page_title: Reversible cellular automaton
section_title: Synchronization
hierarchical_section_title: Reversible cellular automaton / Applications / Synchronization
caption_attribution_description: English: The pattern produced by the Margolus-neighborhood rule Trip-a-Tron, from the Toffoli and Margolus book.
context_page_description: A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor. That is, it is a regular grid of cells, each containing a state drawn from a finite set of states, with a rule for updating all cells simultaneously based on the states of their neighbors, such that the previous state of any cell before an update can be determined uniquely from the updated states of all the cells. The time-reversed dynamics of a reversible cellular automaton can always be described by another cellular automaton rule, possibly on a much larger neighborhood.
  Several methods are known for defining cellular automata rules that are reversible; these include the block cellular automaton method, in which each update partitions the cells into blocks and applies an invertible function separately to each block, and the second-order cellular automaton method, in which the update rule combines states from two previous steps of the automaton.
context_section_description: The "Tron" rule of Toffoli and Margolus is a reversible block cellular rule with the Margolus neighborhood. When a 2 × 2 block of cells all have the same state, all cells of the block change state; in all other cases, the cells of the block remain unchanged. As Toffoli and Margolus argue, the evolution of patterns generated by this rule can be used as a clock to synchronize any other rule on the Margolus neighborhood. A cellular automaton synchronized in this way obeys the same dynamics as the standard Margolus-neighborhood rule while running on an asynchronous cellular automaton.
caption: The rectilinear shapes generated by the Tron rule
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