OBSERVATION 044
ほどけ
Hodoke — Loosening
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.
A tangled path approaches a ring.
Three undulations slowly flatten.
Near and far sections overlap, coming to look like a single circle.
The path never breaks. It comes to trace that circle twice.
Reduce the points and overlapping routes become easier to follow.
A single point moves on, knowing nothing of a tangle.
Has it come undone?
Or has the overlap hidden it?
Read and verify the equation
(i, t,
q = t * .5, a = (i * .61803398875 % 1) * TAU + q,
b = (i * .75487766625 % 1) * TAU,
A = (1 + cos(q)) * .5, R = 82 + 30 * A * cos(3 * a),
vx = -90 * A * sin(3 * a) * cos(2 * a) - 2 * R * sin(2 * a),
vy = -90 * A * sin(3 * a) * sin(2 * a) + 2 * R * cos(2 * a),
vz = 120 * A * cos(3 * a), h = hypot(vx, vy), m = hypot(h, vz),
u = 9 * cos(b), v = 9 * sin(b),
x = R * cos(2 * a) - vy / h * u - vz * vx / (h * m) * v,
y = R * sin(2 * a) + vx / h * u - vz * vy / (h * m) * v,
z = 40 * A * sin(3 * a) + h / m * v,
c = .34 + .3 * sin(q), X = x * cos(c) + z * sin(c), Z = z * cos(c) - x * sin(c)
) => [200 + X, 200 + y * .74 - Z * .67]
Fingerprint of this equation
sha256:64d6b13321685327aa8c07cfd249df32ff77c66fa2f82cd54bd7f16af1131248
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 →