Since the time of the Pythagoreans, people have been interested in using dots to create visual patterns of numbers. One needs only to think about the possible arrangement of pips on a die.
For another example, is it not a big mathematical idea that one can always build a rectangular array with an even number but never with an odd number? Or, consider the visual patterns underlying these names for numbers: square numbers, triangular numbers, pentagonal numbers, polygonal and polyhedral numbers, etc.
What about factiorization of numbers?
Consider the website Animated Factorizations. You can use the arrow keys in the lower right-hand corner to reverse the direction, pause the animation, or even speed it up.
As I watched it (many times!), I found myself trying to predict what the next pattern would be. That is, is there a pattern in the patterns.... I wlll leave you with that thought. Plus, does his dancing sequence ever end?
The visuals were created by Stephen Von Worley, an artist and scientist who researches data visualization. He calls the animated patterns his "Factor Conga: a promenade of primes, composites, and their constituents, arranged with an aesthetically-tuned variation of Yorgey’s rules, one per second."
Read about the entire idea on Von Worley's website.
The original idea of factorization diagrams was proposed Brent Yorgey, a former high school math teacher now getting a doctorate in computer science. If you have never crossed paths with his website The Math Less Traveled, I suggest you make that visit as well....but expect to spend some time there!