File:White-noise-density-animation.gif

#! /usr/bin/env python3
# -*- coding:utf8 -*-

import matplotlib.pyplot as plt
from matplotlib import animation
import numpy as np
from math import *

plt.rcParams['font.sans-serif'] = 'DejaVu Sans'
np.random.seed(0)

fname = "White-noise-density-animation"
nframes = 20
nsamples = 2**nframes+1
t0 = 1.
t = np.linspace(0, t0, nsamples)
X = np.random.normal(0, 1, nsamples)

def animate(nframe):
    nframe = (nframe + 11) % nframes # start with frame 11
    plt.cla()
    dsample = 2**(nframes - nframe)
    plt.plot(t[::dsample], X[::dsample], '.-', markersize=4,
        label=f"$\Delta$t = 1/{nsamples//dsample:.0f}")
    plt.xlim(0, 1)
    plt.ylim(-3, 3)
    plt.grid(True)
    plt.xlabel('t')
    plt.ylabel('X')
    plt.legend(loc="upper center", framealpha=1)

fig = plt.figure(figsize=(520 / 90.0, 340 / 90.0), dpi=72)
plt.xlim(0, 1)
plt.ylim(-3, 3)
plt.grid(True)
plt.xlabel('t')
plt.ylabel('X')
plt.tight_layout()
anim = animation.FuncAnimation(fig, animate, frames=nframes)
anim.save(fname + '.gif', writer='imagemagick', fps=2)