random-wave.py

from matplotlib import pyplot
import numpy as np

n = 10000
m = n // 5
scale = 10


def f(x):
    y = 0
    result = []
    for _ in x:
        result.append(abs(y))
        y += np.random.normal(scale=scale)
    return np.array(result)


def runningMean(x, N):
    return np.convolve(x, np.ones((N,)) / N)[(N - 1) :]


x = np.linspace(0, n, n)

pyplot.plot(x, runningMean(f(x), m))
pyplot.show()