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By his method of coloring this tessellation, Escher has made it easy for us to understand how the tessellation was created. You can divide the design into two portions: equilateral triangles defined by groups of yellow creatures and equilateral triangles defined by groups of red creatures. These two types of equilateral triangles tessellate in a predictable manner. Now the question is, how was each equilateral triangle pattern designed?

The design inside of each equilateral triangle shown above is very symmetrical. Not only do we notice three heads of the yellow creatures inside of an equilateral triangle, but we also notice that each yellow creature is symmetrical itself. The following animation will clarify this point:

So, to create one of the equilateral triangles shown in the original tessellation, Escher had only to design a small portion of an equilateral triangle, which he then reflected and rotated. The process is the same for both types of equilateral triangles shown in the tessellation.