Why is there a Mandelbrot set on Google this morning?

Is today Mandelbrot’s birthday or something? Why is there a mandelbrot set on the google front page…and all sorts of equations etc…etc…?

I don’t know. But, if you click on the actual image itself, it does a google image search on “Gaston Julia”, which I then popped into google and came up with this. It seems that Gaston Julia’s birthday is today.

I wondered the same thing. Apparently the guy studied fractals before computers could draw them.

But on to the real question: Why do the folks at Google care that it’s his birthday?

Computer nerds.

Not that there’s anything wrong with that.

And here I thought you were talking about the Jewish almond cookies, and I got all excited.

Presumably this is the guy they named Julia sets after? I believe Julia sets are a subset of Mandelbrot sets, but IANAM.

Subset isn’t quite the right word. My understanding is that Julia sets can be generated from Mandelbrot sets, but this is not an area that I’m really familiar with.

IIRC - there is a Julia set for each point in the Mandelbrot diagram. The ones inside the set are joined-up, the ones outside the set are broken-up (dusts). The Julia set at a point resembles the Mandelbrot pattern at that point.

Fractint* (dammit where did I put it?) lets you toggle between the two.

*has anyone here not got Fractint?

OK, I got it backwards. The points in the Mandelbrot set are the points whose Julia sets are “nice”.

That needs a bit more explanation, doesn’t it?

For each complex number c, there is a corresponding Julia set J©. The Mandelbrot set M is the set of points whose corresponding Julia set is connected.

A set is connected if you can pick any two points in that set and connect them with a curve that’s entirely inside the set. So 0 is connected, but i is not. Is that clear?

Sure. Oh, what was that middle part again? :slight_smile:

By the way, they have done this for a variety of holidays and birthdays. I don’t know how they decide whose birthdays are worthy, but there you go. The 40th anniversary of the Beatles’ first USA appearance is coming up. I wonder if they’ll do something for that.

To put it in terms of the images that we see, black points are points in the Mandelbrot set. The color of any point in the Mandelbrot map is the same as the color of the very center point in the corresponding Julia map. This site lets you play around with it. If you click on a black point, the Julia map that pops up will be black in the center.

If a Julia map has a black center, it will have areas that are black, which are all connected. If not, it won’t. Some of the images you generate there will have a non-black center but black regions, but this is only because the number of iterations isn’t high enough. If it was taken to infinity, all the black areas would be taken over by color.

That’s Mondelbreight, bubbemeintzeh.