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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is yet a third view of the scene that appeared two days ago on April 9. But whereas in yesterday's reimage we tore the original image to shreds, in today's view we 'renormalize' it into a reasonably symmetrical object. I named today's image "Renormalization". As far as I know, renormalization is something physicists do when the numbers behind their theories add up to infinity or zero, or something else absurd. They simply insert arbitrary terms into their formulas, which result in the formulas accurately describing the ideas they are trying to prove. I'm not sure if this band-aid approach actually proves anything, but it sure eliminates a lot of headaches for the theorists, especially those still searching for that elusive theory of (almost) everything. In today's image I renormalized things by simplifying the orientation parameters to 90,0,0,90, which conveniently draws the 'Rectangular' direction, defined by the imag(c) and imag(z) axes. After much stretching and skewing, this simplification produced a near-symmetrical pattern around the hole at the center, which once was a perfect minibrot. Since the scene was renormalized, the rating could be nothing but 'normal'. But things in the image are not quite as normal as they first appear. Today's orangish pattern has only two rounded points, whereas the Mandelbrot version of the same scene has four points. Where did the other two points go? Most likely, they rolled off into the fourth dimension. The calculation time of today's image is a blessedly brief 34 seconds, fast enough to bring joy even to the hearts of those who don't get the point of fractals. The trip to view the finished image on the FOTD web site at: With a high temperature of 72F 22C, gentle winds, and brilliant sun, Thursday was the best day so far this spring. The fractal cats must have agreed. They got into a spat over who should sit in the sunniest window. My day was moderately active. Tomorrow will probably be the same. The next FOTD image will be created sometime during the next 18 hours and posted in 24 hours. Until that semi-glorious moment breaks upon the waiting world, take care, and renormalize yourself. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Renormalization { ; time=0:00:34.74-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 inside=0 periodicity=10
params=90/0/0/90/-1.749446905449293/6.834887985e-0\
07/-1.749446905449293/6.834887985e-007/2.0000001/0
center-mag=+0.00000000313126323/-0.000000064336418\
7/2.29769e+007/1.4265/-86.5334566310032614/83.7362\
695773166621 float=y logmap=181 maxiter=1800
colors=0000850966A79B8BC9ED9HEAKFBOFBRGCWHD`IDeNEl\
TFoaOuiYvrVzxSzxQzyNzyXzzgzzpzzzI00GA0EK0BUT9_O6_K\
4_F2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcH\
bbIVaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIzzzzzztwso\
rnkieg`XkSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePD\
bMELhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH\
4fH5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBo\
jCmgCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM\
`JIsSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__e\
Y_bW_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCT\
YCUWDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSS\
bPNaMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOL\
JRLIVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCd\
cDceEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzf\
UzXYzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtz\
rozhjzZezPDzrHzkLzdPzZTzS }
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.
