Sound-reactive environment

Twelve cosine plane waves at equal angular intervals, with the \(x\)-axis compressed by \(0.4\times\) before computing dot products. The compression concentrates fringes horizontally and stretches them vertically — the same mechanism as a diffraction grating producing elongated spectra. Hue is assigned by \(H = x \cdot 0.8 + I\pi\), so a left-to-right color sweep is modulated by the interference value at each pixel.

32 waveform samples are plotted as \((w(t),\, w(t + \tau))\) where \(\tau\) cycles through four lag values \(\pm 0.07\) and \(\pm 0.18\). A Gaussian density kernel accumulates over all points, so regions the signal visits often are brighter. Sustained tones trace closed ellipses; percussive transients produce short jagged bursts. Color shifts from cool to warm along the time axis of the trajectory.

Seven heptagonal waves each receive an independent phase offset \(\phi_k(t) = (k+1) \cdot 0.73 \cdot t\) rather than a shared time term. Because the drift rates are incommensurable, the pattern never exactly repeats — it samples an orbit on a seven-torus. The interference sum is passed through \(\frac{1}{2} + \frac{1}{2}\cos(I \cdot 3\pi)\), re-introducing three bands of high-contrast structure within the slowly morphing field.

The 256 FFT bins are arranged left to right (bass to treble); 256 frames of history scroll upward at 60 fps, covering roughly 4 seconds. Hue maps from warm red at the bass end to cool cyan at the treble end. Amplitude sets both lightness and chroma, so silence is black and a full-amplitude bin reaches maximum gamut chroma.

The spectrogram is mirrored left and right about the centre column. Vertical position encodes frequency — bass at the top and bottom, treble near the vertical middle — and the top and bottom halves carry the L and R channels respectively. Distance from the centre column encodes time: the centre holds the current frame, and history fans out toward the left and right edges. Hue rotates through a full cycle every ten seconds.

128 FFT bins appear as vertical frequency bands, mirrored symmetrically left and right. Bass concentrates at the centre; treble fans out to the left and right edges. Each band's hue encodes its amplitude — cool blue when quiet, warm orange when loud.

Like mode 5, but lightness also tracks amplitude — quiet bands are dim and cool-tinted, loud bands are bright and warm. Frequencies that surge in the mix glow visibly against the darker surrounding bands.