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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's image we advance to the newtbasin formula. This formula uses Newton's method of finding the roots of polynomials, and colors the pixels according to which attracting root captures the orbit launched from that pixel's coordinates. I have never done much exploring in the Newton's formulas, which draw lovely images, but seem to me like a long unending scroll that goes on and on with the same beautiful images repeated again and again until eventually, boredom sets in. The newtbasin formula uses a special case of the Newton's algorithm based on the formula (Z^n)-1=0. For today's FOTD I set 'n' to the rather excessive value of 100 and zoomed in on one of the areas of chaos between basins. The resulting image, after a somewhat casual coloring effort, was worth a rating of a lowly 4. But today's image has been rated at a 7, and it is named "WOW", so what happened. Well, while the image was on the screen, Fractal Lady happened to walk into the room, saw the image and exclaimed "WOW!". She claimed it was a 10-rated image if ever she saw one. I still think its rating is closer to a 4, but to make her happy I took the average of our opinions, which was 7, and made that the official rating of the day. Individual viewers are free to rate the image as they see appropriate, anywhere from 0 to 10. I kept the "WOW!" exclamation as the name of the image. The render time of 13-1/2 minutes and rating of 7 give an overall worth of 52. The rendering delay and ratings can be eliminated by downloading the finished GIF image from the FOTD web site at: Heavy clouds, dampness, and a temperature of 50F 10C kept the fractal cat duo indoors all day Tuesday. I tried to lighten their moods with several small treats of tuna and turkey, but they were still sullen until shortly after 8pm, when they settled down for the day. Today is starting rainy; I expect even worse moods from the cats. For me, it's the day before the big 4-day Thanksgiving holiday, and I have a rather sizable chunk of work to clear away before I can enjoy 4 lazy days of doing nothing but watching TV and creating fractals. Of course, even then there is no assurance of total tranquility -- there is always the risk of getting dragged to a huge dinner at the house of one of our friends or relatives. But that would be a small price to pay for four days off. In 24 hours I will return with the next FOTD. Until that time passes, take care, and prosper. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Wow { ; time=0:13:27.30--SF5 on a P200
reset=2004 type=newtbasin passes=1
center-mag=-1.4433336971214/+0.9820033722871455/95
params=100/0 float=y maxiter=1500 bailout=9
inside=zmag symmetry=none periodicity=10
colors=000ttMsrMpqMopMmoMlmMjlMikMhhMehMdgMbgMbfM`\
fM`dM`dM_bK_`KY`KY_KX_KXYKWYKWXKWWKUWKUUKSUKSSKRSK\
RRKRPLPPMPNNNNNMLMKJKJGJKIKLKMPMPPNPRPRSPRSRTURUUS\
VWSVXUXXUXYWY_WY_XX`XX`YXbYYd_Yd_Zf`_g`agbahbchddj\
dgkfhkfimgjngknhmphnpjpqjqrktrkutmwtmxtmxtkvtkstjq\
uhnuhlugjughufewdcwdawb_w`Yw`Xx_Ux_SxYRxXPxXNyWMyY\
Ny`PydRygSzjUzmWzpXzrYzu_zx`zzbzzdzzfzzgzzhzzjzzkz\
zkzzmzzmzzmzynzwnzunztpzrpzqpzpqzmqzkrzjrzhrzgtzft\
zbtz`uz_uzYuzXwzWwzSwzRxzPxzNxzMyzKyzIyzKwzKtzKrzK\
pzMnzMkzMjzMgzNfzNbzN`zNYzNXzPUzPRzPPzPMzRKzRHzRFz\
RBzS9zS5zS4zS0zS0zU0yU2xW2wW4uX4tX5rY5qY7n_7m_9k`9\
j`BhbBgbDfdDddFdbDbdFbfHbfIbgKbgMbhMbjN`jP`kR`kS`m\
S`nU`nW`pX_pY_qY_r__r`_tb_td_uf_wfYwgYxhYxjYykYzkY\
zmYznXzpXzqXzqXzrXztXzuXzwXzwYzuYzu_zu_zu`zu`zu`zu\
bzubzudzudzudzufzufzugzugzugzuhzuhzujzujzujzugzwbz\
yYzzWzzXzzXzzXzyXzyXzxXzx }
END PARAMETER FILE=========================================
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