Julia

Play

boundary · paused

Boundary position0.0%

Traversal speed0.017 cyc/s

Listening default

Complex constant Real part−0.788 Imaginary part+0.1191i Escape iterations32 Boundary grid320² Contour treatmentraw · 0.00 px View zoom1.00×

View center0.000 + 0.0000i

Marching squares finds every closed component; the longest boundary becomes the instrument path. Contour treatment is raw at center, smooths to the left, and reduces points to the right.

Wheel or use View zoom to magnify and resample. Drag empty stage space (or Shift-drag) to pan; drag near the bright boundary to scrub.

Mapping

left rises · 5 oct/turn · basic

Turn polarity

Pitch per full turn5.00 oct Corner glide35% edge

Left turn+ angle → pitch risesRight turn− angle → pitch fallsVertical harmonyquiet voice · bottom: minor third → top: fifth

Self-similarity lab

not traced

Listening experiment Boundary motif2.5% Inverse depth3 echoes Reference duration8.0 s Auditioned branch chain

LocationMove the playhead to choose a boundary motif. Pitch match— Time test— Local proxy—

The inverse maps ±√(z−c) predict all 2^depth related locations; every chain is overlaid while the repeated + or − chain is highlighted and auditioned. Grid resolution determines whether the arcs are sampled; escape iterations determine whether slow-escaping pixels are classified reliably.

Auditions follow the current direction, turn polarity, and Pitch per full turn. Chorus loops every scale together; canon delays its entries; wavelet separates coarse/middle/fine into different timbres; orbit is strict call-and-response; harmony holds an aligned comparison dyad.

Corner glide remains specific to the closed marching-squares boundary; the lab descriptor uses a stronger smoothed tangent heading so grid corners do not erase the time-scale cues.

Local proxies measure analytic signal fidelity; the reproducible report adds distractor retrieval. Auditioning remains the perceptual test—neither number alone proves that a listener recognizes the shape.

Sound

Basic Shepard

Synth Shepard center300 Hz Spectral width8.0 oct

One Shepard voice follows signed boundary turns directly.