Tag: Stephen Wolfram

Using an idea from Stephen Wolfram to show kids how a virus can spread through different kinds of networks

This week I watch an interesting live coding video from Stephen Wolfram:



Right at the beginning of this video Wolfram shows how to use some simple Mathematica commands to make a simple model of how a virus spreads through a network. I thought it would be fun to share this idea with the boys for several common networks.

I introduced the idea on a 2d grid:

Then we moved to a 3d grid:

Then we moved to a type of network called a Delaunay triangulation:

Now we moved away from these relatively simple graph networks and looked at a completely random one:



With these examples out of the way, we moved to two types of networks that more more commonly used to model a network of human interactions. The first was a Watts-Strogatz network:

Finally we looked at a Barabasi-Albert graph:

This was a really fun project and I was really excited to hear how the boys thought about the different types of networks. The math to properly describe what’s going on in these networks is over my head but I am really happy that Mathematica makes it so easy to explore.

Finally, the idea for looking at these 6 different graphs comes from Christopher Wolfram’s fantastic agent based modeling example. In that program he dives into these different networks much more deeply than we do here – this program is definitely worth checking out if you’ve not see it already:

https://www.wolframcloud.com/obj/covid-19/Published/Agent-Based-Networks-Models-for-COVID-19.nb

Day 2 of playing with Stephen Wolfram’s Physics Project

Yesterday we played around with some introductory ideas in Stephen Wolfram’s Physics Project. Today we moved on to looking at the 3d examples in the project. We were entirely on the computer today looking at shapes, so this project was more about experiencing the ideas rather than diving into the details. Still the kids had a great time.

Here’s how the introduction to the 3d shapes went:

Now I had the boys each try to produce one of the 3d shapes using a rule they made up. This part of the project turned out to be a bit harder because of our lack of familiarity with how the underlying details work. Still, though, they produced some neat shapes and talked about them here:

Despite the difficulties today, I’m excited to play with this project a bit more. The math ideas here are something that I think the kids aren’t going to see anywhere else, and I love the lessons about building complex shapes from simple rules.

Sharing some basic ideas from Stephen Wolfram’s Physics Project with my kids

I learned about Stephen Wolfram’s Physics Project last week from a Steven Strogatz tweet:

It looked like something that would be really interesting for kids to see, so I spent a bit of time diving in. This morning I took a shot at introducing some of the basic ideas to them and they were fascinated by what they saw.

I started by talking about directed graphs – the introductory ideas are definitely accessible to kids (sorry this video is a bit out of focus – I forgot to check the focus before we started today):

Now (off camera) we constructed the next step in the sequence of graphs Wolfram is studying. My younger son explains our work below and my older son shows a slightly different way of thinking about it that he thought might be more illuminating.

Now we went to Mathematica to explore a bit. Wolfram has made his code available, so exploring his ideas at home is really easy as long as you have the latest (as of April 2020) version of Mathematica. Just to be clear, I’m using their code and don’t yet fully understand how it all works. I was able to understand it well enough to play around, though. It was fascinating to see how the graphs changed when the boys changed the rules a bit.

But the most important thing I think is in this video is just how interested the kids were in these amazing shapes.

Finally we looked at a selection of graphs made from random rules. Again the boys were fascinated by these shapes and seemed to really enjoy thinking about them.

This project was incredibly fun – hoping to find other ways to share these ideas with the boys.

Revisiting Stephen Wolfram’s MoMath talk

Last week Stephen Wolfram posted an incredible summary of his talk at the Museum of Math:

We did a project using some of the code here:

Sharing Stephen Wolfram’s MoMath talk with kids

I think the ideas from the talk can provide kids with a really wonderful opportunity to explore math. We’ll hopefully revisit the ideas many times!

Today’s exploration follows the same line of ideas that we followed in the first project. The procedure we are looking at goes like this:

(1) Start with the number 1, and proceed to step 2.

(2) Whatever number you get here, cycle the digits to the left -> so, 123 becomes 231, 1045 becomes 0451 (so just 451 for computations), 110110 becomes 101101, and etc . . .

(3) Now multiply the number from step 2 by a fixed number N and add 1.

(4) Take the output from (3) and return to step (2).

We look at the sequence of outputs from this procedure in base 2, 3, 4, and 5 today. Quite amazingly, Stephen Wolfram showed that this entire procedure could be done with some very short code in Mathematica. Here’s a pic of the short code and also patterns we see in the digits when we multiply by 1, 2, 3, 4, 5, 6, and 7 at each step when we reun the procedure above in base 4.

Wolfram.jpg

If this seems way too complicated I’m not explaining the procedure well enough – go back to our first post on the subject or to Wolfram’s blog. I promise you’ll see that the explorations are totally accessible to kids.

 We started our project today by revisiting the results in base 2 and looking for strange or unusual or really anything that caught our eye in the digit patterns.

Also, I’m sorry that the zoomed in shots are so fuzzy (so, the first minute here and basically all of the 4th video). I didn’t realize how bad the footage was until it was published. Even with the fuzziness, though, you can still hear how engaged this kids are and how interesting it was for them to explore all of the strange patterns:

For the 2nd part of the project we looked at the patters of the digits in base 3:

Then we looked at base 4 and immediately saw something that we’d not seen before:

So, having explored bases 2, 3, and 4 we went back to some of the patterns we’d seen and got a nice surprise – we were able to find structure in some of those patterns. This video is the exploration that led to us finding the pattern in base 2.

Again, I’m sorry this video is so fuzzy – wish I would have caught that when we were filming 😦

Now we moved on to exploring some of the patterns that we’d seen in base 3 and base 4 – that exploration allowed us to predict a pattern in base 5 even though we’d not yet looked at any of the digit patterns in base 5!

I can’t wait to play with Wolfram’s ideas a bit more. The ideas are such a great way to expose kids to exploration in math!