Exploring Escher

I have been very fascinated with the art of M.C. Escher the last few years. His designs will captivate your mind. In our October 29th meeting of class,  the professor gave us some background on the geometry behind his work. For my outside of class this week, I would do some exploration on my own. The following is my "Metacognative Memoir" or thought process, on a few of Escher's pieces of art..

My First Piece.

I started by using a "duel" technique.
Steps:
If you find the center of each of the small lizards and place a dot in the same location on each of them. For me I used the top of the back right before the the neck started to turn to the head. Once you have all the locations found, I connected each dot to its neighbor. This formed a series of triangles over the whole paper. I could tell there was a pattern starting.
For it to be "duel" you repeat the process only using the shapes your found from the first step. I took the center of each of the triangles and connected those dots to one another. When I did this last step, I used patty paper over top or the original pictire. Below is my result.

It turns out the figure behind the lizards is an octagon and a rhombus. He used this general out line for the design of his picture. 

I was very excited to see this work. With my excitement I decided to show my advanced class to students the Escher piece.  There enthusiasm was greater than the experience with the Euler Line (see blog post "The Great Result"). When I showed the student the work I showed them another piece I was working on with Geogebra the same way. Geogebra of Echer's Work

This piece took me quite some time to look over. I had about three of four different trials. I don't know if this is even the right path, but it seems to work well. 

Analyzing the Angels and Demons picture on Geogebra. It woks perfectly until you get to the rhombus' and then there are more dots on the paper than are used to make the figures. Also the figures are not as regular polygon as I would think they should be. 

The new insight gained from these pictures gave me an appreciation for his work. I will continue to explore some additional art of M.C. Escher.