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GameHut put together a similar effect for the Genesis/Megadrive: https://www.youtube.com/watch?v=rnCPBcSRt7Y

Web version of http://www.iguanademos.com/Jare/files/Fire/

Iguana! omg I still remember their hearthquake demo. It inspired me to become a developer

Question: is the effect in the article exactly the same as Jare’s with some parameter tweaks? The one in the article is pixelated and sharp from top to bottom, while all the pictures in the links you shared have a lot of blur in them that varies from top to bottom. I’m curious what the relationship is between the two effects, is the blur just optional?

No, this effect is not the same, although of course the underlying ideas are the same. The original was a more straightforward spread + cool, with IIRC a rather strange random component added for the cooling. Fabien's post describes a process with very explicitly random factors. My original was also 80x50