|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Yesterday's image showed Siegel Disks. Today's image wreaks havoc with those disks. Siegel disks are spirals that circle forever but never draw any closer to the center. Today's image not only changes the disks into star-like objects, it totally obliterates the lower halves of them. This craziness came about when I duplicated yesterday's image but rotated the orientation of the slice about 2 degrees from the Julia direction of the Julibrot. To do this it was necessary to use a special Julibrot formula which rotates the slices. I think this is the first time I have used this particular formula in an FOTD image. BTW, the Julibrot is the 4-dimensional assemblage of all the Julia sets and all the perturbed Mandelbrot sets. In four-dimensional space, all kinds of crazy and unimaginable things can happen, and today's image is one of them. In today's image, the lower half of the remnants of the Siegel disks is obscured by a grossly enlarged and distorted view of the part of the Mandelbrot set that corresponds to the Siegel disks. I named the image "Siegel-Disk Sunrise" because that's what it reminds me of. Then I rated it at a 7 to reward myself for the extra 10 minutes or so I spent working on the colors. The calculation time of 1-3/4 minutes can be sidestepped by going to the FOTD web site at: Monday proved to be a lovely sunny day here at Fractal Central. True, the temperature of 88F 31C could have been a bit cooler, but the humidity was not all that bad, and a gentle breeze kept the air stirred. All in all, the fractal cats approved. My day was busier than I would have liked, but the work was finished in plenty of time for the day's FOTD to be completed. The next FOTD will appear in 24 hours. Until then, take care, and choose wisely. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
SiegelDisk_Sunrise { ; time=0:01:49.35-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2a passes=1 periodicity=0
center-mag=0.0337456/0/0.9146906/1/-37.5 logmap=yes
params=88.512/1.442/92.381/-1.198/-0.390541/-0.586\
788/0/0/-5/0 float=y maxiter=3600 symmetry=none
inside=bof60
colors=00000006C0AE0CG5EIAGKFIMKKOPMPUPQZSMcVIhYLm\
_OraQwcTweWwfYwg`whbwicwjdwkewlfwmgwnhwoiwpjwqkwrl\
wsmwtowuqwvsxwvyzzzzzKqgIpeGnbEm_CkYAjV8hS6gQ4eN2d\
K0cILWOeOTYIOQCKIMAMIIQEQXCWbAah8fn6lt4qvEpwNpyWoz\
dotXgoP`iHTdAMLPb2csrkhqfmqbqqYvqUzkVseVl_VeUVZOVS\
IVLCVE7V8IPBTJDbEGm8Iw3Kp2Gj2Dd2A_8BVEBQJBLPBGVBB_\
B6eB1jBHd9W_7kV5zQ4mZC`fKOnSBvZGtYKrYOpYSnYWlY_jYc\
hYggYbb_ZYaVTbROdMJfIEgE9iA5j99e9Da9HX8LT8PO8TK8WG\
KXDVXBeX9pX7`0lmT5lR3TYqYWcEB6HMIJXTLgdNroSlpXfqa`\
qeVrjProJssDswJhzOZoNSeNMWNGVH_UCsXIl_NfaT_dYUgcNi\
hHgjGflGemGdoFcpFbrFasFaaMaLSa4Y_7cYAiWCnUFtTHySNr\
RTkQYdPcYOhRNnKNsEUoI`kMfgQ9wBJh9SU7`F5i04zaDvXKrT\
QnPWjLafHgbDmZ9sV5yYAu`EqbIneMjhRfjVcmZ_obXnXTnRPn\
MMmGImBFm5Bm08hF7dT6`f6Xh5Tj5Ql4Mm4Io4Fq3Bs38t3GnA\
OhHWbOcXVbUWbSWaPWaNWMXU7eSMaP`ZMoWJj_RecY`geWklSn\
sOlmKkhHibDhYAfSimelqfoug }
frm:SliceJulibrot2a {; 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=sqr(z)+c
|z| <= real(p5+9) }
END PARAMETER FILE=========================================
|
times.
