A visual tool for understanding functions, gradients, and directional derivatives
in three dimensions. Plot any surface, place a point, and watch the mathematics unfold.
drag to orbit · scroll to zoom · map to move point
AlGrad
f(x,y) =
d =[,]
Functions
Classic
Waves
ML / Optimization
Special
f(x,y) = x²+y²
dragorbitright-dragpanscrollzoommapmove point
Point
position—
f(x,y)—
Gradient ∇f
vector—
magnitude—
direction—
Direction d = [2, 1]
∇f · d—
∇f · d̂ (unit)—
Δf per step—
Drag the point on the map.
∇f · d = how fast f changes
when you step in direction d.
Gradient points toward steepest
ascent. Its length = steepness.