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I guess they are called lava lamps because they look like lava but what exactly does lava look like? I've only seen it flying out of volcanoes on TV and it doesn't look like this. This looks like globs of molten wax floating in oil which is exactly what it is. I looked it up on Wikipedia and the type of lava it looks like is a type called pāhoeho lava. These were very popular in the late sixties along with fibre optic lamps and wave machines, my family didn't have any of these novelties but I remember trying to make one out of a broken fluorescent tube in an art class.
If you can find one(my brother found this one in a recycling station) it would make a great starting point to an investigation (or EE). As the globs move upwards they cool down resulting in a change of density and hence buoyancy. I would therefore expect the acceleration to get less as the globs get higher. I tried analysing the motion with LoggerPro but it wasn't very accurate due to movements in the camera.
It would be interesting to adjust the power to the heater.