Fourier (Manim)

This repo contains a few Manim Community scenes for Fourier/epicycle style animations, plus a reusable mobject FourierCircles.

Project layout

• fourier_manimCE.py
  • ComplexWave (sum of cosines)
  • FourierStandardFixed2 (epicycles)
  • PiecewiseExample
• mobjects/fourier_circles.py
  • FourierCircles: reusable epicycle/circle-chain mobject
• media/
  • Manim render outputs

Setup

Create and activate a virtualenv, then install dependencies:

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

Notes:

• Manim requires system dependencies (e.g. FFmpeg, LaTeX) depending on your scene.
• On macOS, you typically install FFmpeg via Homebrew:

brew install ffmpeg

FourierCircles mobject

FourierCircles takes a shape (path/Text/MathTex/SVG), samples it, computes Fourier coefficients, and draws an animated chain of circles + vectors.

Minimal usage

from manim import *
from mobjects.fourier_circles import FourierCircles

class Demo(Scene):
    def construct(self):
        epicycles = FourierCircles(
            input_graph=MathTex(r"\pi"),
            vector_number=100,
            n_samples=2000,
            vector_type="arrow",
        )
        self.add(epicycles)
        start_t = epicycles.vector_clock.get_value()
        end_t = 2
        self.play(
            UpdateFromAlphaFunc(
                epicycles,
                lambda m, a, s=start_t, e=end_t: m.set_value(interpolate(s, e, a)),
            ),
            run_time=10,
            rate_func=linear,
        )

Accepted input types

• VMobject/path with point_from_proportion (custom paths)
• Text, Tex, MathTex (a subpath is automatically selected)
• SVG file path or SVGMobject

Examples:

FourierCircles(input_graph="high_clef.svg", vector_number=120)
FourierCircles(svg_file="high_clef.svg", vector_number=120)
FourierCircles(input_graph=SVGMobject("high_clef.svg"), vector_number=120)

Vector style

• vector_type="line" or vector_type="arrow"

Size / fitting controls

• Scale epicycle size: scale_factor=... (alias size=...) scales all coefficients.
• Auto-fit (mainly for Text/MathTex):
  • auto_fit=True/False
  • fit_fraction=0.7 (default)
  • fit_height=..., fit_width=...
  • force_fit=True (force fit even for SVG/path inputs)

Endpoint helper

Use get_end() to trace the final tip:

trace = TracedPath(epicycles.get_end)
trace.set_stroke(YELLOW, 3)
self.add(trace)