Rule 184
Read the cells as cars and this becomes a traffic model
Read the cells as cars on a one-lane road: a car moves if the space ahead is free. The number of cars never changes, and jams travel backwards.
How it works
In plain English, before the notation
Treat each 1 as a car and each 0 as empty road, all moving right. A car advances if the space in front of it is free, and stays put if it is not. That single sentence is exactly what Rule 184 does, and it is enough to reproduce the most recognisable fact about real traffic: jams travel backwards while the cars travel forwards.
Find the critical density
- Open Presets and load "Rule 184 Traffic" — a random road, roughly half occupied.
- Press Play and look at the diagonal streaks. Right-leaning streaks are moving cars; left-leaning ones are jams.
- Press Soup (R) a few times. Below about half occupancy the jams clear; above it they persist indefinitely.
Starting configurations
Loads straight into the simulatorTry any rule
The catalogue covers a few dozen rules. Here you can run any of the 262,144 two-state grid rules, or any of the 256 one-dimensional rules, including ones nobody has written up.
The number is the eight-entry lookup table below, read as a binary number.
Lookup table (10111000) — neighbourhood above, result below
Classification: Class 2 — settles to repeating or nested structures
How it runs: the automaton is a single row. Each cell reads the three cells above it and looks up the answer in 10111000. The canvas is the history — each row is one step later than the one above it.
Well-known rules
Where it came from
Wolfram catalogued the rule in 1983 along with the other 255. Its use as a traffic model came later: Nagel and Schreckenberg’s 1992 freeway model, which is the basis for a large amount of applied traffic simulation, is Rule 184 with a randomised braking term added.
The rule, precisely
What each cell looks at
Three cells on the previous row: (x−1, x, x+1)
What a cell can be
Two states per cell on a single row
The update
Rule 184 = 10111000 in binary, read over the patterns 111 down to 000
The rule is conservative: the number of 1s in a row is the same at every step. Only a handful of the 256 elementary rules have this property, and it is what allows the traffic reading to work.
Two regimes, separated by half
Behaviour is governed by the occupancy of the road:
- Below 50% occupancy the jams clear out and every car ends up moving every step.
- Above 50% occupancy jams are permanent — there are simply not enough gaps for every car to advance.
- Exactly at 50% the system sits at the boundary, where the largest number of cars per step get through.
- Jams propagate backwards through the traffic while every individual car only ever moves forwards, which is the counter-intuitive part and matches what happens on real roads.
Conservative and well understood
Rule 184 is one of the rules that can be solved rather than merely simulated: its long-term behaviour is fully characterised as a function of density.
Traffic, deposition, and annihilating particles
The traffic reading is the most direct, and it is genuinely used: adding a small probability of random braking to this rule gives the Nagel–Schreckenberg model, which reproduces the stop-start waves observed on motorways well enough to be used in planning.
Things to try
- Use the Seed Row tool to draw a solid block of cars on an otherwise empty road, then watch the jam dissolve from the front while its tail stays put.
- Compare a road at 30% occupancy with one at 70%. The two are qualitatively different, and the transition between them is sharp.
- Toroidal boundaries make the road a ring, which is the standard setup for studying this rule.
Frequently Asked Questions
References
The rule table, the conservation property, and the density transition.
The paper that turned this rule into the standard basis for traffic simulation.