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Dan Ramras
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There was a study where they took thousands of digital pictures of "natural images", rendered them in grayscale, and looked at all the 3x3 pixel squares which arose in such pictures. Using topological data analysis they found that (after some normalizations) their data points actually clustered around a Klein bottle embedded in the 7 sphere! Here's a paper that talks about it, and tells you where to look for the Klein bottle:

http://www.math.uiuc.edu/~ghrist/preprints/barcodes.pdfhttp://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf

There was a study where they took thousands of digital pictures of "natural images", rendered them in grayscale, and looked at all the 3x3 pixel squares which arose in such pictures. Using topological data analysis they found that (after some normalizations) their data points actually clustered around a Klein bottle embedded in the 7 sphere! Here's a paper that talks about it, and tells you where to look for the Klein bottle:

http://www.math.uiuc.edu/~ghrist/preprints/barcodes.pdf

There was a study where they took thousands of digital pictures of "natural images", rendered them in grayscale, and looked at all the 3x3 pixel squares which arose in such pictures. Using topological data analysis they found that (after some normalizations) their data points actually clustered around a Klein bottle embedded in the 7 sphere! Here's a paper that talks about it, and tells you where to look for the Klein bottle:

http://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf

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There was a study where they took thousands of digital pictures of "natural images", rendered them in grayscale, and looked at all the 3x3 pixel squares which arose in such pictures. Using topological data analysis they found that (after some normalizations) their data points actually clustered around a Klein bottle embedded in the 7 sphere! Here's a paper that talks about it, and tells you where to look for the Klein bottle:

http://www.math.uiuc.edu/~ghrist/preprints/barcodes.pdf