The pyramid only grows. Give Rule 30 a start word instead of one black square, and you can animate the whole picture: flip one bit of the start, and the picture below changes, but only inside a cone that opens from the flipped square, and the change arrives one step at a time, so it sweeps down the page. Everything outside the cone stays exactly as it was. Each frame here is one flip; the order of flips is yours to choose.
Rule 30 makes a square black when its upper-left neighbour differs from (the square above or its upper-right neighbour). Flip the upper-left square and the square below always flips. So a change moves right exactly one square per step, every time: that edge of the cone is a straight line. Its left edge moves only when the colours let it through, so its speed depends on what it crosses:
through the random-looking inside of the picture, about a quarter of a square per step (the record's 0.246); once it reaches the white outside a finite start, the full one square per step; and a flip at the very right end of the start can stay pinned to the right edge, its change never spreading inward, so its left edge moves right. Inside the cone, the readout counts how many squares change: about half, as if the picture were reshuffled.
A flip to the left of the centre reaches the centre column after exactly as many steps as it is squares away, never sooner and never later, because the right edge cannot slow down. That is the same fact that let the start be built square by square in Make the Centre Say Anything. A flip to the right of the centre has to travel against the grain, at the left edge's slow, wandering pace, so the centre hears about it much later.
Flip the bits in the order of the Gray code, the counting system in which each step changes a single digit, and the frames walk through every possible start word exactly once, each frame one flip from the last. It is the same Gray code that runs inside Rule 30's sideways picture. Which end counts as the least significant digit is a choice, like the order of bytes in a computer: right first makes the rightmost square flip every other frame, left first the leftmost. Sweep across instead and the flipped square moves one place each frame, so you can watch the cone change shape with its position.
The edges' speeds: the rightward one, exactly 1, follows from the rule in one line; the leftward 0.246
is RULE30-PRIZE.md §8.30 and §8.66 (rule30_damage_speed.py: the identity v = 1 − P(heal) E[jump | heal]
is proved, the values are measured), and on white a change can run left at full speed (GC856). Checked for this
page on 20 random starts of 24 squares over 120 steps (Cloud, 10 October 2026, prediction written first): the
change's left edge averages 0.80 to 1.00 squares a step for flips in the left part of the start, 0.21 to 0.25 for
flips in its right half, and below zero for the last three squares, whose change often stays at the right edge
(that part of the prediction was refuted). The right edge was exactly one square a step on every row of every
flip. The share of the cone that changes is counted live, for the picture you are looking at. The page checks itself: every
flip's right edge must sit exactly one square further right on every row, and the readout says if it ever does not.