|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Today's image takes us back to the mysterious Ikenaga function, which was apparently created for the purpose of generating FractInt fractals, and then forgotten by its author, who, as far has I know, has never been definitely determined. Well, it's not exactly the Ikenaga function, since I have made numerous changes and additions to it, but whatever it is, it was inspired by the IkeNewtMand formula that appears in fractint.frm and was written by Ron Barnett, who states in the formula comments that it is based on the Ikenaga function. Several years ago I wrote a series of 12 formulae that I called 'MandNewt**'. These formulae are based on this mysterious 'Ike' function. Today's image was created with number 6 of the series. This series of formulae creates totally unpredictable images that consist largely of 'inside' parts, and therefore must be rendered with an active inside fill. Today's image uses the bof61 fill. The resemblance to some kind of fantastic tree is striking, and inspired the descriptive name, "Ikenaga Tree". The color palette, which uses only a few of the 256 registers, is a model of getting much from little. The rating of an exceptional 8 is fully justified. The frugal render time of 3 minutes is fast enough for all but the busiest fractalists. Of course, the completed GIF image is available as always on the internet at: Another hot, dry, sunny day on Friday here at Fractal Central gave the dynamic cats ample time in the yard. The temperature reached 93F 34C, but cats are native to northern africa, and can easily endure such mild heat. Their day was quite happy. No treat was needed. Today is promising to be a let-down, with clouds and showers possible. But with any luck at all, the duo will have another satisfactory day. As for me, most of my days are satisfactory, which may be because it takes so little to satisfy me. The next fractal will be along in 24 hours. Until then, take care, and good fractal luck. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Ikenaga_Tree { ; time=0:03:28.39--SF5 on a p200
reset=2002 type=formula formulafile=mandnewt.frm
formulaname=MandNewt06 passes=1 center-mag=37.3298\
/-49.3884/0.03536232/1/-30/-2.5056345887009e-014
params=-6.47/-5.23/-1.59/-0.59/1.25/2.08 float=y
maxiter=100 inside=bof61 logmap=yes periodicity=0
colors=B00c`d`cgYeiVhlSkoOmpZkZghIog0re2sd4vc7wa8z\
`CzZDzYHzWIzWKwaUaMzYSzTWzOezLczJazJ`zJYwJWpJTkIQh\
IOdILZIIVFHQEDNB00NO`OUeQ`oSexTkzVozYsz`uzcxzizzqz\
zwzzzzzzzzzzyizwVlwJYxBIxFKtIKqLKmOLkSLgVLdYL`aMYd\
MUgMRiMMlOKoOFrOCuO8rY4qe0nm0lu0sk7x`MzP`zDmz0zzDt\
zPmu`hnkaguW`zPVzK`zLdzLizLnzLswLwsLzoMzkMzgMzcMzZ\
MzVMzZIdaDvIKz0Oz8SzIWzR`xZduhhqpllxpizskzqkypkwok\
tmkplkmlkkkkhildhlaglZglWelSdlPclMalKakP`iUZiYZhaY\
ggWgkWeoVesVdxUczSczSazRazRczPczOdzMdxLetKepIgmIgi\
HheFhaDiYCiUAkP8kM8eVAaaCYhDToDYmCcmAgl8kl8ok7si5w\
i4zh2zh2zg0zg0ze0ze0zg0zg2zg4zg7zh8zhAzhDzhFxiHviK\
siLqiMniPkkRhkSekVckW`lYYl`VlaSlcOldLghIalFWpBRtBL\
xBFzB8zB2zB7zBAyBFuFIpJMlNPhQScTWZYZV`cRceLehHilCl\
o5os0ru0ux0vu0vt0vs0vp0vo4vm5vl8wiAwhDwgFwdIwcKwaM\
w`Ox`Px`Rx`Rx`Sz`Sz`Uz`Uz`Vz`Vz`Wz`Wz`Yz`Yz`Zz`Zz`\
`z``z`az`az`cz`czZ`hVZeYa }
frm:MandNewt06 {; Jim Muth
z=c=(pixel*p1):
a=z^3+(c-p2)*z-c
b=p3*z^2+c-1
z=z-1*a/b
0.000000000000000000000000000001 <= |a| }
END 20.0 PAR-FORMULA FILE==================================
|
times.
