OBSERVATION 041
あわい
Awai — Between
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.
It looks like one. It looks like two.
Points circle a single closed path.
As the path turns, its two swellings overlap.
It may seem to come apart, but the path never breaks.
At six hundred and twenty-five points, gaps appear in the outline.
At forty, separate paths begin to show.
At one, the remaining point still follows the same equation.
One, and two.
Where did the division happen?
Read and verify the equation
(i, t,
a = (i * .61803398875 % 1) * TAU + t * .5,
b = (i * .75487766625 % 1) * TAU,
r = 9 + 7 * (1 + cos(2 * a - t)),
vx = 116 * cos(a), vy = 112 * cos(2 * a), vz = -44 * sin(a),
h = hypot(vx, vy), m = hypot(h, vz),
u = r * cos(b), v = r * sin(b),
x = 116 * sin(a) - vy / h * u - vz * vx / (h * m) * v,
y = 56 * sin(2 * a) + vx / h * u - vz * vy / (h * m) * v,
z = 44 * cos(a) + h / m * v,
q = t * .5 + .22, X = x * cos(q) + z * sin(q),
Z = z * cos(q) - x * sin(q)
) => [200 + X, 200 + y * .91 - Z * .32]
Fingerprint of this equation
sha256:81deec71d2f7b55425c9fa6e9d45cd18e57a50954e8ef6100a8d8e824dd2a5ba
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 →