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Please help me identify and understand this visual pattern, what's the common name used for such mindmap / constellation visualisations?

http://asterisq.com/products/constellation/roamer/demo

http://apps.asterisq.com/mentionmap/#user-scobleizer

I am also looking a for a framework, library or math formula that will help me build something similar. I am especially interested in the auto arranging functionality as I will have plenty of nodes that I need to arrange on the screen in the best possible fashion. What's the math behing auto arranging somethoing in 2D?

I also need combine to that all with extensive zooming and map-like navigation.

If you know about anything that could help achieve my goal please don't hesitate to leave an answer.

My preferred language is ActionScript 3 / Flash but I will be thankful for any info, tutorial or article in any language.

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    check out graphvis. Commented Jul 3, 2011 at 20:42

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The most general term for these is (I think) a node-link diagram of a graph. There are a number of JavaScript libraries out there that can do these. I don't know anything about ActionScript, but maybe they can be used there or converted. Here's a couple of good ones:

D3

ProtoVis

If you google for JavaScript or ActionScript Visualisation Libraries (or similar) you may find one that suits your purposes better.

And here's an ActionScript one (not a Flash user so no idea if it's any good): Flare

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