This is how I managed to depict in C# the normal distribution of randomly falling pixels 
    in accordance with the placement rules (see Fig.), 
    white voids are shock waves in the Burgers equation.
    
            A:
                int rnd_x = rnd.Next(panel1.Width - razm);
                int ostatok = rnd_x % razm;
                rnd_x = rnd_x - ostatok;
                int ostatok_x = (panel1.Height ) % razm;
                rnd_P = new Point(rnd_x, panel1.Height - ostatok_x - razm);
                for (int i = 0; i < rnd_Ps.Length; i++)
                {
                  if((rnd_Ps[i].X == rnd_P.X) || (rnd_Ps[i].X  == rnd_P.X - razm) || (rnd_Ps[i].X  == rnd_P.X + razm))
                    {
                      rnd_P.Y = rnd_Ps[i].Y - razm; 
                    }                    
                }
                for (int i = 0; i < rnd_Ps.Length; i++)
                {
                    if (((rnd_Ps[i].X == rnd_P.X) || (rnd_Ps[i].X == rnd_P.X - razm) || (rnd_Ps[i].X == rnd_P.X + razm)) && (rnd_P.Y == rnd_Ps[i].Y))
                    { goto A; }
                }
                    Array.Resize(ref rnd_Ps, rnd_Ps.Length + 1);
                rnd_Ps[rnd_Ps.Length - 1] = rnd_P;