A hidden world rebuilt
Step by step: how a single well-built experiment reveals the entire rule of a hidden world, and why that makes these worlds too easy.
What we look at
In blackbox mode the agent does not see a world’s rule. It can only run experiments: a starting configuration, a number of steps, and the lab returns the result. Every experiment costs cell updates.
The agent’s first move was to design an experiment that reveals everything at once.
The trick
A two-state rule has 8 entries, one per neighbourhood of three cells. The ring 00010111 has a precise property: reading each cell with its two neighbours, you meet each of the 8 neighbourhoods exactly once. It is a de Bruijn sequence.
Run the hidden world for a single step from this ring, and each cell gives the rule’s output for its neighbourhood. Reading the 8 cells is reading the whole table.
Rebuilding a hidden rule in one experiment
0 of 8 neighbourhoods read
Each cell reads its left neighbour, itself and its right neighbour. On this ring the 8 possible neighbourhoods appear once each, so a single step reveals the whole rule.
Reading the figure step by step
- The top row is the ring 00010111, before the step.
- The bottom row is the same ring after one step of the hidden rule.
- Move window by window: the figure highlights a cell’s neighbourhood and its new value.
- Each window fills one entry of the table.
- After 8 windows the table is complete, and the figure can reveal the rule number. Pick another hidden world to start again.
For a three-state world
A three-state world has 27 neighbourhoods, so 27 entries. The matching de Bruijn sequence has 27 cells:
000100201101202102211121222A four-state world needs 64 cells. The agent built such a configuration for every world in its lab, ran one short experiment, and then knew the entire rule. The rest was computation: exact linear algebra for the laws, a block search for the structures.
What it shows
- A general-purpose agent had a good experimental idea, which cost it 150 to 225 times fewer cell updates than the scripted reference.
- The measurement saw the difference, because experiments are metered.
What it does not show
This is the most important point on this page. If one experiment reveals the entire rule, nothing uncertain is left to infer: experimental science collapses into computation. These worlds are therefore too easy to show discovery in the sense that matters. The next worlds must make inferring the law hard: partial observation, noise, large state spaces, continuous systems.