Having done this for a course I taught in the past, the most common issue I always see people having is going outside the bounds of the array they're using.
If you look at the if statements in your nested for loop, I think you'll find some issues. For instance, in this case, what happens when iii equals (height-1) or jjj equals (width-1)?
for (int iii = 0; iii < height; iii++) {
for (int jjj = 0; jjj < width; jjj++) {
//Count neighbouring cells that are alive
if (now_world[iii+1][jjj+1] == true) {
++neighbours;
You're going outside the bounds of your array and so your results will be undefined. You may get segfaults, but you may just also get spurious data. C++ doesn't enforce you staying within the bounds of the array you define.
Make sure you also handle cases like this:
if (now_world[iii-1][jjj+1] == true) {
++neighbours;
}
What if iii equals zero?
Hope that helps.