What are the factors limiting the height of a "tower" made of typical fired brick and mortar?
By "tower", I mean a structure whos point is to be tall, and can support a human standing on or near its top. I'm interested in the self-supporting structural aspects, not limitations of construction techniques, or environmental factors like wind loading, possiblity of earthquakes, etc. I want to understand what limits such a structure mostly from its own weight and properties of the material.
The point is to maximize height for any given land area the thing sits on. I'm trying to leave reasonable latitude for land area to understand the constraints, but let's not get silly like wrapping around the earth or end up with a star made of diamond, as a similar questions mentioned in a comment devolved to. If a maximum is required to avoid silly answers, let's say about the area of a typical Manhattan city block, with reasonable latitude on shape.
I understand this material can handle high compressive loads, practically no tension load, and has a high density as building materials go. My gut feel (I'm a electrical engineer, not so fluent with structural engineering) is that the optimum (least material for highest result) shape would be a circular crossection, probably with exponentially decreasing diameter with height. How well does that scale due to ground loading? What if this is built on bedrock? Wouldn't that be about the same properties, if not better, than the brick and mortar? Would that allow scaling some shape aribtrarily, or do the proportions of the shape change with size?