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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In the northern hemisphere the atmosphere turns counter-clockwise as it is drawn into a cyclone and clockwise as it is pushed from an anticyclone. In the southern hemisphere exactly the opposite is true. But Fractal Central is located in the northern hemisphere, and since the arms of today's spiral image are moving inward in a counter-clockwise direction and curving to the left as they go, the image can only be called "Cyclonic Circulation". When the atmosphere curves to the left in the northern hemisphere, it causes low-level convergence, which forces the air upward and squeezes any available moisture from it. We have had a lot of convergence at Fractal Central over the past two months, where only 2 of the past 60 days have been clear. People are joking that the farmers prayed for rain all last year, and their prayers are being answered all this year. Now the farmers are praying for dry weather so they can work their fields. Worried about next year, my advice is for them to make their prayers more specific. On a more fractal note, the formula of today's image mixes 1.2 negative portions of Z^(1.4) with 0.3 parts of Z^(-0.8) and adds (1/C). It was calculated by the MandelbrotMix2 formula, which is identical to the MandelbrotMix4 formula, except that it includes the ability to change the automatically calculated value of initial Z. It's a rather lively image, enhanced by a brilliant palette of colors. With other color palettes, the image actually reminds me of rows of shark's teeth, but a man-eating name would give a wrong impression, so I chose the palette that reminds me of a cyclone, and rated the image at a 7. The 4-minuterender time is within reason for an image that rates a 7. And as always, the completed GIF file is available for download on Paul's web site at: Though the clouds hung tough on Wednesday, a bit of afternoon sun did manage to break through, the rain held off, and the temperature reached 75F 24C. As a result, the fractal cats were happy and I saved a can of tuna. If only today could turn out as well... but with rain having already fallen and more due, it most likely will not. The cats are still sleeping, but before long they will get up, go to the door and ask to be let out. They will then see the rain and turn moody. I fear tuna will be necessary. Finishing the day's work will also be necessary, but before I finish, I must start. Until next FOTD, take care, and keep dry, that is if possible. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
CyclonicCirclation { ; time=0:04:04.58--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix2 function=recip passes=1
center-mag=-0.74981462059503250/+0.015225453504671\
47/3.458564e+011/1/-106/-0.0139524412207075732
params=-1.2/1.4/0.3/-0.8/0/525/0/0 float=y
maxiter=500 inside=0 logmap=80 periodicity=10
colors=070070070070070070070472AAAEEHJPPPTVVWb`_id\
dqikxoqzutzzwzzzzv_uoCPg70d74b7EZ7LX7VV7bR7kPHsNRz\
J_zHizGszEszEizC_zCRzCHzA7zA7z87v87s8Co6Gk6Hg4Ld4P\
`4RZ8TTCVNEXHHYEL_8N_2Ra0Vd0Xe0`g0di0ei0bk0`m0Zo0X\
o0Vq0Ts0Ru0Pu4Nv8LxCJzGHzJGzNEzRCzVAzZ8zb6ze4zi8zg\
AzgCzgGzgHzgJzgNzgPzgRzgVzgXzgZzg`zgXzeVzdTzdRzbPz\
`Nz`LzZHzXGzXEzVCxTAvT8uR6sP2oP0mN0kL0gL0eJ0dH0aH0\
eG0iE6oCCsAGv6Lz4Pz2Vz0`z0dz0iz0mz0kz0kz6kzCkzJkzP\
kzVkz`kzgkzmkzskzxmzzozzqxzsvzuozwmsymdzmPzmAzm0zm\
0zm0zm0zm0zm0zm6zmAzmGzqJzvPzzTzzXzzZzz`zzbzzdzzez\
zgzzizzkzzmzzmzzozzqzzszzuzzvzzxzzzzzzzzzzzzzzzzzz\
zzqzzizz`zzTzzLzzCzz4zz0zz0zz0zz0zz0zz0zz0zz6zzAzz\
GzzJzzZzzkzzgzzdzzbzzZzzXzzTzzRzzNzzLzzHzzGzzCzzAz\
z6zz4zz0zz0zz0zz2zz4zz6zz8zz8zzAzzCzzEzzGzzHzzHzzJ\
zzLzzNzzPzzRzzRzzNzzJzzHzzEzzAzz8zz4zz0zz0zz0zz0zz\
0zz0zz4zz8zzAzzEzzHzzLzzP }
frm:MandelbrotMix2 {; 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)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END 20.0 PAR-FORMULA FILE==================================
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times.
