Bird-song attractors

Revealing hidden phase‑space attractors in bird vocalizations

This project explores the hidden dynamics of birdsong using nonlinear time-series analysis.

Birdsong is more than just melodious tunes; it's a complex interplay of biological systems. By applying concepts from nonlinear dynamics, we've uncovered hidden geometric patterns—swirling loops and spirals—that traditional audio analyses often overlook.

🎶 The Complexity Behind Birdsong

Producing birdsong involves a coordinated effort between:

Respiratory Mechanics: Airflow from the lungs.
Syrinx: The avian vocal organ located at the base of the trachea.
Neural Control: Brain regions that regulate timing and pitch.

These systems interact across multiple time scales, resulting in the intricate vocalizations essential for avian communication. Traditional analyses, like spectrograms, capture frequency and amplitude but often miss the underlying dynamics of these interactions.

🎨 Art using Attractors

▶️Interactive demos

📊 Methods

🐦 Species Gallery

Here you can see the attractor patterns

Featured Birds

Red headed bullfinch

Cordillera Azul Antbird

Aberrant Bush Warbler

Visualizing the hidden attractor patterns with Takens' Embedding ?

Using Takens' Time-Delay Embedding Theorem, we can reconstruct the phase space of a bird's song from a single time series. This method reveals:

Attractors: Geometric representations of the system's dynamics.
Loops and Spirals: Indications of repetitive patterns and modulations.
Dimensionality: Insights into the complexity of the vocalization process.

Our Discoveries

Through this approach, we've identified:

Conditional Looping: Not all recordings exhibit loops, but when present, they reflect real syringeal vibration cycles.
Amplitude Envelope: Loop size correlates with changes in loudness.
Frequency Modulation: Loop rotation reveals pitch slides and trills.
Topological Patterns: Unique structures that may serve as species-specific signatures.

How Takens' Time-Delay Embedding Works

Takens' embedding reconstructs the hidden dynamics of a system using only a single observable — like amplitude over time in a birdsong.

It works by creating vectors from delayed versions of the signal:

Each vector represents a state of the system in an m-dimensional space. Plotting these points reveals the attractor — a shape that captures how the system evolves over time.

This method lets us “see” the system’s dynamics, even when we only have one measured variable.

🧪 Try it yourfself - Upload Your Own Recording

Interactively explore the reconstruction of dynamical attractors from birdsong recordings using Takens' embedding theorem.

This demo allows you to:

Apply time-delay embedding to real birdsong data.
Adjust the embedding dimension and time lag parameters.
Visualize the reconstructed attractor in 3D.
Observe how changes in parameters influence the topological structure of the attractor.

👉 Launch Demo App: Attractor Reconstruction from Sound

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