Few months ago, I gave a presentation on R Shiny Apps to an FPM (PhDs) class. Although the session was quite brief in itself, we developed a small central limit theorem demonstrator. Its not feature rich or anything -- just serves the purpose of "seeing" central limit theorem.
The app can be accessed here: http://harshvardhan.shinyapps.io/shiny/.
Central Limit Theorem: https://en.wikipedia.org/wiki/Central_limit_theorem.