ramble AN EXERCISE IN PHYSICAL MEMORY

A SMALL, STRANGE GEOMETRY STUDIO

Give a stone
somewhere to go.

Draw a winding path. Find the solid that
carries that motion in its shape.

No motor. No steering. Just geometry.

Finding the shape of your path…
SPECIMEN 01

Meander

A river, folded into a stone.

Drag to turn it over · Scroll to look closer
DepartureTwo repeats → one full returnReturn

Made here, in your browser. Nothing is uploaded.

Preview: ideal no-slip motion.

THE CURIOUS PART

The path isn’t on the table.
It’s in the object.

These objects are called trajectoids. The shape of their surface gives them a preferred route to roll. Ramble turns that idea into something you can hold, change, and examine.

01

A line becomes a rolling motion.

Imagine rolling a sphere along your drawing without slipping or twisting. Every point along the way gives it a new orientation.

02

The motion carves the stone.

At each orientation, shave away anything that would pass through the table. What remains is a solid with a memory of that route.

03

Two journeys bring it home.

Ramble finds a scale where one repeat makes a half-turn. After the second, the stone has its starting orientation again—and can keep going.

A NOTE FROM THE WORKBENCH

Real geometry.
An idealized journey.

Ramble calculates a solid from your path using rolling rotations and intersecting planes. The preview then moves that solid through the corresponding prescribed no-slip orientations. It is a geometric demonstration, not a free-running simulation of gravity, friction, or collisions.

A physical trajectoid needs its mass concentrated at the center. The original experiments used a heavy metal ball inside a lightweight shell. A uniformly filled print can have a different center of mass and behave differently.

The downloadable assembly is an experimental fabrication starting point. It has a centered ball cavity and two mating halves. Printer accuracy, seam alignment, the core fit, and the slope matter. We have checked its digital geometry, but haven’t physically printed or rolled it.

What is checked here

Contacts are sampled. Between adjacent samples the supporting height can differ by the displayed bound. The outer blank is a faceted approximation. Ramble searches three period-two solutions over a finite scale range; it does not implement a universal existence theorem.

Research & tools

Concept: Sobolev, Dong, Tlusty, and colleagues (2023). Related existence result: Várkonyi (2024). Practical reference: the authors’ repository.

Ramble uses an independently written quaternion solver and polar-dual plane intersection, Three.js for rendering and convex hulls, Manifold for assembly geometry, and fflate for ZIP files. All run locally. The supplied source includes reproducible tests and licenses.

 FROM A LINE TO AN OBJECT

Take a little
geometry home.

Save the solid, the experiment, or just the drawing.

mm
mm

For the kit: a ball you supply, plus 0.25 mm cavity clearance. At least 2 mm of wall. Experimental; physical performance is untested.