I'd like for my image texture to repeat and taper off similar to a color halftone effect, here is a crude example of what I'm thinking I'd like to do with a cross shape image. Thanks!!
You could take the approach in this answer, substituting a blurred version of your dot-shape for the procedurally-generated square-cell distance-function. Depending on how your original is blurred, it will change shape when thresholds are taken on the intensity of the blurred shape.
Here is a method which scales the dot according to the intensity of the underlying image, instead. You may find, though, that in order to get dots which are sufficiently dark in some cells, your dot-shape would have to be clipped.
This version allows variation between a regular grid pattern for the dots, and a scattered distributuion, by changing the 'Randomness' field in a Voronoi node..
The nodes colored red allow pretty good control over the input contrast curve, base scale, and scale-multiplier. They may seem partially redundant, but I've found the combination easy to use.
As you can see, it's tricky to get dark-enough areas without clipping or overlapping your dot-shape..