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Are there any other algorithms that can have these kinds of animations applied? Sorting works well and is easy to animate. What about graph traversal or network flow? I guess my real question is 'can all algorithms be animated in some way'? If not what decides it? If there were more than 4 dimensions I could see that being a problem right there.

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What's the best way to instrument an algorithm for visualization? Snapshot its state at periodic, well-named points, and render illustrations?

I can imagine doing this with an A* search: snapshot the graph, including which nodes are open or already visited, along with the heap ranking of the next nodes to visit. You might also want to show all the newly neighboring nodes and annotate them with their updated cost estimate.

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