Announcing the Rule 30 Prizes (2019)
blog.wolfram.com
Announcing the Rule 30 Prizes (2019)
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Re: Announcing the Rule 30 Prizes (2019)
#2Title: "A man"
Article: "by Stephen Wolfram"
Re: Announcing the Rule 30 Prizes (2019)
#3(2019); more at: https://www.rule30prize.org/
It looks like these prizes are still open.
Re: Announcing the Rule 30 Prizes (2019)
#4Man 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.
Re: Announcing the Rule 30 Prizes (2019)
#5I 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.
Re: Announcing the Rule 30 Prizes (2019)
#6Man 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.
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.
Re: Announcing the Rule 30 Prizes (2019)
#7Man 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.
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.
Re: Announcing the Rule 30 Prizes (2019)
#8Man 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.
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 :)
Re: Announcing the Rule 30 Prizes (2019)
#9I 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.
Re: Announcing the Rule 30 Prizes (2019)
#10Earlier quoted context omitted.
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 :)
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).