You then continue this process around the hexagon by drawing a new line in the third section and pivoting it into the fourth. If you look at the image below, the pivot point is where the pink and green lines intersect in the middle. Relying on the principe of “What you do to one side you must do to the other”, you copy and rotate this line into the second section using the rightmost edge of the line as a pivot point. Now you must determine what shape you would like to make, or you can experiment and see what you end up with! In either case you begin by drawing a line in the first section, from one edge to the other. With the lizard formula (or so we shall call it), you begin by creating a hexagon and drawing lines connecting each point to the centre. The formula changes depending on the shape but that basic principle remains the same. The main principe of tessellating is, “What you do to one side you must do to the other”. Using a simple square, triangle or a more complex polygon, Escher managed to develop extremely intricate and infinitely tile-able shapes. This post is going to explore the method Escher used to create his famous lizard tessellation, which is the method i used to create the turtle pattern in my header above. Escher himself explored numerous equations for breaking down common shapes into repeatable organic forms. Escher’s detailed tessellations can be utterly mind boggling in their complexity, however, creating them is not as difficult as one would think (especially if you use a computer or fancy light table).

Turtle tessellation