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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is named "Julia Broken Up" because it is the Julia set of the center of yesterday's 'All Broken Up' image. As such, it shares many of the features of that image, as well as virtually the same color palette, but at the same time it brings enough new aspects to make it worth being chosen as the FOTD for November 20. With nothing really totally new to offer, the image could hardly be rated much above a 6, and in fact, this is what I rated it. Perhaps the most interesting thing about the image is yet to come. I could have created the image more directly with the type=julzpower formula, but I used the SliceJulibrot4 formula instead. I did this because I am curious as to the appearance of this area of the Z^(4.003)+C Julibrot when sliced in the four remaining mutually perpendicular planes of the four-dimensional space in which it lies. I will check these other orientations sometime tomorrow, and if I find anything of unusual interest, I will include it as tomorrow's FOTD. The calculation time of 4-1/2 minutes is thankfully brief. Even briefer is a visit to the FOTD web site at: Very unpleasant weather prevailed here at Fractal Central on Monday. Not only was it cloudy and just above freezing all day, but the melting slush made walking a major effort. The fractal cats passed the day keeping warm. My day was just busy enough to keep my mind off the miserable conditions. The next FOTD will appear in 24 hours. Until then, take care, and search for the real reality. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Julia_Broken-Up { ; time=0:04:25.07-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
params=90/90/90/90/-1.222743994189852/2.3436721194\
31135e-006/0/0/4.003/0 periodicity=10 inside=bof60
formulaname=SliceJulibrot4 maxiter=2500 float=y
center-mag=0/0/18.8653/1/22.5/0
colors=000RuzThvQdrO_mMWhKTcIQZFOVDMRBKM9HI7EGDHDI\
KGNMKSPNXRRaUUfXYkZ`paducgqbhmbiiajeaka`lY`mU_nQ_n\
UVfYR_aNTeJMgKPiLSjMUlNXnOZoPaqQcsRftShqJbnBXl3Sk9\
PjENjKLiPIhVGh_EfXFeUGdSHcPHaNI`KJ_IJZFKYCLWAMV7MU\
5NT2OS0OQEVORaMchLpnd6mZ8fU9`dLUfIOgKIdOJkOKqSKpWL\
o`MpeMujNznNvjMtgMpdLo`LoYLnVKmRKlOJkLJkIJgJNcKR_K\
UWLYSL`PMdLMgHNkDNn9Or6OuzNrxQowTmvVktYis`grbepeco\
h`njZlmXkpVjrThuRgxPfzNhvPisQjpRkmTliUmfVncWo`YpYZ\
qU_rRasObtLcuIduGetEetCftAfs8gs6gs4ht0is2hr3hr4gq5\
gq6gp7fp8fo9fnBenCemDdmEdlFdlGckHciA_kIcmPgnXjpcnr\
krzswzruzqtwqrwpqvootonsnmrmkrmjrlhrkgrkerjdsidrjc\
rjcrkcqkcqkcqlcplcpmcpmcghxpmczrKyqJxqIwqHwpGvpFup\
EtpDtoCsoCroBrnAqn9pn8on7om6nm5mm4no1mm4lk6ki8jgAi\
eChcFgaHf_JeYLdWNcUPbSSaQU`OW_MYZK_YIaXGdWEfVChUAj\
T8lS6nTCkTIhTNeUTbUY_UcXViUVmRVmOVmLSmOQmROmUMmXKm\
_ImbGmeEmhHmgJmgLmfNlfPie }
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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times.
