How can I convert a monochrome gradient into a dot gradient of only two colors (B&W)

Been scratching my head over this one for a while now. I have an image that has a simple monochrome gradient that goes from black to white. Unfortunately, I need to create an iron-on transfer that will only accept two colors, black and white (it will not accept gray or color of any kind). Is there any way of converting the monochrome gradient to a series of black dots that becoming increasingly denser the darker the gradient becomes?

It would essentially be what a printer does, using dots per square inch to create the fade; I simply need to handle that part in Photoshop first. It doesn't need to be 100% true to the gradient, just something close enough. Any help would be greatly appreciated!

Filter -> Pixellate -> Color Halftone
will get you started.