OBSERVATION 043
ふたえ
Futae — Two Layers
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.
One ring becomes two.
Two sets of points slowly separate.
Their planes tilt, opening space beyond the overlap.
In time, corresponding points return to the same places.
Reduce the points and paths from both sets remain.
At one point, only one path is traced.
The moment of overlap comes, though the other is no longer visible.
How many do you count when they coincide?
Read and verify the equation
(i, t,
q = t * .5, e = i < 20000 ? -1 : 1, j = i % 20000,
a = (j * .61803398875 % 1) * TAU + q,
b = (j * .75487766625 % 1) * TAU,
x = (83 + 10 * cos(b)) * cos(a) + e * 48 * sin(q),
y = (56 + 10 * cos(b)) * sin(a),
z = 10 * sin(b) + e * 54 * sin(q) * sin(a),
X = x * .94 + z * .342, Z = z * .94 - x * .342
) => [200 + X, 200 + y * .92 - Z * .392]
Fingerprint of this equation
sha256:ff276f9821a199ba9868785ea28535932874e1e775353cf3112b938a1ac51536
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 →