Live-cell density
—
Share of all cells that are live.
Final row: —SIMPLE SYSTEMS / STRANGE BEHAVIOR
Small rules.
Unruly worlds.
Three neighbors. Two possible states.
Watch a single rule become a world.
256 rules8 starting states2 edges
4,096 recorded experiments
Change one assumption, track a perturbation, and export the evidence.
02 / UNDERSTAND Follow the questions.Six guided investigations, primary sources, and a classroom route.
03 / BROWSE Inspect the corpus.4,096 stored experiments, with complete trajectories and measurements.
01 THE OBSERVATION WINDOW128 CELLS × 128 UPDATES
R030 / SINGLE / WRAP STORED TRAJECTORY
GENERATION
CELL 000127
Loading the observation…
GEN 000 → 128 LIVE CELL
CHOOSE A RULE
One live cell at the center of an empty world.
The rule, in eight bits
00011110Three cells above decide the next cell below.
Observing recurrence
Checking for an exact repeated state.
Read the behavior
MEASURED OVER ALL 129 ROWS, UNLESS NOTEDActivity
—
Share of cells changing between successive rows.
Across 128 transitionsPerturbation spread
—
Mean difference after toggling the central starting cell.
Final row: —Occupancy entropy
—
Binary Shannon entropy of the live/dead balance.
Balance, not complexityCompression ratio
—
Compressed bytes divided by packed trajectory bytes.
zlib, level 9 · a heuristic02 THE SPECIMEN COLLECTIONA FINITE SPACE, FULLY ENUMERATED
FIND A DIFFERENT WORLD
Browse the atlas.
Order gives way to repetition, motion, and surprise.
Select a specimen to open its recorded experiment.
Page —
03 QUESTIONS BEYOND THE PICTUREMODELS, MECHANISMS, LIMITS
MAKE THE CONNECTION PRECISE
What can a small model teach us?
A useful model gives us a controlled question. The next step is to distinguish what it demonstrates from what the wider world still asks us to measure.
RULE 184 / TRANSPORT
When more cars mean less flow.
Set the density of a closed road. Count the cars that move, watch queues form, and compare the observed flow with the model’s long-run prediction.
Investigate traffic flow
PATTERN / EXPLANATION
A resemblance starts a question.
Natural patterns can suggest local mechanisms. Learn why a convincing visual match still needs a model of the process, measurements, and a test that could prove it wrong.
Read the field investigation04 NOTES ON THE METHODREPRODUCIBLE BY CONSTRUCTION
A LITTLE CONTEXT
Look closely.
Measure carefully.
Generated computational experiments; one record per parameter combination.
A whole world in one line.
Each of 128 cells is on or off. Its next state depends on itself and its two neighbors. The eight possible neighborhoods give us 256 rules. We record 128 updates, plus the initial row, for each rule, starting state, and boundary.
Nothing up our sleeves.
Every observation is a stored trajectory with a SHA-256 digest. Random starting states use a fixed xorshift32 seed; sparse, balanced, and dense states are deliberately nested. Catalog previews run the same rule locally. The main window displays the stored rows.
No single score means “complex.”
Occupancy entropy measures live/dead balance, not algorithmic complexity. Compression is a descriptive heuristic that depends on the zlib implementation. Perturbation compares a run with another whose central starting cell is toggled.
A short window is still a window.
A detected cycle is an exact repetition of a full state in this finite deterministic system. “No cycle observed” only covers these 128 updates. It does not rule out a later cycle.