Any signal can be decomposed to arbitrary precision as the sum of increasingly higher frequency sin and cosine functions, referred to as the basis. wikipedia 
Joseph Fourier wikipedia
In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. wikipedia
Sketch by Stuart Jantzen rendered by Mike Bostock
Grant Sanderson asks,
Do any skilled artists out there have any interest in drawing an abstract sketch of Joesph Fourier's face with one line, preferably formatted as an svg (or some other vector format)? twitter
The Fourier series video out. In this animation, each vector rotates at a constant integer frequency. They're added together, tip to tail. The only control you have is the starting position of each, and from that alone, they'll draw almost anything. twitter
Mike Bostock repeats the feat and then analyzes it a half dozen ways. observable observable observable