Can the Golden Ratio Build a Pattern That Never Repeats?

BEHIND THE WORK

Can the golden ratio build order without repetition?

Begin with ten isosceles triangles arranged around one center. Two local subdivision rules cut their long edges in the golden ratio φ = (1 + √5) / 2. Repeating those rules five times creates a tenfold Penrose-style tiling: highly ordered, yet without ordinary translational repetition. One connected drawing point retraces existing edges as increasingly fine triangles fill the same decagonal crystal.

Artismathic turns equations into visual art—one function at a time.

Music: 'Helium' by TrackTribe

#MathArt #GoldenRatio #PenroseTiling