Rule garden / Experiment guide

The same count, a different journey

A chart can tell the truth and still leave something out. Here, two rules keep exactly one differing cell in every generation. One difference stays in place; the other travels around the ring.

Predict, then compare

1. Open rule 204, scattered seed 7, difference view. Before looking, predict what happens when every cell simply copies itself.
2. Open rule 170 with the same settings. This time every cell copies its right neighbor. Predict which way the difference moves, then compare the picture and chart with rule 204.
3. In both gardens, change the seed to 12 and press Grow. Predict whether the difference changes. Switch to Original garden and press Grow to see what each rule does to the background.

What to look for

Rule 204 makes a vertical line in difference view. Rule 170 makes a diagonal going left: copying the right neighbor carries that neighbor’s value one column left. The diagonal leaves the left edge and reappears on the right. Both count charts stay at 1, very close to the bottom on the fixed 0–801 scale; their captions both report a final and maximum count of 1.

The top row is generation 0. Columns run from 0 at the left to 800 at the right, so the center is column 400. Enter these generations in the garden’s Inspect generation field to read exact counts and columns. These checkpoints let you distinguish motion from growth:

Why the background does not matter here

Rule 204 preserves every cell in both gardens, including their one disagreement. Rule 170 shifts both complete rows left by one place. Shifting cannot create or remove disagreements; it moves the existing one. Scattered seeds change the original picture, but cannot change these difference trajectories.

Hamming distance counts disagreements and discards their positions. Equal count histories alone therefore cannot show that two difference patterns are identical, or that an influence stayed near its starting point. Use the picture alongside the chart.

For a contrast, revisit rule 90: its difference branches and cancels instead of simply shifting. Does a falling count necessarily mean the difference has stopped moving?