Problem 52. What is the next step in Conway's Life?

Created by Cody Team

Solve Later

Given a matrix A that represents the state of Conway's game of Life at one instant (time t=n), return the matrix B that represents the state of the game at the next instant (time t=n+1).
Assume a toroidal game board, so the edges of the matrix wrap left to right and top to bottom.
Examples:
 Input  A = [ 1   1   0   0
              0   1   0   0
              1   1   0   0
              0   0   0   0 ]
 Output B = [ 1   1   0   0
              0   0   1   0
              1   1   0   0
              0   0   0   0 ]
 Input  A = [ 0   1   1   0
              1   1   1   0
              0   0   1   0
              0   0   0   0 ]
 Output B = [ 1   0   1   1
              1   0   0   0
              0   0   1   1
              0   1   1   0 ]

Solve

Solution Stats

3870 Solutions
661 Solvers

Last Solution submitted on Oct 03, 2025

Last 200 Solutions

Problem Comments

12 Comments

12 Comments

Show 9 older comments

David Young on 5 Feb 2012

I think test sets should be designed to encourage general solutions. At present, the test set only has square boards - some more varied examples would make solvers seek code that is general.

mItk on 17 Oct 2016

Is there something wrong with the test suite? function B = life(A) B = A; end produces "Error using life Too many output arguments." See comment on solution 1019804.

mItk on 17 Oct 2016

I suppose the error "Error using life Too many output arguments." is due to shadowing. It seems thet test suite calls \toolbox\matlab\demos\life.m

shahriar memaran on 9 Mar 2017

I had so much fun with this problem. Thank you.

David Verrelli on 7 Feb 2018

Is there a syntax flaw in the Test Suite? Currently the first test displays with a first line of "%%A = [ ...", and in my solution (S 1435695) only the second test is displayed. Although apparently the first test is still being called (S 1435709)?

Hugo on 4 Mar 2022

Game of life is soo cool!

Brandon on 26 Jun 2023

There's a popular solution that is wrong, and people keep posting it. I am highly amused.

Peter on 22 Aug 2023

@Cody Team
The link to "Conway's game of Life" is blank!

Dyuman Joshi on 22 Aug 2023

Thanks for notifying @Peter, I have updated the link.

Jonah on 9 Sep 2023

Am I misunderstanding the rules to the game, or are two of the solutions that the site checks against incorrect

Yufei on 22 Jun 2024

I think the two of the solutions are wrong. Because it may misunderstand the corner...

Matthew on 14 Jul 2025

Pretty neat problem! I made an animation of a toroidal game board of size 100x100. Super cool to see all the bits flipping and patterns.

Solution Comments

Show comments

Problem Recent Solvers661

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 52. What is the next step in Conway's Life?

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers661

Suggested Problems

More from this Author96

Problem Tags

Community Treasure Hunt

Problem 52. What is the next step in Conway's Life?

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers661

Suggested Problems

More from this Author96

Problem Tags

Community Treasure Hunt

Players