Conway's Game of Life in J

Question

I have the following code which produces successive generations of Conway's Game of Life:

life =: 3 : '+./ (>(($ y) $ 1);y) *. > =&(+/ (>,{ ;~(1 0 _1))|. y) each 3 4'

Usage:

RR =: 5 7 $ 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0

NB. First five gens of RR
life^:(i.5) RR

NB. in ASCII
' *' {~ life^:(i.5) RR

Explanation of code:

>,{ ;~(1 0 _1)

Produces all possible 1 rotations of a matrix y.

|. y

Applies 1 rotations to y

+/

Adds all 1 rotations leading to neighbor-count for each cell

=&

Creates a monadic function which takes a single number and compares it to the neighbor-counts

each 3 4

Applies the function to 3 and 4 to find cells with 3 or 4 surrounding cells including self alive.

>

Unboxes to apply bitwise and

(>(($ y) $ 1);y)

I want all cells that correspond to 3 (($ y) $ 1) and only the cells that are already currently living the correspond to 4 (y).

+./

Or the result together to produce the next generation.

I would like to know if there's a better way to do this and shorten code. A lot of the things I did seem very hacky.

Answer 1

I have written APL code on VM/CMS and in DEC's VAX-11 interpreter.

No, I don't see a better way that would shorten the code.

Answer 2

I'm a J newbie myself, but how about:

life =: 3 : '+./ (>(($ y) $ 1);y) *. 3 4 =/ +/ (>,{ ;~(1 0 _1))|. y'

This avoids the box-unbox step caused by using each, and uses fewer chars.