I've been playing with shadertoy a bit, and here is a lil demo. It's probably not the best way to do it, code suggestions welcome.

https://www.shadertoy.com/view/dtlBRM

Here's most of the code for reference:

void mainImage( out vec4 fragColor, in vec2 fragCoord )
{
    // fetch neighbor values from last frame, loop back onto screen if off screen
    mat3 n;
    n[0][0] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(-1., -1.), iResolution.xy)), 0).g;
    n[1][0] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(0., -1.), iResolution.xy)), 0).g;
    n[2][0] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(1., -1.), iResolution.xy)), 0).g;
    n[0][1] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(-1., 0.), iResolution.xy)), 0).g;
    n[1][1] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(0., 0.), iResolution.xy)), 0).g;
    n[2][1] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(1., 0.), iResolution.xy)), 0).g;
    n[0][2] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(-1., 1.), iResolution.xy)), 0).g;
    n[1][2] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(0., 1.), iResolution.xy)), 0).g;
    n[2][2] = texelFetch(iChannel0, ivec2(mod(vec2(fragCoord) + vec2(1., 1.), iResolution.xy)), 0).g;
    
    // sum of neighbors
    float sum = n[0][0] + n[1][0] + n[2][0] +
                n[0][1] +           n[2][1] +
                n[0][2] + n[1][2] + n[2][2];
                
    if(n[1][1] == 0.) {
        if(sum == 3.) {
            // if dead and has 3 neighbors, come alive
            fragColor = vec4(0., 1., 0., 1.);
        } else {
            // otherwise stay dead
            fragColor = vec4(0., 0., 0., 1.);
        }
    } else {
        if(sum == 2. || sum == 3.) {
            // if alive and has 2 or 3 neighbors, stay alive
            fragColor = vec4(0., 1., 0., 1.);
        } else {
            // otherwise, die
            fragColor = vec4(0., 0., 0., 1.);
        }
    }
}