A jam can travel backward.
Cars move right, but holes move left through a crowded region. In the space-time plot, follow the empty cells: a pattern can travel against the motion of its parts.
THE NEXT QUESTION IS YOURS
Change one thing.
Follow the difference.
A rule is only half the story. The starting state, the edges, and the time you observe can change what you see.
Make a comparison. Test an intuition. Take the evidence with you.
Start with a guided investigation01 THE COMPARISON BENCHCALCULATED IN YOUR BROWSER
Two worlds, side by side.
All measurements come from the complete run. The generation inspector lets you look at one row at a time.
Rule 90, identical beginnings, different edges. Look beyond generation 64, when the growing pattern can reach a boundary.
Opening the laboratory…
GENERATION INSPECTOR
Generation
Scrub to inspect both worlds. Time runs down each diagram; scroll inside a plot to explore its full history.
0 / 256
A SMALL CHANGE, MEASURED
The difference over time.
Within each experiment, toggle the central starting cell, rerun the same rule, and count the cells that disagree. This compares each run with its own perturbation.
A — solid lineB — dashed lineVertical marker: inspected generation
Read the difference as a data table
Every generation, including the initial state. Values are percentages of the world width.
| Generation | A difference (%) | B difference (%) |
|---|
TAKE THE EVIDENCE
A run you can reproduce.
The session includes both rules, starting rows, boundaries, exact trajectories, measurements, and the traffic run. PNG exports contain the selected view at integer pixel scaling.
CSV includes density, activity, and perturbation difference for every generation.
02 WHEN THE EMPTY SPACE MATTERSRULE 184 / A RING ROAD MODEL
A REAL QUESTION. AN IDEALIZED MODEL.
More cars.
Less movement?
On this 128-cell ring, a car advances one cell to the right if that cell is empty. All cars update together. Add cars and observe when empty space becomes the limiting resource.
/ 128 cells
EmptyHalf fullFull
Density: 0.500 cars per cell
An exact car count, placed with a deterministic shuffle. Rearranging changes the transient, while the car count stays fixed.
- Observed late flow
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- Steady-state reference
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- Cars conserved
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Flow is car moves per road cell per update. A moving car’s speed is one cell per update. These are dimensionless model quantities, with no conversion to vehicles per hour.
SPACE → / TIME ↓128 CELLS × 256 UPDATES
Ring snapshot · generation Movement →
TEST THE ENTIRE RANGE
The flow–density relationship.
One computed run for every possible car count. Solid line: observed flow over updates 129–256. Dashed line: the long-run Rule 184 reference, q = min(ρ, 1 − ρ).
Observed — solid lineReference — dashed lineCircle: selected density
Calculating all 129 car counts…
Read the flow–density data table
| Cars | Density | Observed flow | Reference flow |
|---|
Movement needs a vacancy.
At low density, cars limit the flow. Above half occupancy, empty cells limit it. A full ring has no space to move, so its flow is zero.
A lens, not a road forecast.
Every car is identical. There is no braking delay, lane change, reaction time, road entry, or randomness during an update. This model isolates exclusion; it is not a calibrated traffic predictor.