OBSERVATION 009
金魚
Kingyo — Goldfish
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.
Five of them, each at a different speed.
The tail turns later than the body.
There is almost no bend at the head. It grows stronger toward the back.
This is how a real fish swims.
No fish moves by shaking its head.
The five speeds are matched to one another.
They look unrelated, but all five must return to the same positions.
Otherwise this observation does not close.
Read and verify the equation
(i, t,
m = i % 5, j = i / 5 | 0, b = j < 4600,
s = b ? j * .618034 % 1 : 1 + .5 * ((j - 4600) * .618034 % 1),
v = (j * .754878 % 1) * 2 - 1,
L = 55 + 9 * m, p = m * 1.9, w = [1, .5, 1.5, 2, .5][m],
A = t * w + p, R = 52 + 15 * m,
cx = 200 + R * cos(A), cy = 196 + R * sin(A) * .46 + 16 * (m - 2),
ax = -sin(A), ay = cos(A) * .46, q = hypot(ax, ay),
H = b ? L * .38 * sin(PI * s ** .7) ** .58
: L * (.05 + .44 * (s - 1) / .5) * (1 + .22 * sin(s * 9 - t * 5 + v * 3)),
Y = L * .12 * s ** 1.8 * sin(s * 2.6 - t * 4 + p) + v * H,
X = L * (s - .45),
Q = [cx + (X * ax - Y * ay) / q, cy + (X * ay + Y * ax) / q],
Dx = 200 + 64 * sin(t + 1.83) + 22 * sin(t * 2 + 3.11),
Dy = 200 + 34 * cos(t + 2.38) + 16 * sin(t * 3 + 1.83)
) => [Dx + (Q[0] - 200) * .68, Dy + (Q[1] - 200) * .68]
Fingerprint of this equation
sha256:98ec897e4468412342a85aefa6ce9700f3c6e5de1dc1ea4b5c889e077e856895
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 →