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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: There are six mutually perpendicular planes through every point of the four-dimensional Z^(2.003)+C Julibrot. The strange rectangle that has appeared in the recent FOTD's apparently exists only in the Julia plane, but I wondered how the rectangle, or the area in which it lies, would appear in the other five planes. Today's image is a slice through the vicinity of the rectangle in a direction rotated 10 degrees from the Oblate orientation toward the Rectangular orientation. Surprisingly, the rectangle still appears quite clearly at the center of the image. The rectangle is obvious, but its surroundings have undergone a dramatic change. Instead of the converging tree-like features, we have near total chaos -- an image that cannot be described and must be seen to be appreciated. I named today's image "Forever Rectangle". It appears that the rectangle will remain visible regardless of the direction from which it is viewed. I gave the picture no rating. If I had rated it, a score of 6 would have been appropriate. The render time of under 11 minutes is slightly slow. But when the image is viewed on the FOTD web site, rendering is not an issue. The web site may be accessed at: Early morning rain gave way to a partly cloudy and warm afternoon, with a high temperature of 77F 25C. The fractal cats paid no notice. They were too busy chasing each other all around the place. They did not settle down until treat time arrived in the evening. My day was average; tomorrow looks to be a repeat. The next FOTD will appear in 24 hours, when I'll see what other havoc I can wreak on that Z^2.003 rectangle. Until then, take care, and be of sound mind and body, but don't be too strong on the sound. You would not want to disturb the neighborhood. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
ForeverRectangular { ; time=0:10:51.64--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 passes=1
center-mag=-0.00016211607850631/+0.000876409345622\
04/1359.729/0.01759/-90/79.5200240071283986
params=10/90/0/90/-1.7435/0/0.00019/0.07388/2.003/\
0 float=y maxiter=15000 inside=0 periodicity=10
colors=000O8tP1yM1vJ1sG1pD1mA1j71g41d11b83_E4XL5VR\
6SY7Pc8Nj9KpAIlDGiFFfIEbKD_NCXPBTSAQU9NW7JZ6G`5Dc4\
9e36h23j10l03j15h17g1Ae1Cd1Eb1G`1J_2LY2NX2PV2ST2US\
2WQ2YP2ZS4ZV6_Y7_`9`cB`fCaiEalGboHbrJcuLcwMZpJVjHQ\
cFMYDISADL89F65948B8BCBDDEGFIIGLLHONISQKVSLYVMaXNd\
_PgaQkdRnfSqkUrpWstYts_rsaprcnrdlqfjqhhpjfpkdomboo\
`nqZnrXknUhjSfgQccO``MZXKWTHTQFRMDOJBLF9JC7HE9GGBF\
ICEJECLFBNHAOI9QK8SM6UN5VP4XQ3ZS2_T7aXBb_GdcKefPgj\
ThmYjqaktbjrbiqbhpbgnbfmbelbdkcdicchcbgcafc`dc_ccZ\
bcZaZH`U0`_EWeSRkeMpsIlqKioMfnNclP`jQYiSVgTSeVPdWM\
bYJaZOcVTdSYeObfLggIlhEqiBuj8tg7se6rc5ra4q_3pY2oW1\
oU0nT3mT5mT7lT9lSBkSDkSFjSHjRJiRLiRNhRPhRRlMSoHTpR\
GpAOrCUsDZtEduFivGowHtxIyuJyrKyoLylMyiNygOyfLteIpd\
FlcChc2cc9dcFecLfHjkNTe76oSC`gNGiKJkHMmFPoCSqAVk9U\
e8U`8UV7UP6TK6TE5T30P95TEAWJFZPKaUPd_VjZUgZTdYSaYR\
ZALnMOeDpMFhSHaYJUcKNhMFn }
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.
