Stephen Wolfram

about Rule 30, I would say this is one of those cases where the money is not the main point, but it just helps motivate somehow the investigation.

No, it's $10,000 for each.

It's just, you know, will it ever become periodic?

Second problem is, are there an equal number of black and white cells?

Down the middle column.

Down the middle column.

And the third problem is a little bit harder to state, which is, essentially, is there a way of figuring out what the color of a cell at position T down the center column is with a less computational effort than about T steps?

So in other words, is there a way to jump ahead and say, I know what this is going to do.

You know, it's just some mathematical function of t. Or proving that there is no way.

Or proving there is no way, yes.

But both, I mean, you know, for any one of these, one could prove that, you know, one could discover, you know, we know what rule 30 does for a billion steps.

And maybe we'll know for a trillion steps before too very long.

But maybe at a quadrillion steps, it suddenly becomes repetitive.

Yeah.

You might say, how could that possibly happen?

But so when I was writing up these prizes, I thought, and this is typical of what happens in the computational universe, I thought, let me find an example where it looks like it's just going to be random forever, but actually it becomes repetitive.

And I found one.

And it's just, you know, I did a search.

I searched, I don't know, maybe a million different rules with some criterion.

And this is