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.
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.
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.
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:
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.
[+] [-] schoen|4 years ago|reply
It looks like these prizes are still open.
[+] [-] OnlyOneCannolo|4 years ago|reply
Article: "by Stephen Wolfram"
[+] [-] ChrisArchitect|4 years ago|reply
https://news.ycombinator.com/item?id=21130098
[+] [-] DeepYogurt|4 years ago|reply
> ... then applying the following simple rule:
Some pictures with no description
Really? Follow the link and it's a 45 page pdf.
[+] [-] concreteblock|4 years ago|reply
* 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.
[+] [-] zen_of_prog|4 years ago|reply
[+] [-] kolbe|4 years ago|reply
[+] [-] concreteblock|4 years ago|reply
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.
[+] [-] schoen|4 years ago|reply
https://www.wolframscience.com/prizes/tm23/
[+] [-] 0-_-0|4 years ago|reply
[+] [-] lifthrasiir|4 years ago|reply
[+] [-] Taniwha|4 years ago|reply
[deleted]