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The formula means that the state of a cell at the current time step $t$ is computed by applying a transition function $f$ to the states of its neighboring cells at the previous time step $t-1$.

Conditions: $t$ represents the current discrete time step or generation index.; $t-1$ represents the previous discrete time step.; $f$ is the transition rule mapping previous neighborhood states to the next cell state.

The formula means that the state of a cell at the current time step $t$ is computed by applying a transition function $f$ to the states of its neighboring cells at the previous time step $t-1$.

Conditions: $t$ represents the current discrete time step or generation index.; $t-1$ represents the previous discrete time step.; $f$ is the transition rule mapping previous neighborhood states to the next cell state.

The simplest cell states mentioned are binary values, specifically 0 or 1, which can be interpreted as on/off, alive/dead, or black/white.

Conditions: The cell state is restricted to the simplest possible example.; The state set is binary.

The simplest cell states mentioned are binary values, specifically 0 or 1, which can be interpreted as on/off, alive/dead, or black/white.

Conditions: The cell state is restricted to the simplest possible example.; The state set is binary.

The circled group of cells and downward arrow illustrate that the future state of a single cell at the next time step is determined by the states of its neighboring cells in the previous generation.

Conditions: The diagram represents a one-dimensional cellular automaton.; The circled cells represent the neighborhood at time $t-1$.; The single box below represents the cell state at time $t$.

The circled group of cells and downward arrow illustrate that the future state of a single cell at the next time step is determined by the states of its neighboring cells in the previous generation.

Conditions: The diagram represents a one-dimensional cellular automaton.; The circled cells represent the neighborhood at time $t-1$.; The single box below represents the cell state at time $t$.

A cellular automaton is defined as a system built from three components: a grid of cells, where each cell has a state and a neighborhood, and a transition rule where the state of a cell at time $t$ is computed as a function of the neighborhood states at time $t-1$.

Conditions: The system is organized as a grid of cells.; Each cell carries a state and has an associated neighborhood.; The update rule uses the previous generation's neighborhood states.

A cellular automaton is defined as a system built from three components: a grid of cells, where each cell has a state and a neighborhood, and a transition rule where the state of a cell at time $t$ is computed as a function of the neighborhood states at time $t-1$.

Conditions: The system is organized as a grid of cells.; Each cell carries a state and has an associated neighborhood.; The update rule uses the previous generation's neighborhood states.