A few weeks ago Grant Sanderson published this amazing video about fractal dimension:

I’ve had it in my mind to share this video with the boys, but the discussion of logarithms sort of scared me off. Last week, though, at the 4th and 5th grade Family Math night the Gosper curve fractals were super popular. That made me think that kids would find the idea of fractal dimension to be pretty interesting.

Here are the Gosper curves that Dan Anderson made for us:

We’ve actually studied the Gosper curve several times before, so instead of just linking one project, here are all of them ๐

A collection of our projects on the Gosper curve

So, today we started by watching Sanderson’s video. Here’s what the boys had to say about it:

At one point in the video Sanderson makes a comment that fractals have non-integer dimensions. I may have misunderstood his point, but I didn’t want to leave the boys with the idea that this statement was always true. So, we looked at a fractal with dimension exactly equal to 2:

Next we looked at the boundary of the Gosper island. I wanted to show that this boundary had a property that was a little bit strange. I introduced the idea with a square and a triangle to set the stage, them we moved to the fractals:

Finally – to clear up one possible bit of confusion, I looked at a non-fractal. For this shape we can see that the perimeter scaled by 3 and the area scaled by 7. Why is this situation different that what we saw with the Gosper Island?

Definitely a fun topic and I think Sanderson’s video makes the topic accessible to kids even if they don’t understand logarithms. I’m excited to find other fractal shapes to talk about now, too!