How do generations over time work in the cellular automaton described here?

Conditions

• Time advances in discrete steps or generations.
• The next state of each cell is computed from the previous generation's neighborhood states.

Reasoning, step by step

1. Begin with a current configuration of cell states across the grid.
2. For each cell, inspect the states in its neighborhood at the previous time step.
3. Apply the transition rule $f$ to those neighborhood states.
4. Record the resulting value as the cell's state at the new time step.
5. Repeat this process simultaneously for all cells to generate the next full configuration.

Example

The speaker explains that at the next moment in time, a cell state is calculated based on a neighborhood of states, mentioning adding them together, averaging them, or looking at the pattern.

Common misconceptions

• Assuming that cells update sequentially one by one, rather than all at once based on the previous generation.
• Thinking that the system evolves continuously over time, rather than in discrete generations.

Watch the explanation

Explore next

• What does the formula Cell state_t = f(neighborhood states_{t-1}) mean?
• Why does each cell need a neighborhood in a cellular automaton?
• What is the definition of a cellular automaton given in this clip?