The Challenge: Explore a toppling sand pile.
Here is my explanation (note, I’m pretty sure I have a mistake in toppling 20)
Here is a video that Numberphile put together describing them as well:
- Is it possible for a pile to topple differently? Does it matter if different stages appear different or is it necessary for the toppling to be consistent?
- What would an isometric (triangular) grid toppling looks like? How about a hexagonal one?
- How might you meld this with computer programming?
- Is there a less or more illuminative coloring for the sand piles? What kinds of coloring may make the sand pile structures more obvious or less?