Number Constellations

Brady Haran (of Numberphile) came to us with an idea of laying out numbers on a grid and highlighting them based on the “family” they belonged to. His video on the Prime Spirals sparked our curiosity and we decided we could take the idea a bit further…

What’s happening?

Here we’re laying out the positive integers (1… 2… 3…) in different ways; a simple square grid, an Ulam Spiral, a Sacks Spiral, and a Vogel (Fibonacci) Spiral. (We also added a triangle spiral and a pyramid). Once the numbers are layed out, we choose some of them based on the Family that is selected in the settings, and we highlight the numbers that are part of that family. This lets you see some interesting patterns!

A very famous way to do this is laying out the numbers in an “Ulam Spiral” configuration and highlighting the prime numbers. Some interesting patterns emerge.

Also, if you share this page with the whole URL intact, it will automatically load with the same settings you see at the time you shared the URL. If you click on a circle, it will show you what number that is in the bottom right.

Did you find anything interesting? See a mistake? Let us know what you think in the comments.