You can do this in the Illustrator as well using the same filters(Effect/Pixelate/Color Halftone) but here am showing how to do it in the Photoshop.

Create a big black dot on a transparent layer with a white background

apply gaussian blur to the dot layer

Now merge all the layers(Ctrl+Shift+E) and apply halftone effect with following details.
(Filter/Pixelate/Color Halftone)

Then you can take this image to Illustrator and apply live trace filter to get a verctor output.

Note: You can run the color noise filter more than once to get the effect you want - repeat applications to the effect seem to widen it.

I just came across a good tutorial on this:
http://vectips.com/tutorials/creating-halftone-effects/

there are also a few tools/tutorials for creating this
kind of effect at bittbox