Interactive model · 3D coordinates

String & Hair Lab

Drive a traveling wave along the string. Orbit the scene, select a hair, and compare its endpoint reach and motion with its neighbor.

TWIST MOTOR · 3Dt = 0.00 s

Drag to orbit · Pinch or scroll to zoom · Tap an endpointAxes: X along string · Y vertical · Z depth

Excitation

Drive pattern Grip radius Base frequency Damping Downward acceleration String wave speed

Geometry & view

Hairs Length variation Camera distance Trail duration

Endpoint trailsPair trails onlyReach lineReach colors

The hairs are linked segments with fixed rest lengths. Color shows endpoint reach divided by total rest length: teal is folded, amber is nearly straight.

Hair interactions

Motor speed Target turns Contact friction Bend resistance Contact distance

Resist crossingsShow contacts

Contact pairs now0

Spatial braid¹0.00

Tip revolutions²0.00

Length error / peak0.0% / 0.0%

The rotating grip supplies the motion that twists these strands.

¹ Net change of the two strands' relative angle along their length in the XZ plane. ² Motion of the ends over time. A circling tip alone does not count as a braid. Open strands can unwind; finite-step contact does not certify a knot.

Endpoint motion

selectedneighbor

Z position relative to each moving anchor, over the last 6 seconds.

What is calculated

The anchor wave is delayed by distance / wave speed. Each hair is a chain of linked 3D segments. In twist mode, rotating end grips work against fixed anchors; bending, damping, contact, and tangential friction shape the path between them. The other modes apply forces to free ends.

Reach = distance(anchor, tip). Rest length = sum of segment lengths. Spatial braid compares the two strands along their length; tip revolutions count their motion across time. Constraints and contact are finite-step approximations.

Hair 08 · rest length—

Endpoint reach—

Reach / rest length—

Model units are arbitrary. The default has no gravitational pull; the twist motor is an explicit mechanical boundary condition. Downward acceleration is an optional test field. This is a discrete elastic-filament experiment, not a model of every force in reality or proof of an extra physical dimension. Open-ended braids can be untwisted, and discrete contact does not guarantee continuous no-crossing.