Chicken or Egg?

Reducing patches of a wireframe

A trove of 3D printing models are available at Thingiverse. Warning: be sure you have available time if it’s your first time to look! If you have access to a 3D printer, you can print your very own models from such Makers as Henry Segerman and Laura Taalman.

A year ago, I taught a seminar on linear algebra in computer graphics and data science based on my MAA book, When Life is Linear: from computer graphics to bracketology.

We used 3D models to motivate rotation matrices. Students downloaded their model of choice and then used 3D rotation matrices to place the wireframe in a desired position on the screen. We used Matlab in the class making the use of an STL File Reader quite helpful.

Some wireframes are quite refined and cumbersome to visualize and rotate. So, we also made use of the reducepatch command in Matlab. This command reduces the number of polygons in a wireframe as seen at the top of this post.

Soon, the students were downloading wireframes, using rotation matrices to place them and then repeatedly executing the reducepatch command. Soon, the process became a game. Who could most closely predict the lowest level wireframe? For instance, what would we get after repeatedly reducing the wireframe of the model of the Peanuts character Woodstock available on Thingiverse posted by Masterdid? I’m not sure if the chicken or the egg came first…but if Woodstock comes first, would the end result be an egg? Make your guess and then click the image below to see what results!

Animated GIF of Peanuts Woodstock character