OBSERVATION 022

折り

Ori — Fold

Play with it

Press the picture or the button to reduce the points.40,000 → 625 → 40 → 1, then back to 40,000.
At fewer points, dots grow and trails linger to help you follow their paths.
“Listen” maps the displayed points to sound.Changing the count rebuilds the sound.

Chapter
The Boundary
Year
2026
Medium
Equation, run live in the browser
Points
40,000
Cycle
5s per turn
Fingerprint
sha256 38828a77…47b9

The more it folds, the more the pleats stand.

The more it opens, the flatter they lie.

The number of folds does not change. Twenty-four, neither more nor fewer.
What changes is only how far each one faces us.

Closed all the way, every face turns edge-on and becomes a line.
Opened all the way, every face turns toward us and becomes one sheet.

The same paper, by orientation alone, is a line and is a surface.

Read and verify the equation
(i, t,
        k = i % 24, m = (i / 24 | 0), u = (m % 60) / 59, v = (m / 60 | 0) / 26,
        O = 1.62 + .96 * sin(t),
        a = ((k + u) / 24 - .5) * O - 1.5708,
        B = sqrt(max(0, 1 - (O / 2.58) ** 2)),
        z = (k % 2 ? 1 : -1) * (u - .5) * 17 * B,
        r = 60 + 120 * v + z * .8
       ) => [200 + r * cos(a), 302 + r * sin(a)]

Fingerprint of this equation

sha256:38828a77ac6295011aeb1cc178551d7753d528cc4a66596361014a0edf0247b9

The same point number and time give the same coordinates.
Trails and the appearance of points depend on rendering settings and the device.

The button above takes the equation out as it is. To count it again yourself:

pbpaste > f.txt && printf %s "$(cat f.txt)" | shasum -a 256

Take it and run it.What appears when you change the equation? Run and rewrite this equation →