Thoughts on Lava Lamp Shapes

So you want to make a lava lamp what shape?

We want to be able to have the light serve a dual purpose of heating the lamp/the wax and to illuminate the glass as well. We probably want the whole thing illuminated so that rules out shapes that do not have a direct line of sight from the top to the bottom. We need the wax to get heated on the bottom as well so that means that the light has to be on the bottom.

What else do we need. Well we need the wax to be able to freely move from top to bottom and vice versa. What does that entail well an unobstructed path both ways for one. We will also need it to displace the fluid to move in each direction so there needs to be space for the fluid to flow in the other direction while the wax is moving. So we need to avoid shapes where hard wax at least on the way down prevents fluid from moving up past it since then it will be able to get in a stuck state ruining the lava lamp experience. How can we accomplish this though? Well we can make sure that the solid pieces of wax are always

a) moving into a space larger than the piece of wax or b) in a space hot enough that they will melt more than they are now.

You will also want the hot wax when it is rising to at least be able to get some momentum before being constricted to allow some force to be generated by the downward moving fluid to sufficiently deform it to move past. If we look not at an actual lava lamp we find that that is exactly what has been done. Hot wax rises to the top where is cools and moves down an inverted conic shape piece of glass which expands until it reaches the melting hot region where it being to constrict bringing the wax closer to the lamp and allowing upward moving wax to get a good start.