Fourier series
Series of sinusoidal wave functions that get added together to generate a different, more complex function. In the context of morphogenesis (form generation), any line drawing can be "deconstructed" into a series of arc segments which can in turn be represented by a series of circles whose radii and rotation speeds correspond to the radii and lengths of the arc segments.
Fourier series and Fourier transforms are deeply mathematical topics with applications and research far beyond the scope of this resource list. They are extremely useful in the field of digital signal processing for noise reduction, compression, audio analysis, and so much more. A very well-known algorithm known as the fast Fourier transform (FFT) enables extraction of waveforms from music for the purposes of audio visualization.
Articles:
- Fourier series on Wikipedia
- Fourier Series on Wolfram MathWorld
- Fourier Series on Math Is Fun
Videos:
- What is a Fourier Series? (Explained by drawing circles) by Smarter Every Day
- But what is the Fourier Transform? A visual introduction by 3Blue1Brown
- Coding Challenge #125: Fourier Series by Daniel Shiffman
- Coding Challenge #130.1: Drawing with Fourier Transform and Epicycles by Daniel Shiffman
- Coding Challenge #130.2: Fourier Transform User Drawing by Daniel Shiffman
- Coding Challenge #130.3: Fourier Transform Drawing with Complex Number Input by Daniel Shiffman