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Serendipity

Can you write LOGO programs for some beautiful irregular tilings?

LOGO Challenge - Tiling with Equilateral Triangles

Stage: 3 Challenge Level: Challenge Level:1

At a maths conference someone said that - "not much can be done when tiling the plane with equilateral triangles."

Below are just four tilings that grabbed my attention.

Try replicating them in LOGO.

Can you extend this catalogue of tilings?
Using ONLY equilateral triangles what other tilings can YOU devise?