Cat and Mouse

thingiverse

George Mason University Math 401: Mathematics Through 3D Printing October 10, 2022 Hannah Robertson For this assignment, we were required to create an ambiguous optical illusion. An ambiguous illusion is an illusion that is meant to shift from one object to another as a person's perception of the changes. The person that does this the best with mathematical objects through 3D printing is Kokichi Sugihara. The object that I created was inspired by Sugihara's ambiguous cylinder. I coded my object in mathematica by using two piece-wise functions. One for the "mouse" which is a classic heart shape, and another one for the "cat" which is like a pointed heart. I called this object "Cat and Mouse" because when I think of the most basic mouse like face you can create it is almost heart-shaped, and a cats face is always identified by it's pointy ears. Both of the piece-wise functions graph of the interval [-1,1], with parts of each function going over the intervals [-1,0] and [0,1]. You can see in the image I've included of my code above the pieces that fit together and the intervals they go over. In mathematica, I was able to use the viewpoint command to view my object in different ways to make sure the illusion was there. One thing that I learned while doing this assignment is that each function you create, the domains must match up. For each of the sums and differences I made to create my optical illusion, I matched each of the f and g functions that had the same domain. Doing this ensure that there were no gaps in my object, and that the curves would line up together to create the different objects you see at various perspectives. I printed this object on a MakerBot Replicator using orange PLA filament. My object is 40mmx40mm, and took about an hour and a half to print. Since my object was stable and almost cylindrical, I did not need supports to print. References: https://divisbyzero.com/2016/07/05/sugiharas-circlesquare-optical-illusion/ http://www.isc.meiji.ac.jp/~kokichis/Welcomee.html