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Computer experiments and visualization in mathematics and physics. A subjective short walk among some historical examples

In this short essay, we show how computer experiments, and especially visualization, allowed for the investigation and discovery of phenomena which would have passed unnoticed. We shall also highlight the importance of interactivity between the computer and the user. We do this by surveying several historical examples from mathematics and the physical sciences. Many pictures, and even hyperlinks to online interactive numerical experiments, are provided. Needless to say that we do not claim to be exhaustive, and that the chosen examples reflect our taste as well as our limited knowledge. Hyperlinks to several online interactive digital experiments are provided.