Based on the blog post, his talk at MoMath must have been incredible!

I decided to try out one of his explorations with the boys tonight. We did the first few parts by hand and the last part using Mathematica and the code from Wolfram’s blog post.

The process we studied works as follows:

(1) Pick an integer to start with and pick a number to multiply by in step (3),

(2) Cycle the digits of the number to the left. A few examples will make the process clear:

123 goes to 231
402 goes to 024, or simply 24
111 would stay 111

(3) Multiply the new number by and then add 1.

(4) Return to step (2) with the new number.
The video below shows how our exploration began. Our initial integer was 12 and we multiplied by 1 at each step (so, starting easy, though I picked 12 at random so I really didn’t know what was going to happen):

Now we moved to a slightly more complicated example -> the same process as in the first part but we’ll be working in binary rather than in base 10.

We started with the number 6 (110 in binary) and multiplied by 2 at each step. Once again we found a fun surprise:

To get one more round of practice in before moving upstairs to the computer we looked at the same situation as in part 2, but this time starting with 1 and looking at several cases – multiplying by 1, by 2, and by 3:

Finally, we went to the computer to explore the process in many different situations. We used code from Wolfram’s blog post to recreate the work from the MoMath talk:

What I *love* about this project is that the exploration works really well with kids on the whiteboard and on the computer. The whiteboard exploration gave us a great opportunity for a little practice with arithmetic, with binary, and with algorithms. We also saw some really fun surprises!

The computer exploration is obviously fantastic, too. I’m so grateful that Stephen Wolfram shared the ideas from his talk!