Plotting multiple polygons as heatmaps?

I’ve been visualising some data using the pyplot fill function, and whilst overlapping polygons do mix their colours and allow for any overlaps to be apparent, I thought that perhaps this would look much better in a heatmap format to better show high levels of change in the same areas.

I’ve tested this using the histogram2d function in numpy using various online examples, and whilst experiments with random data looked nice enough, each set of results data is basically a series of 0’s and 1’s: In a heatmap using the same code, this results in an incredibly long (since there’s about 65000 results) heatmap that’s only a pixel or two in height. Also, I can’t seem to use the tools to zoom in and navigate around this, which is pretty much a requirement given the large number of data rows.

Does anyone know if there’s a way to convert a series of polygon objects into a decent looking heatmap? Any help is appreciated!