OpenMP in Biham-Middleton-Levine BML model - multithreading

Question

I've got a serial version of BML and I'm trying to write a parallel one with OpenMP. Basically my code works with a main witin a loop calling two functions for horizontal and vertical moves. Like that:
for (s = 0; s < nmovss; s++) {
horizontal_movs(grid, N);
copy_sides(grid, N);
cur = 1-cur;
vertical_movs(grid, N);
copy_sides(grid, N);
cur = 1-cur;
}
Where cur is the current grid. Then horizontal and vertical functions are similar and have a nested loop:
for(i = 1; i <= n; i++) {
for(j = 1; j <= n+1; j++) {
if(grid[cur][i][j-1] == LR && grid[cur][i][j] == EMPTY) {
grid[1-cur][i][j-1] = EMPTY;
grid[1-cur][i][j] = LR;
}
else {
grid[1-cur][i][j] = grid[cur][i][j];
}
}
}
The code produces a ppm image at every step, and whit a certain input the serial version produce an output that we can suppose good. But using #pragma omp parallel for inside the two functions H and V, the ppm file results splitted in such zones as the number of threads(i.e. 4):
I suppose the problem is that every thread should be doing both functions in sequence before termitate because movememnts are strictcly connected. I don't know how to do that. If I set pragma at a highter level like before main loop, there is no speed-up. Obviously the ppm file has to be not sliced like the image.

Answer 1

Goin'on I tried this solution that gives me an identical result as the serial code, but I don't excatly understand why
# pragma omp parallel num_threads(thread_count) default(none) \
shared(grid, n, cur) private(i, j)
for(i = 1; i <= n+1; i++) {
# pragma omp for
for(j = 1; j <= n; j++) {
if(grid[cur][i-1][j] == TB && grid[cur][i][j] == EMPTY) {
grid[1-cur][i-1][j] = EMPTY;
grid[1-cur][i][j] = TB;
}
else {
grid[1-cur][i][j] = grid[cur][i][j];
}
}
}
}
Therefore, if i use just one thread more than available cores(4), the execution time "explodes" instead of remain barely the same.