Cellular Automaton Explorer
Explore every elementary cellular automaton rule from 0 to 255, see the rule table, and compare the four Wolfram classes from uniform to chaotic to the Turing-complete Rule 110.
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Eight bits define a universe
An elementary cellular automaton has cells in a line, each either on or off, and each cell's next state depends only on itself and its two neighbours. Three cells give eight possible neighbourhoods, and choosing an output for each gives one byte: 256 rules in total, and the rule number is simply that byte read in binary. It is the smallest interesting computational system anyone has found, which is exactly what makes it worth studying: whatever complexity appears cannot be blamed on complexity in the specification.
Rule 110 computes anything
Rule 110 was proved Turing complete, which means this eight-bit specification, run on a line of cells, can carry out any computation a computer can. That is remarkable because nothing in the rule suggests it: the output for each of the eight neighbourhoods is a single bit chosen apparently arbitrarily. Universality does not require an elaborate design, and this is the cleanest demonstration of that anyone has produced.
Rule 30 is chaotic enough to have been shipped as a generator
Rule 30 produces a pattern whose centre column passes standard statistical randomness tests, and it was used as a random number generator in Mathematica for years. It is completely deterministic and reproducible, so the randomness is entirely in how hard the pattern is to predict rather than in any actual uncertainty. Wolfram's four classes, uniform, periodic, chaotic and complex, come from cataloguing exactly these differences across all 256 rules.
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Frequently Asked Questions
What does the rule number mean?
It is the eight output bits written as a binary number. Each of the eight possible three-cell neighbourhoods maps to one output, and reading those outputs in order gives a value from 0 to 255.
Which rule is Turing complete?
Rule 110, proved so by Matthew Cook. It means an eight-bit specification run on a line of cells can perform any computation a computer can.
Why is Rule 30 interesting?
Its centre column passes standard statistical randomness tests and it was shipped as a random number generator. It is fully deterministic, so the randomness lies in unpredictability rather than in uncertainty.
What are the Wolfram classes?
Class 1 settles to a uniform state, class 2 to periodic structures, class 3 is chaotic, and class 4 produces localised structures that interact, which is where universality is found.
Does the starting row matter?
Considerably. A single cell shows a rule’s intrinsic structure most clearly, while a random start shows how it behaves on arbitrary input, and some rules look quite different under each.
Privacy & Security
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How to Use
Choose a rule number to see the pattern it generates.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.