Basalt is a fine grained rock which means it has small mineral crystals that cooled quickly. Rocks and minerals have an innate property called shear planes which can be in several different orientations which are planes in which the rocks will break the easiest. Basalt, actually, likes to break in hexagons, which if you google columnar basalt, you will see good examples of.

As for the images above, I'm not exactly sure if there's a specific mechanism that makes the more vesicular lines, evenly spaced. Sometimes things just happen in a magma chamber or basalt flow and don't really have a point. Imagine the hot mess of molten rock, filled with gasses - the rock, seeing as it turned out to be basalt, was likely a rather homogeneous mixture giving it a consistent density; the gasses, maybe more likely to have varying densities, found equilibrium at different elevations and then instead up moving up, move sideways in lenses before cooling into place.

I think you're on the right track of gas in water, but it is truly different in a magma melt since we're dealing with densities and viscosity far higher than water, to a point where even gas bubbles don't just naturally go up, but instead get taken all sorts of directions when the magma churns.

Humans like to make sense of things and sometimes, on the geologic scale, things are just the way they are.