A Python/matplotlib script to animate compound interest with an increasing number of terms

plot-compound-interest.py

# Python code to generate an animation showing compound interest taking place with
# increasingly smaller terms. You will require matplotlib to run this code.
# You'll also require ImageMagick installed to generate the .gif animation.
# You can find this at http://usn.pw/blog/maths/2015/04/09/compound-interest

import matplotlib.pyplot as mp
import matplotlib.animation as ma

def gen_data(steps):
    """Creates the data to be plotted in this animation frame."""
    x, y = [0.0], [1.0]
    
    for _ in range(steps):
        x.append(x[-1] + 1 / steps)
        if steps < 1000:
            # If the number of steps is less than 1000, then visually demonstrate the
            # presence of "steps".
            x.append(x[-1])
            y.append(y[-1])
        y.append(y[-1] * (1 + 1 / steps))

    return x, y

limit_x, limit_y = [0, 1.02], [2.7183, 2.7183]

fig, axis = mp.subplots()

def frame(i):
    """Creates the animation frame."""
    axis.cla()
    axis.plot(*gen_data(i))
    axis.plot(limit_x, limit_y, 'g--') # Show the actual value of e with a dotted green line
    if i >= 1000: # If the number of intervals is 1000 or greater, assume infinity (if only)
        display_intervals = "\u221e" # Unicode infinity, thank you Python 3!
    else:
        display_intervals = str(i)
    axis.set_title("Limit of compound interest with %s intervals" % display_intervals)
    axis.set_xlabel("Time")
    axis.set_xlim([0, 1.2])
    axis.set_ylabel("Value as fraction of initial value")
    axis.set_ylim([0, 3])

animation = ma.FuncAnimation(
        fig,
        frame,
        # The repeated values in the following array slow the animation down for key points.
        # I don't know matplotlib well enough, so there may be a better way, but this works.
        [1, 1, 1, 2, 2, 3, 4, 6, 10, 15, 20, 30, 50, 100, 150, 250, 1000, 1000, 1000, 1000],
        interval=25,
        blit=True)
animation.save(
        'anim.gif',
        writer='imagemagick',
        fps=4)