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Building Gnomons

Age 14 to 16 Challenge Level:

This screenshot shows you how to use the Cellular resource to build gnomons from scratch. Alternatively, you can choose the "build gnomons" starter drawing and manipulate them in the same way.

How to build gnomons

Here are the perimeters of $G_6$.

Here are the perimeters of $G_6$ rewritten in terms of their Fibonacci numbers ($F_1 = 1, F_2 = 1, F_3 = 2, F_4 =3$ and so on).

Can you draw a diagram showing what happens more generally?