If that goes off to infinity, you're out in this purplish region.

If that sticks around, you're in the black region.

Now mathematicians knew that these dynamics were interesting

in the early 1900s, but

they did know how interesting the dynamics were or what was going on.

And it wasn't until plotted this.

Using data visualization to plot the results of these points,

to find that the dynamics were very interesting.

You got all this great structure.

You could zoom into a little section here, and see even more, and more detail, and

that was something we just hadn't encountered before in mathematics, and

so visualization kind of revolutionized this area of mathematics in our

understanding of this area of mathematics by basically getting the data

out of this mathematical equation and through our visual

perception into a cognitive process so we could better understand it.

So, if If you pick a point inside this and

you start to look at the dynamics, you get what's called a Julia set.

And this plotted in the complex plane.

And one of the things I worked on with this

was to take this complex Julia set and look what's going on in the quaternions.

And again, data visualization is really helpful because you get

these whorl patterns.

That are basically connecting different parts of this Julia set to other parts of

this Julia set through these additional dimensions, and

you couldn't understand that very well without actually being able to visualize

how those connections are being made.