Part two! This is an illustration of a neat fact that I noticed a few days ago. Made with mint patties and licorice. I’m worried that the illustration is a bit opaque, so clarification is below. Just in case.
Essentially, what I tried to illustrate is this: If you count in binary, starting at 0, (the left column) and at each step tally up the 1s in your number, you get a second sequence: 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, … (the right column). The gif above shows a cool property of this second sequence — to be specific, if you remove every other element, the overall sequence remains unchanged.