∿fieldtripLAB · R9
TAKE YOUR CURIOSITY FOR A WALK
Public lab: curated experiments work immediately. Local AI: connect your installed Gemma through Ollama. Connection settings alone do not verify inference.
✦ THE LAZY VECTOR CALCULUS LAB

Don't just solve it.
Step inside it.

Ask a question. Follow the flow. Let the mathematics reveal itself.

✧
CURATED EXAMPLE · NO MODEL CONNECTED
LIVE FIELD EXPLORER

A little rotation. No expansion.

CURL ≠ 0 · DIV = 0
THE VORTEX FIELD
field flowboundary curvetest surface
DRAG TO ORBIT · SCROLL TO ZOOM
Follow the flowParticles illustrate trajectories; density is not a divergence measurement.
Counterclockwise boundary · upward normal
✓

Two ways to measure. One result.

Stokes' theorem · independent numerical integrations

BOUNDARY CIRCULATION—∮ F · dr
≈
CURL THROUGH SURFACE—∬ (∇ × F) · n dS
CHECKING
OPEN WEIGHTS. YOUR CHOICE.

Bring your own Gemma.

Connect an Ollama endpoint to generate a structured experiment plan and explanation. Curated examples and calculations work without a model.

Requests go directly to your endpoint. For local HTTP inference, run this app locally too. The hosted HTTPS app may require an HTTPS model proxy and allowed origins. No model is running on this site.

WHAT'S ACTUALLY HAPPENING

Beautiful, with the working shown.

Gemma chooses a supported experiment and explains calculated results. It cannot execute arbitrary code. Without Gemma, the question box selects curated examples by keywords.

Custom fields accept a restricted mathematical expression syntax. Symbolic derivatives use math.js. Line and surface integrals use independent midpoint quadrature; numerical agreement is evidence, not proof.

The singular-field example intentionally violates the disk's smoothness assumptions. No claim of new mathematical discovery is made.

Three.js draws the 3D scene; a projected Canvas renderer supports browsers without WebGL. Particle paths use numerical integration. Sources and setup instructions are included in the source download.

Review your experiment

Check the formula before running the experiment. Validation checks syntax, not whether the interpretation matches your intent.