I am trying to convert grayscale images to black and white, where I hope to have certain artistic effect, called stippling:

I have tried two methods; dithering (with ColorQuantize)

and a stochastic method, where the probability of a pixel being black is proportional to the darkness of corresponding picture:

The image I applied this to is the following:

So, the dithered image is "too regular" in some sense and seems to be too local, there is too much white on the top.
The stochastic version is too irregular; real randomness can give clusters, which is undesirable in this case. The artistic picture above have much fewer clusters of dots/pixels, and gives a nice uniform distribution in areas of similar shade. So, what I seek is something between the dithered and the stochastic version, where the dots are all somewhat "repelling".