LEVEL

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  in-game

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Inspiration

We wanted to make non-Euclidean geometry feel like something you could play with, not just read about. The idea behind LEVEL came from asking a simple question: what if returning to the same point did not mean returning to the same height?

What it does

LEVEL is a short puzzle game built around Nil geometry. You plan a route on a simple Euclidean Survey Glass, then execute that same route in a 3D world where the path itself changes your height.

For closed loops, the vertical change is equal to the signed area enclosed by the path. That means walking the same loop in reverse makes you descend, while opposite areas can cancel each other out.

How we built it

We built LEVEL with TypeScript, Three.js, and WebGL.

The movement system uses the Nil geometry relation

[ dz=\frac12(x\,dy-y\,dx) ]

and each straight segment is evaluated exactly. The puzzle system, Survey Glass, 3D movement, camera sequences, audio, and visual effects were all built around that same rule.

Challenges we ran into

The hardest part was turning the math into an actual game instead of a visualization.

Our early versions mostly showed the player what the geometry could do. We redesigned the controls so players now create their own paths, make mistakes, and use what they learn to solve later puzzles.

It was also difficult to make the 2D planning view and 3D world feel like one coherent experience.

Accomplishments that we're proud of

We are proud that the mathematics is not just part of the theme—it directly controls the gameplay.

The player can experience path dependence, signed area, reversed orientation, and cancellation through the puzzles themselves.

We also built automated tests to verify the movement system and puzzle solution spaces.

What we learned

We learned that explaining an unusual mathematical idea is much more effective when the player discovers it through interaction.

We also learned that good puzzle design is less about adding mechanics and more about giving players the right sequence of problems to build intuition.

What's next for LEVEL

We would like to expand LEVEL into a larger puzzle game with more handcrafted stages, deeper uses of Nil geometry, and other ways to turn unfamiliar mathematical spaces into intuitive gameplay.

Built With

• elevenlabs
• html
• three.js
• typescript
• webgl