
# 13.3: Visualizing Two-Dimensional Scalar and Vector Field


Plotting scalar and vector ﬁelds in Python is straightforward, as long as the space is two-dimensional. Here is an example of how to plot a 3-D surface plot:

The scalar ﬁeld $$f(x,y) = \sin{\sqrt{x^2 + y^2}}$$ is given on the right hand side of the zvalues part. The result is shown in Fig. 13.3.1.

And here is how to draw a contour plot of the same scalar ﬁeld:

The clabel command is used here to add labels to the contours. The result is shown in Fig. 13.3.2.

If you want more color, you can use imshow, which we already used for CA:

The result is shown in Fig. 13.3.3. Colorful!

Finally, a two-dimensional vector ﬁeld can be visualized using the streamplot function that we used in Section 7.2. Here is an example of the visualization of a vector ﬁeld v = (vx,vy) = (2x,y−x), with the result shown in Fig. 13.3.4:

Exercise $$\PageIndex{1}$$:

Plot the scalar ﬁeld $$f(x,y) = \sin{(xy)}$$ for $$−4 ≤ x,y ≤ 4$$ using Python.

Exercise $$\PageIndex{2}$$:

Plot the gradient ﬁeld of f$$(x,y) = \sin{(xy)}$$ for $$−4 ≤ x,y ≤ 4$$ using Python.

Exercise $$\PageIndex{3}$$:

Plot the Laplacian of $$f(x,y) = \sin{(xy)}$$ for $$−4 ≤ x,y ≤ 4$$ using Python. Compare the result with the outputs of the exercises above.