I am currently reading Game Engine Black Book: Wolfenstein 3D by Fabien Sanglard and I can very much recommend it. Following the author on Twitter (@fabynou), I found his interesting tweet on the Doom Fire Effect.
In his blog post he explains in much detail how this nice little effect was done and how it can be implemented.
This effect seemed like a good addition to that 32x32 RGB LED matrix I have sitting in my home office which is rendering different kinds of animations (I blogged about quite some time ago).
After that, it was easy to port the code to the actual Arduino sketch driving the RGB matrix.