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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The most recent FOTD took us to a scene deep in East Valley of the classic Mandelbrot set. Today's FOTD takes us to a scene deep in North Valley of the cubic Mandelbrot set. Just as East Valley is located on the real axis of the quadratic M-set, North valley is located on the imaginary axis of the cubic M-set, and most of what is true of East Valley is also true of North Valley. The main difference is that, in today's image, triangles are everywhere instead of squares. And the features surrounding the small central midget are arranged in ascending powers of 3 rather than powers of 2. The cut-off nature of the elements is again very prominent, though not so obvious as in the most recent 'deepeast' image. The terraced effect of the image was achieved by rendering it with the outside set to 'tdis'. The image is also rather striking when rendered using the conventional 'equal-iteration-band' method. I named today's image "Deep in the North" and rated it at a 7. The overall value rates an 11. The image does not use a super-fast hard-coded formula, but rather a formula I wrote several years ago. The result is a parameter file that takes over 53 minutes to run. Luckily, the pre-rendered image will soon be available for download on the FOTD web site at: Sunday was cloudy and cool, but dry -- temperature 72F 22C. Monday was partly sunny and quite pleasant (81F 27C) here at the Old Fractal Central, soon to be moved to the New Fractal Central. Today it is raining. The cats enjoyed both Sunday and Monday. It's too early to see how they will take today's conditions. I don't know about the cats, but I'm going to make it a work-day. We still have quite a bit of work to put behind us. The next FOTD will appear in 24, 48, 72 or 96 hours. Until then, take care, and cheer up. Life is just a big fractal hologram. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Deep_in_the_North { ; time=0:53:57.87--SF5 on a P200
reset=2003 type=formula formulafile=slices.frm
formulaname=MandelbrotCube passes=1 inside=0
center-mag=+0.00000001446441666/+1.088667239670043\
00/4.657424e+011/1/30.0026626496268527/-8.93078864\
284968521e-007 params=0/0/0/0 float=y maxiter=50000
outside=tdis periodicity=10 mathtolerance=/1
colors=000rGwtHwsIurJtrKsqLrpMppNooOnoPmnQkmRjmSil\
ThlUg`SeQQdFOcFMadW`hVckVfoUhrUkvTnyTpwRiuPcsOYqMS\
oLMnMJmNHlOElPCkRGjSKjTOiUShVWhW_gXcfYgfZjbWi_UiXS\
hUQhQNhNLgKJgHHfDEfACf7Ae48e16e78dD9cIAcOBbTCbZEad\
F`iG`oH_tI_pKbmMejNggPjdQl`SoYUrVVtSXwPYyIVpBSg5PZ\
6S`7Pa7Mc8Jd8Ge9DgAAhA7jB4k4Eg5Ch6Ai78j8`X6Wd4Ql3L\
t6Kr9JpCInFHlIGjKFhNEfQDdTCbWB`ZAZ`AXVC_PEbJFeDHh7\
Jk1Kn2Nm3Ql3Tk4Wj5Zi5ah6dg7gf7je8md9pc9rcCWjFApIEo\
KInNLnPPmSSlUWlX_kZbjafjciifmhhphgqjgqkfqlfqmfqneq\
oeqperqdrrdrsdrtcrucrvcrw_quXptUpsRoqOopLnoImmFmlC\
lk9li6kh3kg4ee4`c4Wa4Q_5LY5GW5AU55S50QFDOOPNX`LelK\
bhJ`eIYbHW_GUXFRUEPRDMOCKLBIIAFF9DC8A9786A63F8AKAH\
KQJKSLKQDKT0KUMPYOUXNReVaiXcmYeq_guaiyckzhnzmqzrtz\
wwzzzYLkbBrf1yg4vg6th8rhAphCn_QfRc_IqTLoWOnYRm_Tka\
WjcZieaggcfifelicnlbpnarq_ttZvwYxyXzsYynZxi_wc`vZa\
uUbtPcsf4yh6yj8xlAxnCxpEw }
frm:MandelbrotCube {; Jim Muth real(c),imag(c)
z=p1, c=pixel+p2:
z=z*(sqr(z))+c,
|z| <= 16 }
END 20.0 PAR-FORMULA FILE==================================
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