Exploratory vs. explanatory visualization
Although exploratory and explanatory visualizations have slightly different aims—to discover hidden patterns vs. to communicate insights and messages in the data—good exploratory visualizations explain what is going on and good explanatory visualizations let people explore the ideas.
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Animation and interactivity can be surprisingly effective in explaining complex mathematical concepts or techniques. For instance, take a look at Bret Victor's article "Explorable Explanations" (play with the examples), or this amazing projects called "Explained Visually", which is inspired by the "Explorable Explanations". Here are more of my favorite examples: Animated Bézier curve beautifully explain the algorithm of Bézier curve, which is a popular method to draw arbitrary smooth curves. Mike Bostock, the creator of
D3.js, made many superb explanatory visualizations including Visualizing algorithms where he demonstrate the power of visualization to explains complex algorithms. Here are other great examples: