Harry Beck used a fish eye distortion for this exact purpose, when he designed the classic London Tube map in 1931. The scale is larger in the dense inner city, where the stations are closer together, and smaller in the outer suburbs, where the stations are further apart. The net effect is that the density of the stations is roughly constant across the map.<p>[1] <a href="https://en.wikipedia.org/wiki/Harry_Beck" rel="nofollow">https://en.wikipedia.org/wiki/Harry_Beck</a>
It's great that the distortion isn't done on a pixel level but rather at the object level -- it's mesmerizing to see the edges move ever so slightly when mousing over a region
It's funny how the objects at the edge of the distortion are compressed; information here is lost rather than created. I'd rather see the distortion spread to the image boundaries. Then I can still see the whole image, but there is no weird annulus of compression.