If I wanted to display data in an interactive way not available through any existing tools, where do I begin? Is there a language/platform/framework?

1

Matplotlib

If you want to do something local, matplotlib is a pretty decent tool.

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2

D3.js

If you want to do this on the web, D3js is pretty neat.

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3

Shiny

But you might consider Shiny, which doesn't get recommended a lot, but is a very flexible interactive data visualization tool. You have to be willing to R, though.

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