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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: While working with today's image, I discovered that there is a problem with the type=mandel formula in Fractint. As a result, I needed to write a new version of the SliceJulibrot formula to calculate today's image, which is a different view of yesterday's type=mandel image. This new version, SliceJulibrot3, is included in the parameter section at the bottom of this letter. The new version calculates the square root of the number entered as (p4), or the starting point of Z. I needed the new version because the high-speed type=mandel formula in FractInt calculates the square root of the complex number that is entered as the starting-point parameter rather than the entered number itself. (Actually, I already knew this, but for some reason it did not come to mind.) As mentioned above, today's image is a different view of the spectral bud that was illustrated in yesterday's FOTD. But the angle of today's view is close to 90 degrees from that of yesterday's view, and as a result, the spectral bud has been stretched to a few near-straight features in the background. The foreground spiral however has really come to life, and has changed into a sinuous series of curves, which no longer form a perfect spiral, but are rather pleasant to look at anyway. These swirling features inspired the name "Iterative Currents". While studying the image, I got the distinct impression of convection currents swirling on the surface of a newly-poured cup of hot coffee. My original impulse was to rate the image at a 7, but then I realized that some people do not drink coffee, and dropped the rating to a 6. Combined with the render time of just under 16 minutes, this gives an overall value of 38. With more work, the coloring could have been better, but I spent so much time trying to find why the first formula didn't work that I had too little time to devote to coloring the image. The finished image is available on Paul's FOTD web site at: A lack of sun and a temperature of 41F 5C here at Fractal Central on Thursday kept the cats' outdoor time limited to less than one hour, but, perhaps due to their increasing age, this was all the duo needed to satisfy their ever-shrinking urge for adventure. Today is starting sunny and milder. This promises good things for the duo. For me, the work is still heavy. But it is not heavy enough to keep me from fractal land, and whatever I find there will become tomorrow's FOTD. Until then, take care, and keep your fractals in alphabetical order. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Iterative_Currents { ; time=0:15:54.50--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot3 passes=1
center-mag=-0.00263587632006605/+0.004641457407512\
89/79.37667/23.269/0/-32.6192430711928907
params=82.7/-41.3/-91.4/74.8/-0.23020724/0.6448031\
5/0.3991/-0.6312 float=y maxiter=40000
inside=0 logmap=464 periodicity=10
colors=000pzMpyMpxNpxNpxOpxOpxOpxPpxPpxQpxQpxRpwRp\
wSpwSpwTpwTpwUpwUpwUpwUpwUpvUpvUpvUpvUpvUpvUpvUpvU\
pvUpvUpuUpuUpuUpuUpuUpuUpuUpuUpuUpuUptUptUptUptUpt\
UotUotUotUotUntUnsUnsUmsUmsUmsUlsUlsUlsUksUksUksUj\
sUjrUjrUirUirUirUhrUhrUhrUhrUgrUgrUgrUfqUfqUfqUeqU\
eqUeqUeqTdqTdqSdqSdqRdqRdpQdpQdpPdpPdpOdpOdpNcpNcp\
McpMcpLcpLcoKcoKcoKcnJcnJcnJcnJcmIcmIcmIcmIblHblHb\
lHblHakGakGakGakG`jF`jF`jF`jF_iE_iE_iE_iEZhDZhDZhD\
ZhDYgCYgCYgCYgCXfBXfBXfBXfBWeAWeAWeAWeAVc9Vb9Ua9U`\
9TZ8TZ8SZ8SZ8SZ7SZ7S_7T_7T_6U_6U`6Tb5Uc6Ud7Vd8Ve9V\
cAWbBWaCW_DXZEXYFYYHYYKYXNZXQZWTZWW_WZ_Va`Vd`Ug`Uj\
aUnaTqaTtbSwbSzcSzcRzcRzdRzdTzdVzeXzeZzf`zfbzfdzgf\
zghzgjzhkzhkzilzimzinzjozjpzjqzkrzkrzlrzlrzlrzmrzm\
rzmrznrznrzmrznrznrznrznrznrznrznrznrznrznrznrznrz\
nrznrzorzorzorzorzorzorzorzorzorzorzorzorzorzorzpr\
zprzprzprzprzprzprzprzprz }
frm:SliceJulibrot3 {; 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)+sqrt(p4):
z=sqr(z)+c
|z| <= 9 }
END 20.0 PAR-FORMULA FILE==================================
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