Yes, you are absolutely correct. When a candle burns on earth, the flame heats up the air around it, causing that air to rise. This allows fresh oxygen to move in towards the candle flame so the flame can keep burning.
In microgravity, there is no such effect as 'hot air rises' so this can't happen. The hot air tends to stay very close to the candle flame, and without any sort of outside ventilation to keep the air moving, the flame will burn at a much lower temperature than on Earth and the candle will eventually burn itself out. And since the hot air doesn't rise away, the flame is spherical in shape:
Another interesting thing about this is that the typical candle flame in space will produce virtually no smoke, because the flame's temperature is too low.
But this all relies on the air in the room being perfectly still. If there is a breeze, then the flame will be 'blown' into a different shape, and it will have plenty of fresh air so it will not burn itself out. Of course, once it burns up its fuel it will die out just like on Earth, but that may take a while.
For more information on research and experiments currently being performed on flames in microgravity, check out NASA's Candle Flames in Microgravity Home Page
p.s. Your idea about a self-sustaining pattern is very reasonable. Such things do exist. However, I gather from Tamara's links that in practice that sort of instability isn't found here. /mw
(published on 10/22/2007)