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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The autumnal equinox is almost here, heralding the season of blue skies, colorful falling leaves, and acorns. The mystery is why the leaves, which are so enjoyable while they are on the trees, become so unenjoyable once they fall to the ground and have to be raked up and disposed of. The answer to that mystery may never be known, but the fact that eight colorful oak leaves appear in today's FOTD image cannot be denied. The formula that produced the leaves subtracts 1.3 parts of Z^0.9 from 1.3 parts of 1/Z, then adds 1/C, resulting in a scene on the verge of evaporation. Indeed, if the value of the imag(p3) parameter, which sets the bailout radius, is increased, the image soon breaks into scattered fractal debris, and then goes totally blank, changing into an evaporated all-inside image that can be seen only by using an inside fill something like bof61. Curiously, if imag(p3) is decreased, the image also goes blank, though in this case the image consists of flat outside material. The parent fractal of today's image consists of a very distorted Mandeloid with an open eye, perhaps the all-seeing eye of you-know-what, lying just to the right. The scene itself lies in a valley that is not really a valley, which separates the Mandeloid from the eye. I originally intended to rate today's image a 7, but upon re-viewing it after a restful night, I decided a 6 would be more appropriate. I named the image "Autumnal Equinox", and why not? The equinox is but a few hours away, and at least in the northern hemisphere, the leaves are starting to turn colors. The 20-minute render time drags, but as always, the completed GIF image is or soon will be available on the FOTD web sites at: The weather Saturday was partly cloudy and humid, with a temperature of 88F 31C. Showers threatened in the afternoon, but never moved in. The fractal cats, being intrepid, ignored the threat of rain, and had a pleasant afternoon in the yard, doing little but sitting and thinking. As for me, it's Sunday morning and all is well. If I simply relax and let nature have its way, things could remain well all day. The next FOTD will appear on Tuesday the 24th. Until then, take care, and don't lose your way in the valley of the lost fractals. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Autumnal_Equinox { ; time=0:20:20.72--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.07306512309502931/-0.035159792779246\
05/9.071547e+007/1/5/-2.20061751078637347e-007
params=-1/0.9/1/-1/0.3/100 float=y maxiter=2500
inside=0 logmap=363 periodicity=10
colors=000nAIpA9rA1oD7lGCiJIfLNcOS`RYYTbVWhSZmQ`rT\
asVbsXct_dtaetcfuefuhgujhvlivojvqkwslwulwsltqlrolo\
mlmkljilhhlfflcdlablZ`lXZlUYlSWlQUlNSlLQlIOlGNlELi\
DKgDJdDIbDH_CGYCFVCETCDQCBOBALB9JB8GB7EB6BA59A46A3\
4A22A35D48F5BH6DJ7GL8JN9LPAORBRTCTVDWXEZ_F`aGccHfe\
IhgJkiKnkLpmMsoNvqOxsLolIfeFYZCPS9GL68ECBFHDGMFGRH\
HWKI`MIeOJjQKoSKnUJnVJnWInXImZHm_Hm`GmaGmbFldFleEl\
fElgElhDkjDkkCklCkmBknBjpAjqAjr9js9jt9hoEfjIeeMcaQ\
bXU`SY_NaYJeXEiV9mU5qV7mW8jW9gXAdXCaYDZYEVZFSZHP_I\
M_JJ`KG`LDZMFYMHXNIWNKVOLTONSPORPQQQRPQTOQUMRWLRYK\
SZJS`ITaGTcFUdEUfDVgCViBVjAWiAYhAZh9`g9af9bfFYdKTc\
QOaKJKXIbZIc_IdaIeZIaaIefIhhIiiHjkHkmHlnHmpHnrHosH\
puHqvHruGpuGnuGmtGktGjtGhsGgsGesGcrGbrG`rG_rGYqGXq\
GVqGTpGSpGQpGPoGNoGMoGKoGJkOFgVBcU7_UZYUcXUhVUmUSt\
SNwRJzQFzSEzUDzVCzXCzYBz_Az`Azb9zc8ze7zf7zh6zi5zk5\
zl4zn3zo2zq2zr1zg9zi9zlAz }
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 20.0 PAR-FORMULA FILE==================================
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