OBSERVATION 045
うらおもて
Uraomote — Front and Back
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.
The far side turns toward us.
The band carries a half-turn of twist.
As it rotates, a surface narrows to an edge, then regains its width.
You were following the front. Which side are you watching now?
Reduce the points and you can see through the band.
A single point offers neither front nor back.
Yet its turning path remains.
Where did it turn over?
Read and verify the equation
(i, t,
q = t * .5, a = (i * .61803398875 % 1) * TAU,
v = (i * .75487766625 % 1) * 2 - 1,
r = 87 + 35 * v * cos(a * .5),
x = r * cos(a), y = r * sin(a), z = 35 * v * sin(a * .5),
c = q + .45, X = x * cos(c) + z * sin(c), Z = z * cos(c) - x * sin(c),
d = .82 + .18 * sin(q)
) => [200 + X, 200 + y * cos(d) - Z * sin(d)]
Fingerprint of this equation
sha256:d9b4231378af4f5328c4e94809e1ce54422d4a69129c3d76bd24faccb31565c2
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 →