Animations

Although a graph is a very useful tool to visualize a simulation, sometimes it’s more insightful to make an animation. Python offers the possibility to redraw a figure again and again. That gives a multitude of possibilities to create movement. We will demonstrate a small example, in which we move a line (and point) along $f(x)=sin(x)$ over the screen. We build up the function in 3 steps, where in each step we add 1 element. With the help of this functionality you can create an array of animations.

A moving dot

When you draw a point (one $x$-value and one $y$-value) of which the $x$ and $y$ change over time, then the point appears to move over the screen. In the code below we let $x$ increment, calculate $y$ and draw the point on the screen. We also use commands xlim and ylim to specify in the plot what $x$-values and $y$-values we want to display.

import math
import matplotlib.pyplot as plt

def arange(start, stop, step):
    my_list = []

    while start < stop:
        my_list.append(start)
        start += step

    return my_list

# take small steps in x between 0 and 2pi
for x in arange(0, 2 * math.pi, 0.05):

    y = math.sin(x)

    # plot graph
    plt.plot(x, y, 'bo', markersize = 10)  # blue point
    plt.xlim(0, 2 * math.pi)
    plt.ylim(-1, 1)

    # update graph
    plt.draw()
    plt.pause(0.001)

    # clear graph
    plt.clf()

As you can see, we call the function pause() in our code. We do this to give pyplot the opportunity to draw a new figure on the screen. This only happens during the pauses we give to pyplot.

A moving line

Creating a graph by using lists: a list of $x$-values and a list of $y$-values. If you repeatedly expand those lists you get the following effect: the function $f(x) = sin(x)$ represented by a red line:

import math
import matplotlib.pyplot as plt

def arange(start, stop, step):
    my_list = []

    while start < stop:
        my_list.append(start)
        start += step

    return my_list

x_coords = []
y_coords = []

# take small steps in x
for x in arange(0, 2 * math.pi, 0.05):

    y = math.sin(x)

    x_coords.append(x)
    y_coords.append(y)

    # plot graph
    plt.plot(x_coords, y_coords, 'r-')   # red line
    plt.xlim(0,2 * math.pi)
    plt.ylim(-1, 1)

    # update graph
    plt.draw()           
    plt.pause(0.001)

    # clear graph
    plt.clf()            

As you can see, the code only changed by three lines as opposed to example 1. The result is as follows:

A dot, a line and text

You can also draw the dot and the line at the same time as well as display information to the screen about the $(x,y)$ position of the dot on the screen.

import math
import matplotlib.pyplot as plt

def arange(start, stop, step):
    my_list = []

    while start < stop:
        my_list.append(start)
        start += step

    return my_list

x_coords = []
y_coords = []

# take small steps in x
for x in arange(0, 2 * math.pi, 0.05):

    y = math.sin(x)

    x_coords.append(x)
    y_coords.append(y)

    # plot graph
    plt.plot(x_coords, y_coords, 'r-')               # red line
    plt.plot(x, y, 'bo', markersize = 10)  # blue dot
    plt.xlim(0, 2 * math.pi)
    plt.ylim(-1, 1)

    # text on the screen      
    plt.text( 0.25, -0.8, "(%.2f,%.2f)" % (x, y) )  

    # update graph
    plt.draw()           
    plt.pause(0.001)

    # clear graph
    plt.clf()