July 19, 2010: The Wrong Angle | July
18 |
July 20 | 2010 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Today's image is a zoom into the bit of Seahorse Valley that was
stretched across the center of yesterday's image. It took quite
of anti-distorting to undo the stretching distortion in yesterday's
image, but once this was done, the result was very near perfect.
The incredible thing with today's image is that it calculates in 13
minutes, but shows the spider-web, peanut-hole features that normally
lie much deeper in Seahorse Valley and take hours to calculate.
The name "The Wrong Angle" refers to the fact that in the image,
Seahorse Valley is viewed nearly edge-on, yet appears quite
undistorted. The rating of a 7 is mostly for mathematical
interest.
The calculation time of 13-1/2 minutes is admittedly a drag, and I can
give no guarantee that the result will offer full compensation.
BTW, I have simplified the new logo for the FOTD web page, which was
getting over-worked and over-complicated. It shows my favorite
fractal and the six perpendicular slices of the 4-D Julibrot.
I'll send it to Paul on Monday.
Typical midsummer weather continued here at Fractal Central on Sunday,
with lots of sun and a temperature of 93F 34C. The fractal cats
made the most of things by sleeping all day. The next FOTD will
be posted in 24 hours. Until then, take care, and if the world
ends within 24 hours, there might be no more FOTD's.
Jim Muth
jamth@mindspring.com
jimmuth@aol.com
START PARAMETER FILE=======================================
The_Wrong_Angle { ; time=0:13:36.14-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 center-mag=-0.838351136\
47022960/+0.01718083180624014/204.918/427.74/90/\
0.0214321089199651232 params=-45/0/90.1/0/-0.7514/\
0/0/0/2/0 float=y maxiter=125000 inside=0
colors=000QJoRIpSHqTFrUErVBtUBsTArSBpRCoRDmRDlQDkP\
DjOEhODhNDgNEfMEdMDcMCcLDbLCbKCaJCZHCYHBVGAUFAUFAU\
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gj`fj`eiaehaehadgadfadfacebddbccbccbbbbbabaac``c`_\
c`_c`Zc`YaaXb`Yc`Yc`Zd`Ze`_e`_f`_ge`ge`heaieaieajd\
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_va_vaZwaZw`Yw`Yx_Xy_Wz_WzZVzZVyZUyYTxYTxXSxXSwXRw\
WRwWQvVPvVPvVOuUOuUNuUNtTOtSOtSOsSOsSNsSNrRNrRNrRM\
qRMqQMqQMpQKpQKpQKoQKoQKo }
frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================