> And even place bricks and plates at an angle, using Pythagorean triples or careful rotations

Can you explain this a bit more? I'm having trouble visualizing what you mean.

Pythagorean triples: for example, 3^2+4^2=5^2. For a length-6 plate the distance from the first to the last stud is 5, so you can place it at an angle of approximately 25 degrees, i.e. arctan 4/3, as long as there are no studs in the way (which you can achieve easily using tiles). On LDD you can place it horizontally, choose the rotate tool, and the constraint engine will automatically forbid invalid angles around arctan 4/3, where the plate would overlap with the stud, and "snap" to the right one.

An example of a rotation is to build two rectangles of the same size, and then place the topleft-bottomright diagonal of one rectangle on top of the topright-bottomleft diagonal of the other. The diagonals don't have an integral length, but the lengths are the same so it just works.

Ah, I thought you meant arranging them vertically, not diagonally across the horizontal directions. This makes a lot more sense.

Oh yeah gearing. I guess this really does deserve the title of CAD software at that point.

Even without gearing, and staying within the studs-based construction system, the possibilities are really endless. Search YouTube for "creator expert" Lego timelapse videos ("speed build").

Even kids-oriented sets sometimes enjoy using advanced build techniques. You can start with "Lego 31036 speed build" as the search query to enter the rabbit hole from.