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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I had to do it. I just couldn't help myself. I had to take a perfectly lovely little midget in the Mandelbrot set and turn it into a parody of itself. Since the image is just for fun, I could not give it a rating, but the parameter file is quite fast, and even if the image brings no enjoyment at all, little effort will be wasted calculating it. The midget is located on a filament in the vicinity of the East Valley of the large midget on the negative stem of the M-set. To see the original midget in its full glory, bring up the 'Z' screen, change real(p1) to 45, imag(p1) to zero, real(p2) to 45, and imag(p2) to zero. Then go directly to the <f6> screen and change the x-magnitude to 1 and the skew angle to zero. Strike the <enter> key twice. You will find that the true midget is really quite attractive, with its ring of 8 parading elephants. Too bad I spoiled it. What I did was picture the midget from an oblique angle in the four-dimensional body of the Julibrot. The stretching and skewing was necessary to undo the natural distortion that results when Julibrot elements are sliced at slight angles. I named the image "The Joker Laughs". The Joker has always been one of my favorite villians in the Batman series. And the calculation time of under 2 minutes will try no one's patience. As always, the completed image is posted for viewing on the FOTD web site at: A hazy sky which noticeably dimmed the sunshine kept Tuesday from being another perfect 82F 28C day here at Fractal Central. The fractal cats ignored the weather. They were too busy watching the pigeons scrounging for food on the sidewalk. When the birds flew away, the cats thoughts turned to fun and treats. My day was busier than Monday, but well under control. The next FOTD will appear in 24 hours. Until then, take care, and look for the bright side of dull, drab fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Joker_Laughs { ; time=0:01:56.82-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2 inside=0 periodicity=10
params=131/-44/-97/72/-1.7481510383921/0.001201805\
9621/-1.7481510383921/0.0012018059621 maxiter=15000
center-mag=-0.00000000032727888/-0.000000000154431\
44/2.437256e+008/1.8621/177.600282113802905/56.750\
2624222490368 float=y
colors=000asYlscnpdondgj`dfKabPZZUWUZTPcQKhNFbKAYH\
5SD5MA6H76B4751705929B4CD6GF8KH9NJBRLDUNFYPGaRIdTK\
hVMkWNmXOoYOqYOsZPt`PubPxePzhQykQymQwnQvlRriRmfRhe\
RcbSZ`SUYSPWTKUTART5OT2MU2JU2HU2FV2CV2AV28VCFQMLMV\
RIdYEncAwi6tlHroSorbmumntjnthotfotcptapt_qtYqsVrsT\
rsRssPssMtsKtsItsGupFumFujEugEvdDvaDvZCvWCvTBwQBwN\
AwKAwH9wF9wQIw_QwiYvjWukUtkSslQrlOqmMpnKpnIooGnoEm\
pClqAkq8jr6jr4kp5kn6kl7kk7ki8kg9kfAkdAlbBlaCl_DlYD\
lXElVFlTGlSGkTGjVFWOlWSiWVeWZbWaZXeWXiSXlPXpLXsIXw\
EXzBUtGRoLOjQLdVJ_ZGVcDPhAKm8FqBJmEMjHPfKScMV_PYXS\
`UVcQYfN_iJblGeoChr9ju6fh8bXAZKCV8EXDDZID`MDbRDdVD\
e_DgdDihDkmDmqDovDpzDqxHqwKqvNruQrtTrsWrrZqo_qm_qk\
_ph_pf_pd_oa_o__oY`nV`nT`nR`mO`mM`mK`mI`iPceVea`gY\
fiVlkTkeRk_PjUOjOMiIKiCJi7Ih9HgAGfBGeCFdDEdEDLmDMl\
CNkBOjAPiAQh8Rg7Sf6Te5Ud4Vc3Vf4Xd4Zb5``Ab_FeYKhWPj\
VUlTZoRcqQhsOmuMrsGwsMzsS }
frm:SliceJulibrot2 {; 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| <= 9 }
END PARAMETER FILE=========================================
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times.
