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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image in the Z^(1.618034)+C Mandeloid looks quite like a real three-dimensional scene. The three-dimensional effect was created by the coloring, but when I saw it, I started pondering the nature of reality. The question "What is the ultimate reality" can be logically answered in several ways. The specific answer depends on the world view and mind-set of the one who gives the answer. A materialist will confidently state that the material universe is the one and only reality. A true religious believer will agree that the material universe is real, but he will just as confidently add that there is a second reality, a spiritual reality where spiritual things such as God, angels and the spirits of the dead exist. A mystic will answer that both the material and spiritual worlds are basically illusions and that only consciousness is real. A fractalist will ask where fractals fit in. And I wonder where I fit in. Returning to the topic, I named today's image "Mossy Fractal Garden". Something about it reminds me of a pleasant little garden at the edge of a brook that I used to visit as a child. I can still remember the mossy rocks piled along the banks. The rating of 7-1/2 includes 1/2 point bonus for the coloring, which creates the mossy effect. Actually, the image is one of the better minibrots I have found in the Mandeloids with exponents between 1 and 2. Today's exponent, 1.618034, is the golden ratio, not that it makes much difference in the resulting fractal. What does make a difference is the fact that I now use the function 'ident' instead of 'floor'. Using 'ident' is the same as using no function at all. I made the switch because the images created with the 'floor' function jump about in an irregular manner, while those created with 'ident' move smoothly up the logarithmic ladder, making animations feasable. (Not that I have any plans of creating any animations.) Today's image was created at ground level of the logarithmic ladder, where the parent fractal resembles an overturned turtle, with the scene of today's image located on a filament extending from the turtle's belly. The calculation time of 2-3/4 minutes is quite reasonable, as also is viewing the finished image on the FOTD web site at: Much colder weather moved into the Fractal Central area on Friday. With the winds, the temperature of 36F 2C felt more like 25F -4C. The fractal cats kept close to any available source of heat for most of the day, while I kept as far from the local shopping mall as possible. The next FOTD fractal will appear in 24 hours. Until then, take care, and reality is all around us, if only we had eyes to see. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
MossyFractalGarden { ; time=0:02:43.18-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC3 maxiter=5000 outside=tdis
center-mag=-0.694457057472/+0.729050695061/1536961\
/1/-72.5/-1.2758e-005 params=1.618034/0/0/0 float=y
function=ident passes=1 inside=0 periodicity=10
colors=00008Y06_06a04b02d01f00g00i00k00l00n00nzXpz\
TnzRntQlpOikNgfJfaI_OGXLETGDRBBO68N26L04I02G01G00G\
02G06I09J0DL0GO0JR0LV0OY1Ra4Va6_bDfdTkdiqdzxdzzdzz\
dzzdzzdzzbiwaTn_DdYBXX9NV8ET69R42Q20Q06_0Ei0Nq0Vz0\
bz0iz0gz0gz0fz0fz0dz0dz0bw0bt0aq0an0_k0_g0_d1Ya1YY\
2XX4XT4VQ6VN8TJ8TG9RDBR9BR8DT9EV9EX9GY9GY9I_BJaBJb\
BLdBLdBNfDOgDOiDQkDQkDRlETnETpEVqEzqEzpGzpGznGznGz\
nGzlGzlGzlIzkIzkIzkIziIziIzgIzgJzgJJfJJfJJfJIdJIdJ\
IdJJfIJfGJgGJgEJiDJiDJkBLk9Ll9Ll8Ln6Ln6Lp4Lp2Lp2Tq\
RaqpiqznftsXdxNOzD8z20z60z80z91wD4tE8sGBpIEnLIlNLi\
OOgRRfTVbVYaXa__dXagVbkTdlnJQz04x40n90dB0_G0VJ0QN4\
LQ9ITEDXL8_Q2bV0f_0kd0ia0g_0gY0fX0fV0dT0dR0bO0aN0a\
L0_J0_I0YG0YE0VD0RB0Q91N84J68I4BI4EI2IJ1JJ0NJ0OI0Q\
E0RB0T90R60R20V10X00R00V10Y60b90gE0lJ0qN1wR2zX4z_8\
zd9ziBzlEzqGzwIzzLzzNzzOzzRzzTzzVzzYzzazzbzzfzzgzx\
kzsnznpziszftzax0BV0BX09Y }
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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