Ruler Range

The ladder that does the work

Peak height at generation g is set by one number: how many bits of the edge are simultaneously at phase zero. That depends only on v₂(g+1), so the whole range is a function of how divisible a column index is by two.

Read the gaps, not the bars. A ruler sequence would climb by one every step. This one jumps +6 at v=6, +8 at v=8, +5 at v=12 — three whole mountain classes that appear from nowhere. That is the spectrum's own structure, and it is the part noise cannot imitate.

What to look for

Self-similar, not repetitive. Zoom out with 1× and the same shape of range appears at every scale, because the sequence is built that way. Noise gives you variety; this gives you hierarchy.

The peaks are on a lattice. The tallest summit in view sits at the most 2-divisible index in view — or on the shoulder of a bigger one just off-screen. That is honest and visible: drag around and you can predict where the next big one is. Whether that reads as structure or as grid is the real verdict, and it is yours to make.

The massif slider is not a noise knob. Turn it up and the peaks merge into fewer, more distinct groups — measured over 4,096 columns, 75 peaks become 36 and the height spread widens 24%. The displacement comes from the one branch indexrng throws away for carrying a ramp; a ramp is a defect in a generator and a gradient in a world.

Nothing here is stored. Every column is recomputed from (seed, g) on the way past. Travel a million generations and come back; it is the same mountain.