Transformation Tessellation Tuesday

Last week I demonstrated how you can transform a single-shape tessellation to make additional single-shape tessellations. This week I will demonstrate transforming a multiple-shape tessellation.

First, I begin with a 4-patch block as shown below.

This is what nine blocks looks like.

There are four distinct Shapes in this tessellation. I have outlined them below.

Now, in order to transform these shapes, you will have to "borrow" a piece of one Shape to add to another. Below, I have shaded a piece of the smaller Shape and shaded where that same piece touches the larger Shape. The lower tessellations show how the Shapes have been transformed by adding the shaded pieces to the larger Shape, and deleting the shaded pieces from the smaller Shape.

Below, I have shaded a piece from a different Shape and also shaded where that same piece touches the larger Shape. The lower tessellations show how the Shapes have been transformed by adding the shaded pieces to the larger Shape, and deleting the shaded pieces from the medium Shape.

You are neither limited to the number of pieces you trade between Shapes, nor the number Shapes you transform. Below, I have shaded two different pieces of two of the Shapes. The remaining tessellations show these pieces added to two different Shapes. Yet it still remains a multi-shape tessellation, though quite different from the Shapes I outlined at the beginning of this post. Amazing!!


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