Taking a look at the raw data on Wolfram Alpha, it seems like a lot of the super low income countries are muddying the data. There are many low income countries with Gini coefficients all across the spectrum. I don't have the time to do it now, but you might find a pattern in the data if you filter out countries with GDP/capita <$5000 or <$10000.
For some reason, the plot defaulted to log for me. If you put it in linear mode, you can probably eyeball it. I mean we're looking for an obvious trend and it appears to just be completely random.
