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A theorem by Paley and Wiener says that a Fourier series with random coefficients produces Brownian motion on [0, 2π]. Specifically, produces Brownian motion on [0, 2π]. Here is a plot of 10 instances of this process. Here’s the Python code that produced the plots. import matplotlib.pyplot as plt import numpy as np def W(t, […] The post Random Fourier series first appeared on John D. Cook....