Understanding Tessellations

Zoom in if desired to be able to manipulate the tessellation using the blue points
Choose one point and move it, observing the changes in the tesselation. What does it change? Why? Do all of the points do similar things? What happens when you create a self-intersecting polygon? Does it still tessellate? What happens to it? Can you manipulate the shape into something more familiar/recognizable? Write down a few conjectures for creating tessellations based on your observations.