Branchbound: Uncomputable Garden

Branchbound: Uncomputable Garden

Open a small mathematical laboratory inside Branchbound and experiment with ideas whose full versions grow beyond any ordinary game.

Busy Beaver Lab

Predict a curated two-symbol Turing machine, reveal its finite execution step by step, and compare the observed runtime and tape marks with the disclosed limit.

Forbidden Trees

Build a bounded sequence of finite labelled rooted trees. A choice is forbidden when an earlier accepted tree embeds into it while preserving labels and branches.

Finite by design

Every bound is shown. ‘Still running at the limit’ never means ‘never halts’. The DLC does not compute Busy Beaver generally and does not compute or approximate TREE(3).

• Two deterministic, replayable experiments.
• Fully offline; no account, server, consumables, or runtime AI.
• Requires the base game Branchbound.