary to make science work.)
Jim Muth
jamth@mindspring.com
jimmuth@aol.com
START PARAMETER FILE=======================================
World-Wide_Webs { ; time=0:01:42.19-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=MandelbrotBC3 function=floor logmap=133
center-mag=-0.8745118926611518/+0.566229601300528/2\
83049.1/1/-55/0 float=y maxiter=1750 periodicity=10
params=1.83/0/18/0 passes=1 inside=0
colors=00050050050250950F50K50Q50X50VB0TH0OM0OT0MY\
0IiBgvazzzzzvzzozzizzdzzXzzQzzKzzFzz9zz_zxzzozzzXz\
z0zz0zt2zdFzOQz9dz0oz5goFaVOX9YQ0gK0eV0dd3a_2_Y0YX\
0XV0XT0VQ0TO0QM0QK0OI0QH0VD0_A0eA0hA0mA2pA5sA7vEBx\
IFzMIzQKzSOzUOzWOzYOqTOgOOY0OO0OF0O50O00O00O00O00O\
00O20O95OF9OMFVVK_aQgiXno_vxezzlzzqzzxzzzzIz_QzXXx\
VdxQlvMqvKztHztFzqBzq9zzezzzzzzxqoideXOVIBK50B0020\
000000002303905F07K09O03H00B003000000700D00I00O00T\
00X00_00d00g53lB9oHFtMIxTOzYVzdYzidzngz_QzM9z90zD2\
zF7zIDvKInOOeQVYV_QXeI_lBaq3ex0gz0lz0zzzTzzzzz0zzz\
zz0zzzzz0zzzzz0zzzzz0zzzzzzzzzzzzzz2zz3zz7zz9zzBzz\
Q0zM0zI0zH0zDBz9Mz7Xg3gO2qI0za0zi9zoOzvdzztzzzzzzz\
zzvdz_0Xqd0zz7znFzIMz0Bz30lH0XXzFiz0xz0zz0zz0zz0zz\
0zz0zz7dzFHzK0zV0zd0zn0zx0zz0zz0zz0zz0zz0zz7zzHzzO\
zzKzzHzzDzz9zz5zz2zz0zz0zz0Kz2ez3zz5zzYzzzzzqzzizz\
azzVzzMzzFzz7zz0zz5nzngzo }
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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