Algorithm (and tools) to create a weighted-cartogram from a shapefile?

Question

What algorithm can I use to produce a weighted-cartogram such as the one below: ?

I can generate a shapefile plot using code from R, .NET libraries and also using PostGIS. However I can't find the search terms to use to find an implementation of the algorithm used to produce these warped shapefile plots. Not necessarily looking to plot only world maps, so must be able to work with an arbitrary shapefile.

Answer 1

So as mentioned in the OP's comments, these are called area cartograms. The neatest lil implementation I know of is cartogram.js, which relies on the magical D3 library. If that page ever happens to go down, you should be able to find a similar page by Googling "D3 area cartograms", and if that doesn't get you anywhere then the original paper on the topic was Dougenik 1985.