I saw a really neat blog post from Stephen Wolfram last week:
The blog post has so many different ideas that you could share with kids, but I decided to spend the weekend exploring various versions of Collatz-like sequences with my son.
We started by looking at some simple code in Mathematica to generate Collatz sequences:
Next we looked at how long it took various numbers to get to 1 in the Collatz sequence and looked at a histogram of the numbers. We got a fun surprise:
We wrapped up today’s project by looking at what happens when you replace the 3x + 1 rule in the Collatz conjecture with a 5x + 1 rule. I don’t remember ever seeing this idea before and it was one that really surprised me reading through Wolfram’s blog post this morning:
Tomorrow we’ll extend today’s project by looking at the 4x + 2 and 7x + 1 version that Stephen Wolfram mentioned in his tweet. Hopefully that’ll make for a really fun project, too.