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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The Newton formulas are not really escape-time formulas, but they work in much the same way. Today's image was created by the complexbasin Newton formula. This formula uses Newton's method of finding roots, and colors the points according to which complex root they converge on. In the Newton's fractals, much of the interest lies where areas of different colors appear to touch. The different colors do not actually touch however, they merely exist close to each other. At every color boundary a fractal pattern exists that separates the colors. This pattern exists even at the smallest scales. Since I have done very little exploration in the Newton's formulas, I am not familiar with the things they can do. They certainly can do more than I have done with today's image, where I have used negative and imaginary parameters, and rendered it with the outside set to 'fmod'. Even the little bit I have done rates a 5 however. Maybe when my tour of the built-in Fractint formulas is finished, I will return to the Newton's formulas for further exploration. I can see by the sharp cut in the image that it is but one level of an infinite spiral, much like the branch-cut fractals I often work with, though in this case, it appears that the unseen levels would appear similar. All things considered, I rated the image at a 5. I named it "The Right Root" for no particular reason. Due to the render time of only 19 seconds, the rating of 5 leaps to an incredible and grossly inflated 1534. The completed image is or soon will be available for download on the FOTD web site at: The perfect weather here at Fractal Central on Sunday kept the cats relatively happy. They would have been perfectly happy if we had not gone out in the afternoon and brought them inside. But half a perfect day is better than no perfect day, and when we returned in the evening, they ran to greet us as eagerly as ever. Today is starting almost perfect. Only a chilly temperature of 48F 9C is keeping it from being absolutely perfect. For me, being caught up in the commercial work leaves that much more time for fractal work. The next fractal will appear in 24 hours. Until then, take care, and be on the lookout for the fractal UFO's. Jim Muth jamth@mindspring.com jimmuth@aol.com |
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