Question: Suppose you are given a 1-dimensional and 2-dimensional array of pixels in which each pixel is set to blue independently with probability p and all

Suppose you are given a 1-dimensional and 2-dimensional array of pixels in which each pixel is set to blue independently with probability p and all other pixels are off. How would you describe the distribution of the contiguous regions of blue as function of p? For example, how many regions are expected and how large are they expected to be? Can you prove any statements about the probable or improbable existence of large regions of blue?

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