Animation update function in Matplotlib - Time & Space Complexity

Time Complexity: Animation update function

O(n^2)

Understanding Time Complexity

When creating animations with matplotlib, the update function runs many times to redraw frames.

We want to know how the time to update grows as the animation length or data size changes.

Scenario Under Consideration

Analyze the time complexity of the following animation update function.

import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

fig, ax = plt.subplots()
line, = ax.plot([], [])

xdata, ydata = [], []

def update(frame):
    xdata.append(frame)
    ydata.append(frame ** 2)
    line.set_data(xdata, ydata)
    return line,

ani = FuncAnimation(fig, update, frames=range(1000), blit=True)
plt.show()
    

This code updates a line plot by adding one point each frame and redraws the line.

Identify Repeating Operations

Look at what repeats every time the update function runs.

• Primary operation: Appending one new point and updating the line data.
• How many times: Once per frame, for all frames (e.g., 1000 times).

How Execution Grows With Input

Each frame adds one point and redraws the entire line with all points so far.

Input Size (frames)	Approx. Operations
10	About 55 (1+2+...+10)
100	About 5050
1000	About 500,500

Pattern observation: The total work grows roughly like the square of the number of frames.

Final Time Complexity

Time Complexity: O(n^2)

This means the total time to run all updates grows roughly with the square of the number of frames.

Common Mistake

[X] Wrong: "Each update takes the same small time, so total time is just O(n)."

[OK] Correct: Each update redraws all points so far, so the work per frame grows as more points are added.

Interview Connect

Understanding how repeated updates affect performance helps you write smoother animations and shows you can analyze code beyond just loops.

Self-Check

What if the update function only updated the newest point instead of all points? How would the time complexity change?