Fourier drawing

The drawing on the home page is this example. Its notebook, examples/fourier.py, samples a closed path, computes its Fourier coefficients, and keeps the frequencies up to a slider's value. The scene turns one vector per coefficient and traces the tip of their chain, after 3Blue1Brown's But what is a Fourier series?

Notebookscene.pyExported page

Open the notebook and its view in Studio from a clone of the repository:

pixi run edit fourier

Two paths

Path	Sampled from	Vectors that draw it
manim-marimo mark	Five rotating vectors the notebook lists	5
TeX's italic m	The outline of $m$, from matplotlib's TextPath	Every one kept

manim-marimo's mark is marimo's looped circle drawn by rotating vectors: one turns four times while four short ones let the loops drift. The notebook samples it, and the Fourier transform finds exactly those five vectors again. TeX's italic m needs many more. Move the slider to see how few frequencies still read as an m.

The notebook computes the coefficients

all_coefficients = np.fft.fft(signal) / sample_count
frequencies = np.array([k for n in range(1, pairs.value + 1) for k in (n, -n)])

The scene reads terms, one [frequency, real, imaginary] row per vector with the longest first, and traced, the path the chain's tip draws in one turn:

terms = np.asarray(value("terms", default=[[1, 0.25, 0.0]]), dtype=float)
traced = np.asarray(value("traced", default=circle), dtype=float)

A second scene, spectrum.py, draws one stem per frequency with the vector's length as its height. The view's page plays both movies beside the notebook's controls and comparison cells.