This problem is about the behaviour of a uniform distribution of points in high-dimensional spaces. Generate a dataset of 1 million random points in d-dimensional space (d varying as 1, 2, 4, 8, 16, 32, and 64). Assume that the points are uniformly distributed over [0,1] in each dimension and that the dimensions are independent. Choose 100 query points at random from the dataset. Examine the farthest and the nearest data point from each query. Compute the distances using L1, L2, and L. Plot the average ratio of farthest and the nearest distances versus d for the three distance measures. Make sure to not include the query point itself in the nearest data point computation. Explain the results.

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