How to fill a shape with a dot grid

1. Apply a solid fill to the path.

2. Object>Rasterize.

3. Object>Create Object Mosaic. Use Ratio. Delete Raster.

4. Ungroup.

5. Select one of the resulting white rectangles. Select>Same>Fill & Stroke.

6. Delete.

7. Select all the remaining rectangles.

8. Effect>Convert To Shape>Ellipse. Absolute.

That will give you whole circles.

JET

You can do something like this by creating an object mosaic of the map. Then use Round Corners and Transform Each to modify the mosaic tiles.

I know it sounds trivial, but using Area Type Tool works quite well. Simply type zillions of dots, inside the map shape, in a preferred font family (Arial Rounded?), adjust the font size, leading, baseline shift, and tracking for best result. I promise interesting and diversified results . After you're satisfied, create outlines.

mpc,

You may create a large dot pattern extending past the factor shape and expand it so you have individual dots, then simply delete the unwanted dots; you can do that in larger numbers, and decide whether each individual dot that is both inside and outside should extend past the factor shape or be deleted.

To create and expand the dot pattern, you may start with a single dot, then use Effect>Distort&Transform>Transform with a horizontal Move and many copies, then the same vertical move with many copies, then Object>Expand Appearance.