Penrose Aperiodic Tiling

What you are seeing: a Penrose P3 rhombus tiling built by Conway-Penrose deflation from a 10-fold "Sun" seed. Two prototiles (thick 72/108 and thin 36/144 rhombi); 10-fold local symmetry; no global periodicity. The A/B count ratio converges to the golden ratio $\phi = (1+\sqrt 5)/2 \approx 1.618$

Figure 1. Penrose P3 tiling after N Conway-Penrose deflations from a 10-fold Sun seed; A/B count ratio converges to phi. Method: deflation of Robinson triangles.

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WHAT TO TRY

Add deflation steps: each step subdivides every rhombus into smaller ones, growing the Penrose tiling while keeping its perfect five-fold symmetry and never repeating.
Read the A/B tile ratio: the count of thick to thin rhombi converges on the golden ratio, the irrational number that forbids any periodic repeat.
Spin and zoom the patch: you never find a translation that maps the tiling onto itself, the hallmark of aperiodic order that also describes quasicrystals.