Recently (See
http://www.cnn.com/), a group of computer algorithm experts were looking for ways to make periodicity checking more efficient. They realized that in some cases, it created horrible results, changing with each pass of their guessing algorithm, giving spotty black parallelogram globs. As an experiment, they created "virtual screens", all of the same fractal; a fairly simple Newton. They put them at the same location, but then shifted each screen on the order of e^-(pi*pi). (The fractal was at magnification==1 - this shift was chosen for "mathematical purity".) Then, they plotted each shift as corresponding to a location on the screen, and colored according to the overall amount of "incorrect inside" being mapped to a color gradient. After waiting for the slow computation to finish, they got an amazing result - it was the exact same fractal! The only difference being a few areas; one was very noisy, which they have decided to call the "Karma area". The other component was relatively smooth, and all three parts of the image used the same gradient they had chosen for their mapping. They are now requesting a $10,000 research grant to try to find the origin of these areas. Here is what they saw on their screen: (I have added many line breaks so it doesn't spoil!)
October 19, 2006, 06:18:37 AM
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