Games · Phase Portraits
A direction field flashes on screen. Before the timer runs out, name what's sitting at the origin — saddle, node, spiral, or center — just by reading the arrows. Build a streak; the matrices get closer to the boundary as you go.
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Read the arrows: do they spiral, curve into straight lines, fly apart in an X, or just circle forever? Pick an answer before the bar runs out.
Saddle — arrows rush in one way, out another, forming an X.
Stable node — every arrow flows straight into the origin.
Unstable node — every arrow flows straight away.
Stable spiral — arrows curl inward, decaying.
Unstable spiral — arrows curl outward, growing.
Center — arrows circle forever, never approaching or leaving.
What's actually being tested: for the linear system ẋ=ax+by, ẏ=cx+dy, the classification is fully determined by the trace T=a+d and determinant D=ad-bc of the matrix — D<0 is always a saddle, T²<4D means complex eigenvalues (spiral or center), and the sign of T decides stable vs. unstable. This game is training the same pattern-recognition the Phase Portraits lab lets you explore at your own pace — and the same eigenvalue logic from the theory page.
EngineeringCandy · Games · classify it fast, build the streak, learn the eigenvalue patterns by feel