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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Discard the formula that came with yesterday's FOTD, and substitute today's formula. Yesterday's formula has a small error, which I found soon after posting the FOTD. While working with yesterday's formula, I noticed that I was constantly getting two extra lobes on the elements. This is because I had forgotten to subtract 2 from the number entered as real(p5). This oversight explains why the elements in yesterday's image had 7 lobes instead of 5. But today's formula, which I am pretty sure is the final version, sets everything right. As an example, the value of real(p5) in today's formula is 5, and the image is filled with five-sided elements, indicating that all is once again well in fractal land. Today's image is a Julia set of a small valley at the outer edge of the third bud out the negative X-axis of its parent fractal, which resembles a moth-eaten Mandelbrot set. I did not rate it because I'm still not familiar with the potential of this latest formula. I named the image "The Mystic Star". Fractals are at least as mysterious as anything traditional mystics have been telling us. I wonder what a tiny rotation away from the Julia orientation would do to today's image. Perhaps we'll find out in tomorrow's FOTD. The calculation time of 1-1/2 minutes may make the trip to the FOTD web site at: We certainly did not deserve the perfect weather that prevailed here at Fractal Central on Friday. After all, it's supposed to be midsummer, when we go around wiping away the perspiration or hiding within our air-cooled cocoons. Today's blue skies, puffy cumulus clouds, low humidity, and temperature of 86F 30C were unexpected but fully welcomed by human and cats alike. With not much work to do, this human worked on a fractal formula, while the fractal cats worked on trying to get an extra treat. The next FOTD will appear in 24 hours. Until then, take care, and if the mysteries of mysticism are not mysterious enough, look to modern science for some real mysteries. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Mystic_Star { ; time=0:01:28.15-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot logmap=11 periodicity=10
center-mag=0/0/3.963356/1/-90/0 float=y maxiter=1600
params=90/90/90/90/-5.4262/0/0/0/5/4 symmetry=none
inside=0 passes=1
colors=000UGXUIXUKXUMXUOWUQWUSWUUWUWVUYVU`VUbVUdUU\
fUUhUUjUUlTUnTUpTUrTVxRUtTUqVUmXUjZUf`UcbU`dSaeRbe\
PceOdeMdeLeeJfeIgeHgeFhfEifCjfBkf9kf8lf6mf5nf4nf6k\
d8icAgbBe`Db_F`ZGZXHXWJUVKSTLQSMOROMPPJOQHNRFLTDKV\
AJW8HY6GZ4FZ2E_5G_8I_AKaDLbGNdIPeLRfOShQUiTWkWYmYZ\
m``ncbsdenecjebfeabe`Zf_VfZQfXMfWIgVEgUAgT4eQ6gS8h\
UAjWBkXDmZFn`GpaIqcKseLtfNvhPwjQxkRvjSuiSthTsgTrfU\
qeUpdVodVmcWlbWkaXj`Yi_YhZZgYZfY_dX_cW`bV`aUa`Ta_S\
bZRbYRYrjakfeeciZ_mTXqMTuGQxANdRVeTWfUWfVWgWWgXWhY\
Wh_Wi`WiaWjbXkcXkdXlfXlgXmhXmiXnjXzxhnkXc_MTOBxuOv\
tNusMsrMrrLpqLopKmpKloJjnJrnIzmHzlHzkGzkGzjFziFziE\
zhEzgDmiCcgDUfETeFSdzoczQaHP`IO_JNZKMYLLXLKVMJUNIT\
OHSPGRQFPQEORDNSCMTBLUCJTBKUBLVBMWAMXANXAOYAPZ9P_9\
Q`9R`9Sa8Sb8Tc8Uc8Vd7Ve7Wf7Xg7Yg6Yh6Zi6_j6_jB`hGaf\
LbeQccVdaZd`V`bRYdOUfKRgHNiDKk77tAHlCQeEZZJdnGgST`\
OdUKoNGpNHRorSelTWgUMbUDY }
frm:DivideJulibrot {; draws slices of DivideBrot Julibrots
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),
aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001,
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=sqr(z)/(z^(-aa)+bb)+c
|z| < 1000000 }
END PARAMETER FILE=========================================
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times.
