No?

One way to generate aperiodic tiling is to take a regular lattice and cut it with a plane with a transcendental slope. Project each lattice point down onto the plane and then choose tiles appropriately [0].

Algebraic numbers are those as roots of (finite) integer/rational polynomials. Though things get convoluted depending on what domain you're talking about, the algebraic structure, in this context, if I have it right, means there's periodicity. Aperiodicity requires there not to be such structure.

I only read the headlines so my apologies if I'm way off base.

[0] https://en.wikipedia.org/wiki/Aperiodic_tiling#Cut-and-proje...