Thursday, 11 July 2019

Penrose tiles - a program to build Penrose tilings

Here's a free program for drawing Penrose tiles (tessellations) with PowerPoint.

Add, snap, deflate, inflate, grow, shrink and format kites and darts with it. It is very easy to use and the functions allow you to rapidly create huge numbers of tiles properly arranged. Record to date is 22,523 tiles.

If the toolbox is enlarged, buttons to label tile vertices and produce a report on the slide also become available. The box at the bottom gives information and sometimes error messages.

To get the program just download the macro enabled PowerPoint file here (0.8 Mb) and open it. Macros must be enabled and the first slide  contains instructions how to get started. There are another four slides which contain interesting ready-made patterns and some useful info.

The program was implemented in Microsoft PowerPoint VBA and tested on Office 365.

There is more on this site about Penrose tiles here and full documentation on the program here (10 Mb). It contains some big pictures and the proof of why the ratio of the sides of kites and darts is the golden ratio is ##\phi## where $$\phi=\frac{1+\sqrt5}{2}$$This formula was known to the ancient Greeks and appears in many mathematical formulas. I have not seen a proof of this for Penrose tiles anywhere else. It is always just stated as if it was obvious.

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