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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The rating of today's image is no typo. I feel it is actually worth a 10, making it only the second FOTD image to achieve this supreme rating. Not only is it one of the most unusual fractal images I have yet seen, everything about it excels. The coloring is excellent; the mathematical interest is excellent; the uniqueness is excellent. In short, the image is so close to perfection that when I considered its minor faults, the rating still rounded off to an actual 10. The name "Tessellation" was inspired by the branch-like arms in the upper half of the image, which appear to have been covered with a tile mosaic. By contrast, the lower half of the image consists of a carnival-like riot of brilliantly colored bits and strips of fractal debris. The dividing line between the upper half and lower half is extremely sharp, yet the features still appear continuous across the divide to some degree. The image was created by the formula (-Z)^1.2*(C^0.1)+C, which is the same formula that created the 'No_Cigar' image of Feb 24. In today's image I picked a point near the northern shoreline of the main bay of the parent Mandeloid, but still located some distance offshore, and calculated an almost-Julia set rotated only 0.2 degree from the Julia direction. When this open figure is rendered with the 'inside=0' option, it is blank. Most of the active inside fills work wonders with it however. I chose the 'inside=bof61' option for today's image, but the other inside options are well worth a try. The render time of 10-1/2 minutes is well within reason for such an outstanding image. For extra convenience, the completed GIF image has been posted to the FOTD web site at: Limited sun, a temperature of only 36F 2C, and snow-covered ground, kept the dynamic fractal cats safely inside all day Friday here at Fractal Central. They did venture briefly onto the porch to check conditions, but turned back inside before the door was closed, to spend the rest of the afternoon on their comfortable shelf by the window. Today is starting about the same as yesterday. I expect the duo to have a similar day. For me the work is light, but fractal lady is thinking about a browsing trip to one of the local antique and collectible emporiums. Maybe seeing some of the old stuff people have thrown away will give me a few new fractal ideas. The next FOTD will not rate as high as today's, but it will appear in 24 hours. Until then, take care, and don't be disappointed. Some day we might find another FOTD that rates a 10. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Tessellation { ; time=0:10:31.42--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multXYZWcompjb-min function=flip/ident
passes=1 center-mag=0.343582/0.0348611/0.8796844
params=89.8/90/1.2/0/1.1/0/0/0/0/0.814 float=y
maxiter=1000 inside=bof61 logmap=yes periodicity=10
colors=000P0zK0zk0WzW0W00z00W00s00Q00S02U03W05Y06_\
09a0Dc0He0Kg0Ni2Rk5Um9XoA`qDdtHhvInuSwmbzhkzcqzduz\
dxzdyzdzzfzxfztfzqfznhzihzfhzchz`izWizSizPizMhzKfz\
IfzHdzFdzDczCcxAbv9`t6`q5Zp3Zm2Xk0Xh0Wf0Wd0U`2SW9R\
SFPNMNKSMFZKCcMFdMIdMKdMNdMRdNSfNWfNXfN`fNcfPdhPhh\
PkhPmhPphPqhWfcbX`hNWmDSs3Ny0Kz0Hv5MnPRfhWZz`RzcRz\
WRzNRzFRz6Rz0Rz0Rz0Sz0Uz0Wv2Xq6ZmD`hIbcPcZUdU`fPdh\
KkiFp`IdRMWINK9RA0U00W00X00X00Z02Z03`06`29b3Cb5Fc6\
Hc9KdCMdDPfFRfHUhIWhKSfMPdMMcMIcMFbMC`N9ZN6ZN3XN0W\
N0UP0UP0SP0RP0RP0PR0NR0MR0MR0KR0IR0HR0HR0FS0DS0CS0\
CS0AS09S06S06S03S02S00S00S00S00S00S00S02`CIfPZm`ns\
UhpNbmHWiAPf5IcAWsDhzmzzmzzmzzmzzmzzmzzmzzmzzmzzmz\
zmzzmzz0zz0zz0zz0zt0xq0vp0tn0sm0qk0pi0nh0mf0kd0hc0\
fb0d`0cZ0bX0`W0ZU0XS0WR0SP0000RN0PM0NK0MI0KH0IF0HD\
0FC0CA0A909606505303202000000000000000000000P00S20\
W60ZD0bI0dP0hW0kS2cf2qk3z }
frm:multXYZWcompjb-min {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5,
q=(c^(p3-1)):
z=(-z)^(p2)*(q)+c,
|z| < 400 }
END PARAMETER FILE=========================================
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times.
