Saw a couple of neat tweets on a new paper in Nature by Kevin P. O’Keeffe, Hyunsuk Hong, and Steven Strogatz:
It looked like playing with the “swarmalator” program would be a really fun way for kids to experience ideas from current math research even though the math underneath these results is a bit out of reach.
So, this morning we just played. Here’s how I introduced the ideas of the program – the two most important ones are (i) the strength of attraction of similar colors, and (ii) the strength of the desire for neighbors to have the same color (and both of these “strengths” can be negative):
After that short introduction I had my younger son (in 6th grade) play with the program to see what he found:
Next I let my older son (in 8th grade) play:
Finally, to talk about the ideas a bit more we went through 4 of the 5 examples at the bottom of the web page of the program we were using. I had the kids try to guess what was going to happen before we set the coordinates. Here are the first two examples:
Here are the last two examples – in this video the boys are getting the hang of how the program works and have several pretty neat things to say about what they are seeing (and what they expect to see):
We played with the program for about 20 min more after we turned off the camera. This program is definitely fun to play with and it was really fun to hear what the boys were guessing the various different states of the program would look like. Even with just two parameters, the kids really had to think hard to talk about the expected behavior. I think that lots of kids will really love playing around with this program.
Mike's Math Page 
Hi Michael,
I’m delighted that you guys are playing around our model! And I’m impressed all of your intuitions, and explanations — it took me a long while to figure out what these things were doing & be able to explain them in any coherent way.
One thing: in the third movie, when your son increased the number of swarmalators and the animation looked a bit hectic, you were right to suspect that the numerics were doing something fishy. You need to decrease dt in order to make the simulations stable (since Rudy — who wrote the animation — is just using the forward Euler method.)
In particular liked the descriptions of the “splintered phase wave” state. Steve, Hyunsuk and I were calling it the “pizza” or “gum drop” state for a while, but I never thought of “lava lamp”! (One challenge for mathematicians — could you predict the number of slices that form in this state? My collaborator Theo Kolokolnikov has come up with a heuristic for doing so. See the endof our new https://arxiv.org/abs/1709.00425)
Anyway, thanks for such nice video. It was inspiring to see both you and your kids have such curiosity