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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image springs from a new formula, one that I wrote on Sunday and named 'DivideBrot2'. The formula is so new that I have little idea what it does or how it works. Today's particular parameters create a parent fractal that resembles a Mandelbrot set with two main bays. But even though the parent resembles the M-set, the minibrots in it are quartic. And though today's image is located in what appears to be Seahorse Valley of the parent fractal, the elements in the image more closely resemble those of an East Valley. Since I have very little idea of what the formula can do, I had no idea how to rate the image. The name I gave it -- "Quartic Minibrot" -- is nothing more than a description. This formula appears to get more out of a quartic fractal than the simple formula Z4+C. Hopefully it will do the same for some of the higher order fractals. I'll work with the new formula for a day or so before deciding whether to consign it to the storage bin. If anything of unusual interest turns up, I'll post it as a FOTD. Today's image is rather slow, taking almost 9 minutes to finish on the fastest machine. Any budding impatience may be nipped by visiting the FOTD web site at: The weather was good enough here at Fractal Central on Sunday, with sunny skies and a temperature of 84F 29C. The clouds that moved in at 5pm and the light thunder-shower than followed arrived too late to spoil the day. The fractal cats spent most of the day watching for squirrels and passing tomcats. My day was appropriately lazy, and if I have my way, tomorrow will be the same. The next FOTD will appear in 24 hours. Until then, take care, and if it doesn't make good sense, question it. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Quartic_Minibrot { ; time=0:08:58.05-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot2 passes=1 inside=0 float=y
center-mag=-1.045188369333446/+0.03206533434293096\
/1.098195e+012/1/82/0 params=2/-2/1/0 maxiter=15000
periodicity=10 mathtolerance=0.05/1
colors=000YmXXhUWdRV_OUWLSRIRNFQICPE9O96N53M10O32P\
44Q56R68T8AU9CVAEWBGYDIZEK_FM`GNZFOYEPXDPWCQUBRTAR\
S9SR8TQ7TO6UN5VM4VL3WK3WQDUVMT`WSedQknPpwOltTirYfp\
bbmg_klXipVfmTdjRagP_dNXbLV_JSXHQUFNRDLPBIM9GJ7DG5\
BD39B88GD7LH6PM6UR5YV4b_3fd3kh2om1tq1xq2Zq39o5Dn6G\
m8Kk9NjBRiCUgDXfF`eGccIgbJjaKm`Mk_OjZQiYShXUgWWfVY\
eU_dTacSbbOcaKc`Gc_CdZ8dY5dX6IRBNSGRTLVTP_UUcUZgVb\
lWgpWltXpxXjpUeiS_aPVVNPNKKGIE8F91DB6JDBOFGTHLYJQc\
LVhN_mPdrRhwTdqU`kVXeWT`YPVZLP_HJ`DEeGMjIUoKatMiyO\
qSvqOmgLeYIYOFQECI4FH8HHCJHFLGJNGMPGQSFTUFXWF_YEc_\
EfaEjcEm`FlZFkXGjVGjTHiRHhPIgNIgKJfIJeGKdEKdCLcALb\
8Ma6MaTVgSThSRhSQhSOhSNhSLhSKhRIhRGhRFhRDhRChRAhR9\
hU8gW7gZ6f`6fc5ee4eh4dj3dm2co2cdWaVx_YwX_vVauSctQf\
tNhsLjrIlqGnpDqpBso8un6wm3ym1xj4xg6wd8waAvZCvXFuUH\
uRJuOLtLNtJQsGSsDUrAWr7Yr5_s4Ys4Ws3Us3Ts3Rs2Ps2Os1\
Ms1Ks1Jq2ICqb9sdNuc`vcZq_ }
frm:DivideBrot2 { ; Jim Muth
z=0, c=pixel, aa=real(p1), bb=imag(p1),
dd=real(p2), ff=imag(p2)+64:
z=z^aa/(z^bb+dd)+c
|z| <= ff }
END PARAMETER FILE=========================================
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times.
