KipKay has a nice, simple DIY project that shows how to make a small dry ice fog machine. He does it at the scale of a coffee can, but mentions that you could scale it up to a 55 gallon barrel if you like:
The other fog machine alternative is the fog juice variety. These machines heat up fog juice to turn it into smoke, as shown here:
It is definitely easier (and probably cheaper) to buy one of these rather than to build your own, but if you wanted to try making your own, you might be able to scavenge the heating element from something like a coffee maker to heat the juice.
The bigger question is, What’s in the juice? Here’s the answer (mute the sound during the intro, then turn up the sound when he talks):
The following video shows you why the fog chiller is important, by showing you how to build your own fog chiller and demonstrating the effects. You end up with denser, ground-hugging fog:
If you want an even denser fog, consider a foam machine instead:
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