Neural Oscillation Simulator: Brainwaves, Coupling & EEG Rhythms

simulator intermediate ~10 min
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f_dom = 10 Hz α — classic posterior alpha rhythm

Default parameters produce a dominant 10 Hz alpha rhythm with moderate theta-gamma coupling, simulating the resting-state EEG of a relaxed, eyes-closed adult.

Formula

x(t) = A_α × sin(2π × f_α × t) + A_γ × (1 + κ × sin(2π × f_θ × t)) × sin(2π × f_γ × t)
P_α = A²_α / 2 (spectral power)
MI = κ × A_θ / A_γ (modulation index)

Rhythms of the Mind

The brain never rests — even in silence and darkness, billions of neurons fire in coordinated rhythmic patterns detectable as electrical oscillations on the scalp. These brainwaves, first recorded by Hans Berger in 1929, span frequencies from the slow delta waves of deep sleep to the rapid gamma oscillations of conscious perception. This simulator lets you compose and visualize the spectral landscape of neural activity.

Frequency Bands and Function

Each frequency band is associated with distinct cognitive states. Alpha (8-13 Hz) dominates relaxed wakefulness and may actively inhibit irrelevant cortical regions. Beta (13-30 Hz) is linked to motor planning and maintaining the current cognitive set. Gamma (30-100+ Hz) emerges during perceptual binding, attention, and working memory. Theta (4-8 Hz) in the hippocampus is critical for memory encoding and spatial navigation.

Cross-Frequency Coupling

The brain's oscillatory bands do not operate independently — they interact through cross-frequency coupling. In theta-gamma coupling, the phase of slow theta oscillations modulates the amplitude of fast gamma bursts. This 'neural syntax' may organize discrete items in working memory: each gamma burst within a theta cycle represents one memory item, explaining why working memory capacity correlates with the theta/gamma frequency ratio.

Clinical Significance

Abnormal oscillatory patterns are biomarkers for neurological and psychiatric conditions. Excessive theta in ADHD, reduced gamma synchrony in schizophrenia, and pathological beta oscillations in Parkinson's disease all illustrate how disrupted rhythms impair cognition. Neurofeedback and transcranial alternating current stimulation (tACS) attempt to restore normal oscillatory patterns as therapeutic interventions.

FAQ

What are neural oscillations?

Neural oscillations are rhythmic patterns of electrical activity generated by synchronized populations of neurons. They span a wide frequency range: delta (1-4 Hz) in deep sleep, theta (4-8 Hz) in memory encoding, alpha (8-13 Hz) in relaxed wakefulness, beta (13-30 Hz) in active thinking, and gamma (30-100 Hz) in perceptual binding.

What is phase-amplitude coupling?

Phase-amplitude coupling (PAC) occurs when the phase of a slow oscillation modulates the amplitude of a faster oscillation. For example, gamma burst amplitude is often maximal at a specific phase of theta — this cross-frequency coupling may organize neural computations into temporal windows.

What does alpha rhythm mean?

The alpha rhythm (8-13 Hz) was the first brainwave discovered by Hans Berger in 1929. It is strongest over posterior regions during relaxed wakefulness with eyes closed and is thought to reflect cortical 'idling' or active inhibition of task-irrelevant regions.

How are neural oscillations measured?

Neural oscillations are primarily measured using electroencephalography (EEG) — electrodes on the scalp detect voltage fluctuations from synchronized postsynaptic potentials. Magnetoencephalography (MEG) and intracranial recordings provide complementary spatial and temporal resolution.

Sources

Embed

<iframe src="https://homo-deus.com/lab/cognitive-neuroscience/neural-oscillation/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub