Setting the Colormap to be Consistent Across Axes

(Originally posted on Doug's MATLAB Video Tutorials blog.)

I love getting short, concise questions from fellow MATLAB users. One that I got recently looked like this:

I have some data that I want to plot with contourf using a colormap that spans from 0 to 1, but with everything I have tried the range keeps resetting to the range of the current data being plotted. I want a constant colormap range so that I can accurately compare plots with data that span different ranges.

This is a question that is applicable to many people, in different situations. The short answer is that you set the CLIM property of the axes. The long answer is in the video!