📡 Live Values
t (parameter)0.00
x(t)—
y(t)—
r⃗(t)—
|r⃗(t)|—
point—
💡 Understanding
t — The Source
t is like the water source. It flows forward in time. Every value of t produces exactly one output.
x(t) — Horizontal Branch
The X-pipe controls left/right position. Its tube width represents how fast x changes — a wider tube means faster change.
y(t) — Vertical Branch
The Y-pipe controls up/down position. Together, x(t) and y(t) draw a path no single function y=f(x) could describe.
r⃗(t) — The Position Vector
r⃗(t) = ⟨x(t), y(t)⟩ is the vector from the origin to the point. Its magnitude |r⃗| = √(x²+y²) is the distance from origin. The arrow you see on the canvas IS r⃗, born from the merger of both pipes.
KEY INSIGHT:
At each moment t, the water flows into BOTH branches simultaneously, producing a 2D point (x, y). The curve is the trace of all these points.