|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: It looks like a very busy day coming up here at F.C., so today's discussion will be short, to the point, and perhaps a bit too intuitive. For today's image I returned to the workhorse MandelbrotMix4 formula, which has been almost totally ignored during the past month. Exponents of Z between zero and one do not usually make fractals, but when the difference between two exponents in this range is magnified, as it is in today's formula, a fractal surprisingly results. Today's image is based on the tiny difference between the square root of Z, which is Z^0.5, and Z^0.5001. It reminds me of diced vegetables, so I named it "Diced Midget". The wildly clashing colors might work well as party decorations, but they do not make a great fractal. As a result, I could rate today's image no higher than a 5. The surprising thing about differences between exponents of Z in the range between 0 and 1 is that, like negative exponents, they produce fractals that are sensitive to changes in the bailout radius. If the bailout (imag[p3]+100) of today's image is raised, the image soon breaks apart and evaporates. But unlike the fractals that result from negative exponents, the empty 'inside' area that is left over from images such as today's has little of interest that might be revealed by an inside fill such as 'bof61'. Hopefully, the preceding analysis is reasonably correct, with the rush that is expected, I wrote it without checking. One thing certain however is that the image takes almost 29 minutes to render on my machine. But this render time may be avoided by downloading the finished image from: Another very pleasant day on Tuesday here at Fractal Central left the cats satisfied. They enjoyed themselves in the holly patch until sunset, which is just after 5pm at this time of year. My day was reasonably satisfactory. Today is starting sunny and only slightly chilly. Until the next FOTD, which will appear in 24 hours, take care, and look for light. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Diced_Midget { ; time=0:28:51.14--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+5.91382457401014100/+2.748610007654852\
00/343217.3/1/-172.5/8.37328130443015795e-009
params=10/0.5/-10/0.5001/1150/25 float=y
maxiter=7500 inside=0 outside=summ periodicity=10
colors=000Q_ePUbOP`NKYIiYKZXLPWHW4IT9JQEKNILKNMHSa\
dVYZWVUWSPWPKW4SNANQGJTcL1B3DE9GHEIKJKNOMQTPTYRWbT\
YgV5fEChJJiOQkTXlYcnbjogpplkihfbeaWaXPZSIWQXjPUgOR\
eOPcNMaNK_MHYMgSMcTM_TMXUMTUMPVMMVMIWQW6PTAPRDOPGO\
NJNLNNJQMHTQA2PCAODHNEPtPHoNJkMLfLNbKPZIRUHTQGVAQL\
DNOFLQIJSKHUKh2Lb8LXEMRKMLQMQvOnvNbmMRdnVP_NTOycNs\
bNmaNg`Na_MWZMQYMKXW3BT6HR9MOCR2nC5iF7eHA`KCXMFSPH\
ORKJUNWuMTqMRmMOiMMfMJbMHZ2Yh6Ue9RcCOaGL_JIYUC_SDZ\
RDYQEYOEXNFWEghFcfG_dHXcITaJP_KMZLIXBT4DQ9FOEHMIJJ\
NLHSMcCMZGMUKMPOMKSYzeWscUlbSe`RZ_PSYNLXTRDPLNe2px\
l6ncDdWJVNQV1oFzOJbSE4qG7lI9hJBcLD_wEGjFMYFRWhxRUi\
vjhlbdcVaVNZ4pL7iNAcPDYRGRTJLVgKIaIMXHPRGT5`U8XVBT\
VEQVHMWKIWdoQ`hRYbSVXTSRUPLV8WqATmCRjEOgGMdIJaKHZl\
oScbUVRVolAieFcZJYSOSLS7UFARICPKENNGLPIJSKHUwWKrTM\
mRNhPPdNQ_LSVJTQHVlMUhLVdKV`JVXIWTHWPGWNJzMHoMGe_X\
RXUSVRTTOUQLVOIWUomSijRdg }
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
|
times.
