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There is no minimum number - it is simply not possible.

Given any n points in 2-dimensional space, it is possible to find a polynomial of order (n-1) that will generate a curve going through each of those points. There are other functions which will also do the trick. So, given any number of points, it would be impossible to determine whether they were generated by a fractal or a polynomial (or other function).

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Q: What is the minimum number of data points needed to identify a fractal with x and y axes?
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