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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is still another view of the Julia rectangle in the Z^2.003 Julibrot. I should not call it a rectangle today however, for today's orientation has been rotated 0.63 degree, which is just far enough from the Julia direction that the rectangle has been stretched into a near perfect square. But the square is only a small part of today's image, which resembles some fantastic bird in flight. Having been shrunk to near insignificance, the square lies where the wings are attached to the body of the big bird. This resemblance of the entire image to a bird in flight inspired the name "First Fractal Flight". I rated the image, perhaps a bit over-enthusiastically, at an exceptional 8. When the render time of 13 minutes is figured in, its overall value rates a 60. This value may be increased by saving the time that would otherwise be spent rendering the image. And this may be done by downloading the finished image from the FOTD web site at: Cold winds, only occasional sun, and a temperature of 41F 5C limited the cats' outdoor time to less than an hour on Sunday, but a generous treat of tuna in the evening kept their moods from becoming too sullen. This morning it is still windy and the temperature is down to 28F -2C. It looks like another less-than-ideal day for the fractal duo. I have near the normal amount of work to finish before retiring to fractal land. Today, I will bid a temporary 'good-bye' to the rectangle, and set out for unexplored territory. What I find there will appear as tomorrow's FOTD. Until then, take care, and float like a fractal, whatever that means. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
FirstFractalFlight { ; time=0:13:21.14--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 passes=1
center-mag=-0.000138176/-0.00692793/21.92537/1/-40\
/-5.05012698326368081e-014 params=90/90/89.27/90/\
-1.7435/0/0.00019/0.07388/2.003/0 float=y
maxiter=60000 inside=0 logmap=29 periodicity=10
colors=000RASSATTAUUAVVAWWAXXAYYAZZA__A``AaaAbbAcc\
AddAeeAffAggAhhAiiAjjAkkAllAmmAnnAooAppAqqArrAssAt\
tAuv9vtCurEuqGtoJtnLslNskPriSrhUqfWqeZpc`pbbo`do_g\
nYinXkmVnmUplSrlPumRtlTskVrjWqjYpi_ohanhbmgdlfflfh\
keijdkidmhcogbpfbreatd`ud`sc_qc_oc_nc_lbZjbZibZgbZ\
ebZcaYbaY`aYZaYYaYW`XU`XS`XR`XP`XN_WM_WK_WI_WH_WIY\
UJXTKWSKVQLUPMTONSMNRLOQKPOIQNHQMGRLESKDTJCTIAUH9V\
G8TC8VF7XH7ZJ6_M6aO5cQ5dT4fV4hX3jZ3ka2mc2oe1ph1rj0\
tl0qn0kf7gZEiRLkJRmLSoNUqPVsRXuTYwVZyX`zZaz`czbdzd\
fzfgzhhzjjzlkznmzpnzrpztqzvrzrszoszlsziszeszbsz_sz\
XszUszUszUszUszUszUszUszUszUszUszUrzWqzYqz_pzapzco\
zeozgnzinzkmzmlzolzqkzskzujzwjzyizzizzhzzhzzhzzgzz\
gzzgzzfzzfzzfzzezzezzezzdzzdzzdzzczzczzczzazz`zz_z\
zZzzYzzXzzWzzVzzTzzSzzRzzQzzPzzOzzNzzMzzKzzJzzIzzH\
zzGzzFzzEzzDzzEzzEzzFzzFzzFzzGzzGzzHzzHzzHzzIzzIzz\
IzzJzzJzzKzzKzzKzzLzzLzzN }
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 20.0 PAR-FORMULA FILE==================================
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times.
