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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image returns us to the complex logarithmic hyperspiral, which we have not visited in about a month. The parent fractal was created by the formula Z^(1.875)+C as it appears 33 levels up this abstract spiral when the 'floor' function is used. This parent resembles a ragged, somewhat squashed Mandelbrot set rotated so that its main spike points northeast. I chose the exponent 1.875 because it is 7/8 of the way from 1 to 2, which is close enough to 2 to create minibrots resembling recognizable quadratic ones, yet far enough from 2 to create fractals of infinite variety. Today's scene is located in a filament extending from the period-5 bud on the southwest shore line of the large minibrot on the main spike of the parent fractal, very near the point where the hairline filament emerges from the chaos. I named the image "Naturally Fractal" in recognition of the fact that nature is filled with and possibly made of fractals. I rated it at a 7 because it not only leads to pondering, it also is attractive in its own way. And no one will complain about the calculation time of a mere 30 seconds. For added convenience, the finished image is posted for fast if not instant viewing on the FOTD web site at: Another perfect midsummer day went unrecognized by the fractal cats of Fractal Central on Tuesday. The temperature of 86F 30C was made quite bearable by the low humidity. My day was a bit too busy for total enjoyment, but I still managed a half-hour under the mulberry tree, pondering the mysteries of the outer world and man's pathetic efforts to comprehend it. The next FOTD, which BTW is still a mystery, will be posted in 24 hours. Until then, take care, and fractals can cause deep thinking. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Naturally_Fractal { ; time=0:00:29.98-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC3 function=floor logmap=70
center-mag=+1.298046570238266/+1.385392696646682/1\
.09e+007/1/65/0 float=y maxiter=1200 periodicity=10
params=1.875/0/33/0 inside=0
colors=000OKOOKNOKNOKLOKKOKKOKKOKKOKKNKJMKILKEKKAJ\
J9II8HH7GG7FF6EA5B54814K46P77V99bCAgJCiHDzfCoJEzzD\
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LTzLTzKTzKTzKTzKTzWkzTfzQazNXzgfzfeueetddscdrccqbc\
zabz`bz`az_azZazY`zX`zX_zW_zVZzUZzUYzzYzzXzRXzzXzQ\
WzzWzzVzzVzzUzMUVzTzzTzz2zz3Cz3Cz4zz4zz5zS5zz5zR6z\
z6Ez7Fz7Fz8zz8zz8zQ9Gz9zzAHzAHzBzzBzQBzPCzzCzPDJzD\
zPEJzEzPEzOFKzFKzGLzGLzHLzHLzHzzIMzIzzJzzJzzKNzKzz\
KzzLzzLOzMzzMPzNPzNPzNQzO }
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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times.
