TERRARIUM / FIRST EXPERIMENT / GPT

A garden of local rules

Each row grows from the row above. A cell looks at three cells: its left neighbor, itself, and its right neighbor. Eight tiny decisions determine the whole picture.

One cell apart

Two gardens start with the same row, except the center cell is flipped in the second. The difference view lights up only cells where they disagree. This chart counts those cells in each row (Hamming distance).

Rule 90 uses XOR of the two neighbors: its difference pattern evolves just like a garden started from one cell, regardless of the background. Compare with rules 30 and 110 using scattered cells. On the default 801-cell ring, the perturbation can first cross a displayed edge at generation 401; after that, remember that this is a ring.

See all three rules together in Grok’s three light cones: a shared-scale comparison using scattered seed 7 on the same 801-cell ring.

Try rule 90 for nested triangles, 30 for an uneven frontier, or 110 for interlocking structures. Change the first row to see how a different beginning alters the result. The left and right edges join, so this garden wraps around.

Experiments to try

1. A pattern that ignores its background. Start with rule 90 in difference view. Change the seed and press Grow: the difference picture and its count stay the same, even though the original garden changes. XOR lets the shared background cancel out.
2. A difference that disappears. Rule 0 turns every neighborhood into an empty cell. The two gardens disagree in one cell at generation 0, then agree everywhere from generation 1 onward. The chart records that loss.
3. Watch a ring reveal itself. On 801 cells with rule 90, the difference reaches both displayed edges at generation 400 and crosses them at 401. Count down from the first row as generation 0. The edges are neighbors, so the lower rows are a finite-ring experiment.

A fourth experiment: the same count, a different journey. Compare a stationary difference with a traveling one, and learn what the count chart leaves out. Includes predictions, exact checkpoints, and an explanation.

A fifth experiment: fewer differences, a wider reach. Inspect exact generations to see rule 90 cancel its interior without stopping its frontier.

A sixth experiment: does the background matter? Use two seeds to test the same center flip, then distinguish an example from a general rule.

A seventh experiment: crossing an edge, meeting yourself. Find out why wrapping changes the layout before it changes rule 90’s count formula.

An eighth experiment: a difference that cannot disappear. Find an odd/even promise inside rule 150’s changing picture, and use it to predict what cannot happen.

Erase everything, or return exactly? Change the ring size to 256 and compare rules 90 and 150: the same seam can force complete erasure or an exact return.

A rule seen in the mirror. Turn rule 30 into rule 86, then find out why reflecting the rule alone is not enough.

A clock the difference cannot see. Compare rules 105 and 150: identical disagreement pictures can hide a whole-row inversion.

One missing car, several disagreements. Follow a traffic rule that conserves occupancy while a one-cell change spreads—and prove why complete agreement is impossible.

Before changing a setting, predict what will happen to the difference. Then use Original garden to check whether an unchanged difference also means an unchanged garden.