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http://www.gibney.de/does_anybody_know_this_fractal

Is this some known kind of fractal?

Update: This one got a lot of great feedback from around the net. I summarized it in the section labeled "Update 24.10.2012".

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    Isn't that somewhat of an overreaction of someone who's been on this website for two days and isn't aware of norms? Furthermore, I don't see any "nofollow" attributes in the source of the edits, if they were added that was an automatic addition.2012-10-17

2 Answers 2

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Probably a part of what we see is due to rounding in your program: note that the value at $c$ is the same as that at $ic$ so that the image should be symmetric under rotation by 90 degrees. This roughly is the case, apart from the deformed squares all over the place. In fact, they all occupy one quadrant like region with one vertex at a point with a high value, probably due to rounding. Without the squares you would have a better approximation to the real picture.

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    I suspected that for a while, but it looks like there are no rounding errors involved. See this update: http://www.gibney.de/does_anybody_know_this_fractal_-_part_22012-10-23
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The intensity as defined is $0$ for almost all values of $z$, so it is unclear how the visualization relates to the definition. If you post the code that generated the images you will have a better chance of getting a satisfactory answer, and that would also address @doetoe's observation of what are apparently artifacts.

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    You are right. The check if the result of a division is a gaussian integer is actually checking if the result is near a gaussian integer. Thats why the intensity is higher then 0 for most values.2012-10-23