Fluid mechanics lends itself to some beautiful visualizations and images. I won't cover anything too complicated here, just potential flow, which any undergrad who has taken a fluid mechanics course should be (at least somewhat) familiar with.

I won't really cover the math or theory here; I'm ...

Let's say you have some continuous data with a continuous error (or variance) measurement. Typically, you would just call matplotlib's errorbar function:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 2 * np.pi)
y_sin = np.sin(x)
y_cos = np.cos(x)
plt.errorbar ...