Let's take a look at shapes that tile the plane or tessellate the plane that have all the same length sides and congruent angles. These are called regular polygons; it turns out the only regular polygons that tessellate the plane are: equilateral triangles, squares, and regular hexagons.

Now we have these basic regular shapes. How can we modify them in an artistic way? Let's start with a square. Mutate the left side in any way. Then take the mutation and translate it to the right side. This modified square will still tessellate the plane. Repeat this procedure on the other two sides. It will still tessellate the plane. Add eyes, ears, etc to make it more artistic. This is our first artistic tessellation of the plane.