|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Do not give up hope. The FOTD CD is past the halfway point, and sometime this summer the 1,700 or so fractal images and discussions will be available for distribution. Even better news is that, when the CD is completed, the ongoing FOTD will return to the daily schedule, while hopefully increasing in quality. The midget at the center of today's image, which exists in the fractal created by the formula (Z^3)+0.4(Z^5)+C, is located in the suburbs of a larger midget in a cut-off feature deep in an un-named valley of its bloated parent fractal. Since the feature in which today's midget lies is cut off from the main body of the fractal, the midget itself is cut off from its surroundings. I needed to include the <mathtolerance=/1> entry in the parameter file because of the magnitude of the image, which, at close to 9*10^12, is in the borderline range where strange things begin to happen. In fact, strange things are already happening. The pattern surrounding the midget is infinitely disconnected. Regardless of how close to the actual shore-line of the midget a particular feature lies, that feature will be disconnected from the main body of the midget. The situation is somewhat similar to that of the Newton's images, where the areas leading to different roots lie adjacent to each other with no space between them, yet at no point do they actually touch. The boundaries between the basins are fractal in nature. I have named today's image "Cutoff Disconnected", a redundant name that emphasizes the nature of the midget at the center. I rated it a 6, a rating I have been using quite a lot since cutting the frequency of the FOTD's by 2/3. The image is nice, it is interesting, it is curious, but such words really mean nothing. IMO, today's image is worth no more than the present rating. With a render time in the vicinity of 20 minutes, the parameter file of today's image is a bit of a drag to run. Wise fractalists, (that is everyone), will let Paul and Scott do the rendering, and download the completed GIF image from one of their web sites. Paul's site is at: The fractal weather Monday here at Fractal Central was mostly sunny, but with occasional cloudy periods. The chilly temperature of 59F 15C combined with the breaks in the periods of sun kept the dynamic duo of fractal cats dashing in and out all afternoon. As for myself, I've got to dash off to finish some important work so that I can get back to the fun work on that FOTD CD, which despite fears is progressing just a bit behind schedule. I shall return on the 24th with another fractal to amaze and delight even the mathematically challenged. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
CutoffDisconnected { ; time=0:22:23.97--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix2 function=ident passes=1
center-mag=+0.09846970716854085/-0.977478678397672\
90/8.71082e+012/1/-144.990106256018947/-0.00765988\
837549030216 params=1/3/0.4/5/0/0/0/0 float=y
maxiter=2000 inside=0 logmap=446 periodicity=10
mathtolerance=/1 colors=000ONTRQWTTZWVaZYd``gccjee\
lggmhinjkpkmqmnrnntpouqpvspxtpzuozrowpornomlphjqdh\
rafs_dsYbtV`uTZvQXwOVxMTyJRzHPzF_ze`wdardcmbehagc`\
ic_kcZmdYoeXqgWshVujUwkTxlSneOdZKVSGAADAAERNETOEWP\
EYQF`RFbSFeTFhUGjVGmWGoXGrYHtZHw_Hy`HHWJJXMLXOMXQO\
XSQXURXWTXYVX_WXaYXc_Xe`XgTVaMUWFTR8SL1RG4OJ7MLAKO\
CIQFGTIDVKBYN9_Q7bS5hQ6cP6cO6bM6bL6aK6aI6`H6`G6_E6\
_D6ZC6ZBBbBFfBJiBNmBRpBVtBZwD`uEbtFdsGeqHgpJioKkmL\
llMnkNpiPrhQsgRueSwdTxcRq`PkYNeVL_TJUQHONFILGKMGMM\
GNMGPMGQMGSMGTMGVMGWMGYMGZMG`MGaMGcMGdMI`LJXLLTLMQ\
LOMLPIKRFKSBKU7KV4KT4IS4HR4FQ4EO4CN4BM4AL48K47I45H\
44G42F41E40MgXHbPCZI7UB2Q4AUDHYLOaUVdaSb`Qa_O`ZM_Y\
KZXIYWFXVDWUBVT9US7TR5SQANNEILJDIN9GO7BR8CU9DXAE_A\
FbBGeCHhCHkDInEJqEKtFLwGMzIMwKLuMKrOKpQJnSJkUIiWHf\
YHd_GbaG_cFYeEVgETiDRkDTmHUmKWmNXmQYmT_mX`m_bmbcme\
dmhbmgamf`me_mdZmcYmbWmaVm`Um_TmZSmYRmYMmQ }
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==================================
|
times.
