This blog post introduces Penrose tiling, a type of aperiodic tiling discovered by mathematician Roger Penrose in the 1970s. Penrose tilings are constructed using specific shapes (tiles) that can cover a plane without repeating patterns. The post focuses on the P3 tiling scheme, which uses two rhombus-shaped tiles derived from Robinson triangles with side ratios related to the Golden Ratio ($ϕ$) and its inverse ($ψ$).