Announcing the Rule 30 Prizes (2019)(blog.wolfram.com)
blog.wolfram.com
Announcing the Rule 30 Prizes (2019)
https://blog.wolfram.com/2019/10/01/announcing-the-rule-30-prizes/
18 comments
(2019); more at: https://www.rule30prize.org/
It looks like these prizes are still open.
It looks like these prizes are still open.
Man I hate how that guy writes.
> ... then applying the following simple rule:
Some pictures with no description
Really? Follow the link and it's a 45 page pdf.
> ... then applying the following simple rule:
Some pictures with no description
Really? Follow the link and it's a 45 page pdf.
In case anyone is wondering, the way to interpet the rules is as follows.
* The state of the system is a black-white assignment of colors to the grid.
* The rules tell you how to compute the next state of the system.
* To update the state at a certain cell x, you look at the colors of x-1, x and x+1. (left, self, and right). Then use use the table of rules to determine the new color of the middle cell. For instance, the first rule tells you that if you see three black cells in a row, then in the next time step the middle cell is white.
* This update is done simultaneously over all cells, so you compute all the new cell colors and then update them all at once.
* The state of the system is a black-white assignment of colors to the grid.
* The rules tell you how to compute the next state of the system.
* To update the state at a certain cell x, you look at the colors of x-1, x and x+1. (left, self, and right). Then use use the table of rules to determine the new color of the middle cell. For instance, the first rule tells you that if you see three black cells in a row, then in the next time step the middle cell is white.
* This update is done simultaneously over all cells, so you compute all the new cell colors and then update them all at once.
If the pattern matches the top three tiles, then the tile below is defined by the bottom tile in the rules. This is done top down, row by row for each 3-tile section of a row. You're totally right though.
Just so I understand; some tile on row n in column m would depend on three tiles in row n-1 where those three would be in columns m-1, m, and m+1?
How does that work for edges and for the first tile? Also is the pattern just implicitly started with a single tile?
Thanks for the explanation :)
How does that work for edges and for the first tile? Also is the pattern just implicitly started with a single tile?
Thanks for the explanation :)
Yes, that's correct.
There are no edges, it's an infinite grid. You start with 1 black cell and all the other cells are white.
Because the triple-white configuration does not produce a black cell, you can compute up the any finite time step with finite computational power.
(Actually, later in the article he talks about finite grids with periodic boundary conditions. That means that, if you're on the edge, you 'wrap around' to the other side of the grid).
There are no edges, it's an infinite grid. You start with 1 black cell and all the other cells are white.
Because the triple-white configuration does not produce a black cell, you can compute up the any finite time step with finite computational power.
(Actually, later in the article he talks about finite grids with periodic boundary conditions. That means that, if you're on the edge, you 'wrap around' to the other side of the grid).
Gotcha. Thanks for taking the time :)
I don’t think anyone on Earth has obsessed over Rule 30 as much as Stephen Wolfram. And I think there are maybe single-digit number of people who are more intelligent than he is. So, if he can’t answer some Rule 30 related problem, I seriously doubt anyone else can.
The problem seems to have the same flavor as the Collatz conjecture. Simple dynamical system - very difficult to tell what happens in the long run.
Perhaps these things are too hard for (human) mathematics. I wonder if anyone has proved any theorems that make this precise. E.g. "Most cellular automata rules cannot be analyzed efficiently".
I don't know enough complexity theory/set theory to formulate this precisely.
Perhaps these things are too hard for (human) mathematics. I wonder if anyone has proved any theorems that make this precise. E.g. "Most cellular automata rules cannot be analyzed efficiently".
I don't know enough complexity theory/set theory to formulate this precisely.
> Perhaps these things are too hard for (human) mathematics.
I'm guessing this thought is partly inspired by Erdős's remark about the Collatz conjecture?
https://hsm.stackexchange.com/questions/6389/paul-erdos-quot...
I'm guessing this thought is partly inspired by Erdős's remark about the Collatz conjecture?
https://hsm.stackexchange.com/questions/6389/paul-erdos-quot...
Though, to be fair, Wolfram did run a previous prize contest about a conjecture that he had thought about but not solved, and someone else successfully solved it:
https://www.wolframscience.com/prizes/tm23/
https://www.wolframscience.com/prizes/tm23/
And that was all about proving that Rule 110 was capable of universal computation. (They first found a way to map Rule 110 to the tag system put forth in that prize.)
This zoo of 3-predecessor cellular automata is an impressive lot.
This zoo of 3-predecessor cellular automata is an impressive lot.
Intelligence is not the only relevant factor. You probably know a lot of things that the most intelligent person on the planet doesn't. Some of those things might help you solve a problem that nobody can.
It's probably the other way around: Wolfram wants to make more people obsessed over Rule 30.
It's not really about Rule 30 specifically. It's more about Rule 30 being a particularly simple example, probably, of Wolfram's Principle of Computational Irreducibility.
From what I can tell, he'd love to drop that "probably", or move on from Rule 30 to the next simplest system that could possibly work.
From what I can tell, he'd love to drop that "probably", or move on from Rule 30 to the next simplest system that could possibly work.
Plenty of old discussion on the main site
https://news.ycombinator.com/item?id=21130098
https://news.ycombinator.com/item?id=21130098
Article: "by Stephen Wolfram"