We did a project called “A Cycle of Differences”

Here is a link to the project sheet:

http://blogs.canisius.edu/themathcircle/wp-content/uploads/sites/33/2014/02/CycleDiff.pdf

We did LOTS of experiments.

We found an example of a starting square that lasted 8 or 9 steps. We also found what happens for all possible ways of starting with 0’s and 1’s.

We also investigated whether it was possible to “work backwards”.

We found that a starting triangle ended at a different stable pattern.

We also investigated a starting pentagon.