Explore. Life from a rule
A row of cells, each on or off, and a rule that says what each cell becomes from itself and its two neighbors. Run the rule and a world unrolls down the page, one row for each moment of its time.
A one-dimensional cellular automaton whose cells switch on and off according to a simple rule is lawful, causally closed, and counterfactually robust, and it may be far too simple to hold anyone however long it runs. It is a reality all the same, a small and empty one.
A world from a rule
Each row is one moment, the first at the top. Select a cell to make it otherwise. With the keyboard, the arrow keys move between cells and Enter or the space bar changes the one you are on.
From a single cell it grows a widening triangle whose inside never settles into a repeating pattern.
From a single cell it draws triangles inside triangles, smaller and smaller, for as long as it runs.
Out of a random start it builds small structures that travel through the world, meet, and change one another.
Its cells move like cars on a crowded road, closing into jams that drift slowly backward.
Its events have causal powers of their own. Each state of the world produces its successors according to the world’s laws, and the things within it act on one another directly, without borrowing their behavior from a dreaming mind or a stored record.
Had it been otherwise
Choose any cell in the world’s history and make it otherwise. A running world answers: every later moment is worked out again from the changed one, and whatever the change reaches lies inside a wedge that widens by one cell each moment. Then make the world a recording of itself and try again.
It is counterfactually robust. Had any earlier state been otherwise, the world would have answered in the ways its laws require.
Chapter 1, What a Reality Is, ¶ 57
Had the woman hesitated before setting down her cup, the world would have answered her hesitation. A recording cannot answer anything.
Chapter 1, The Recording, ¶ 40
What separates a running computation from a wall that happens to pass through the right states is the same thing that separates a world from its recording. The difference lies entirely in what would have happened otherwise.
Small and empty
It holds together independently of the beliefs, wishes, and attention of any mind it contains. Its objects persist when no one attends to them and keep their characters whatever anyone believes about them.
Chapter 1, What a Reality Is, ¶ 57
Whether something counts as a reality settles very little. The questions that matter fall in the second and third tiers, whether a world could hold anyone and whether anyone is there.
How the world works
The world is a row of 101 cells joined end to end into a ring, so that it has no edge, and the page shows its first 96 moments. At each moment every cell becomes on or off at once, according to the rule’s entry for itself and its two neighbors. The eight entries, read as binary digits, make a number from 0 to 255, the usual name for such a rule. A random start is the same each time it is chosen until you ask for another. When you change a cell in a running world, every later moment is computed again from the changed one by the same rule. In a recording, the stored history is kept and only the cell you chose is altered.