This demo is showing a tall, skinny flame with 20 control points and 8000 individual flame points.
The simulation works by having the control points climb with a random chance of moving off to one side (so that up higher there is more variation after having more time to have moved sideways). The flame points drop off in brightness based on their distance from the nearest control point (or from the center of the base of the flame). The flame points also have a velocity component, which varies randomly a bit as it climbs. The shape isn't all that realistic, but the billowy dancing of it looks pretty flame-like, and I find it quite mesmerizing to watch.