Frank Farris’s patterns

A couple of weeks ago Evelyn Lamb’s article Impossible Wallpaper and Mystery Curves introduced me to Frank Farris’s work. On Saturday I stumbled on his book at Barnes and Noble:

  

I was excited to try out some of his ideas with the boys even though they use complex numbers and exponentials which are over their heads. We did the whole exploration this morning using Mathematica.

To start, we just explored the exponential function.

Next we moved to looking at sums of two exponential functions. The boys were surprised by the graphs and we played around with a few more examples. They had some interesting ideas about what the pictures looked like, and I’m glad that the pictures also reminded them a little of Anna Weltman’s loop-de-loops.

Next we moved on to sums of three exponential functions motivated by the idea of trying to produce another kink in the loop. There was a little discussion at the beginning of this part of the talk about complex variables. I thought going down this path was going to be too difficult to explain, so I tried to bring the conversation back to the sums. I love the ideas they had about symmetry here.

Next we looked at Farris’s “mystery” shape and played around a bit more with the ideas. These shapes also led to fun conversations about symmetry:

Finally, I let the kids just play around. As I was writing up this project I got a “hey dad, come here and look at this cool shape” call:

  

So, despite the math underlying these shapes being a little over their heads, the kids seemed to really enjoy seeing these shapes. I loved hearing their ideas and I loved seeing them play around with the ideas for a long time after we turned off the camera.

Also, Farris’s book is absolutely amazing – you’ll love the ideas and the presentation, and probably most of all the incredible pictures he creates from the ideas!

Extending Anna Weltman’s loop-de-loops with Frank Farris’s “Creating Symmetry”

We’ve had a ton of fun in the last couple of weeks with Ann Weltman’s loop-de-loop ideas:

  

Here are two of the projects that we did:

Anna Weltman’s loop-de-loops

Anna Weltman’s loop-de-loops part 2

Last night we stopped at a Barnes & Noble after dinner and I found a book that Evelyn Lamb had written about last month:

  

Here’s Evelyn Lamb’s piece:

Impossible Wallpaper and Mystery Curves by Evelyn Lamb

The book is absolutely wonderful and has so many cool examples. I’d hoped it would be easy to make some of the graphs in the book using Mathematica, and after a little documentation reading to kick off some rust, it wasn’t too hard:

 

At least visually the curves you can make from the idea in Farris’s book remind me of the loop-de-loops. I don’t really think it will be that productive to talk in detail with the boys about exponentials and graphing in the complex plane, but I do think they will like seeing the pictures and talking about them. I’m excited to show them some of the ideas from the book tomorrow morning.