The penrose tiling is a combination of 2 shapes with rules that make it only possible to ”tile the plane non-periodically” this means it is Aperiodic. This means the pattern of tiling tiles the plane all the way to infinity without ever repeating.

Simple Penrose tiling make-up §

Roger Penrose’s Tiling is made up of a thick rhombus and a thin rhombus.

The Golden Ratio §

For some reason the The Golden Ratio appears within the tiling. ( irrational) ( appears in darts to kite ratio idk were he got darts and kites from but it is another way to make a penrose tiling).

The penrose tiling contains a “5 fold symmetry” something that is very related to The Golden Ratio.

Parallell Lines §

Drawing the lines below onto the penrose tiles of darts and kites. When Layered together into the full penrose tiling pattern, these lines connect together to form 5 sets of overlapping parallell lines. if you look at one of the 5 sets of parallell lines that are all in parallell to eachother, you see that they are not all equally spaced out, going to each “section” (whatver that is), you can count up all the “long” and “short” gaps and you end up with the Fibonacci Sequence

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