[jharsman]

I can't get your example code to work, but that is a completely different technique, ray marching a volume displaced by a noise function. This gives nice 3D-looking flames, but the movement tends to look like a scrolling noise function. And it's harder to use arbitrary burning shapes, my simulation supports drawing anything and it will burn.

[steaminghacker]

Sorry, this version wont just paste back as is in shadertoy. Also it needs a random 256x256 bitmap in channel 0. The effect is the same as ozzy's original, except change ITERATIONS to 13 in his code to see the change (which is only slightly better). The other changes were for performance, which i improved slightly.