#### Thursday, July 29th, 2010...4:44 pm

## Adding heat to a hot movie

While I have yet to see the movie, I’ve been the recipient of considerable buzz about the movie *Inception*. Given this is one of the hot summer movies and simply how amazingly hot it has been this summer, it seems fitting to compose a post on the heat equation!

The heat equation is a partial differential equation. For fun, I’m going to apply the equation to a grayscale image of the *Inception* movie poster. We see the poster below.

The grayscale value of each pixel represents the heat of that point on our rectangular plate. It just so happens that the heat is distributed in the exact image of the movie poster! Keep in mind that dark colors are cooler temperatures. To see how the heat is distributing across the plate we will create a contour map. On a topographical map if you travel along a line you stay at a constant altitude in the 3D landscape. In this contour graph, if you move along a line you stay at a constant temperature.

The heat distribution is possibly more easily seen when we add color to our contour map with red being hot, blue being cooler and white being a temperature of 0.

We haven’t apply the heat equation! Let’s do that now. We will apply the heat equation for a small interval of time and see how the heat distributes in the poster! Keep in mind this is done on a computer using numerical algorithms. What happens? Just look below.

Not a fan of inception? Try it yourself or for that matter on yourself. In fact, I started by heating up my own face which is also easily done by simply walking outside! Below you see the grayscale contour map and the animation.

Cool, eh? Or should it be, hot stuff, eh?