[T.K.]

Thank you blenderificus for the comments. Here is the PyNodes script I made.

 
from Blender import Node
import math
 
sqrt_2 = math.sqrt(2)
 
class DotsNode(Node.Scripted):
    def __init__(self, sockets):
        radius = Node.Socket('radius', val=4*[1.0])
        grid = Node.Socket('grid', val=10.0, min=1.0, max=100.0)
        fg_color = Node.Socket('fg_color', val=3*[0.0]+[1.0])
        bg_color = Node.Socket('bg_color', val=4*[1.0])
        color = Node.Socket('color', val=4*[1.0])
        sockets.input = [radius, grid, fg_color, bg_color]
        sockets.output = [color]
 
    def nearest(self, coords, grid):
        """Return the nearest grid coordinate to coords."""
        x, y = coords
        gx, mx = divmod(x, grid)
        gy, my = divmod(y, grid)
 
        x = gx * grid
        y = gy * grid
 
        if gx % 2 == gy % 2:
            if grid - mx > my:
                return x, y
            else:
                return x+grid, y+grid
        else:
            if mx > my:
                return x+grid, y
            else:
                return x, y+grid
 
    def __call__(self):
        input = self.input
        coords = [self.shi.pixel[0], self.shi.pixel[1]]
        grid = input.grid # pixels
        radius = (1.0 - input.radius[0]) * grid
 
        # Get the square distance from coords to nearest grid point
        nearest = self.nearest(coords, int(grid / sqrt_2))
        sqdist = (coords[0]-nearest[0])**2 + (coords[1]-nearest[1])**2      
 
        # if sqdist is less than the scaled radius squared than color one
        if sqdist < radius**2:
            self.output.color = self.input.fg_color
        else:
            self.output.color = self.input.bg_color
 
__node__ = DotsNode

I also uploaded the movie clip to Vimeo and added a new link to it to the last post.
IMHO the compression quality is not satisfactory. I will learn more how to upload
movie clips to Vimeo in a better quality.