This video explores the mathematical concept of approximation in terms of both qualitative and quantitative aspects.
Qualitative aspects of approximation theory are shown along the vertical axis: the same images are approximated using four qualitatively different dictionaries (consisting of straight lines, curves, frames from Godard's movie Alphaville, and Chinese characters).
Quantitative aspects of approximation theory are shown along the horizontal axis: the same images are approximated using more and more elements from each of the four dictionaries. As more elements are used, the reconstruction is closer to the original image but the distinctive character of the dictionary becomes less marked.
This video is part of the Approximation Theory project by Felipe Cucker and Hector Rodriguez. More information on the project at: