The convergence dynamics of gradient descent on a scalar quadratic function $f(x) = \frac{\lambda}{2} x^2$ can be visualized programmatically by plotting the decay term $(1 - \eta \lambda)^t$ over successive time steps $t$. For instance, fixing the learning rate at $\eta = 0.1$ and iterating over a set of curvature values (such as $\lambda \in \{0.1, 1, 10, 19\}$) produces distinct trajectory curves. These plots practically reveal that values satisfying $0 < \eta \lambda \le 1$ yield smooth exponential decay, values where $1 < \eta \lambda < 2$ exhibit oscillatory but converging behavior, and values approaching the theoretical limit of $\eta \lambda = 2$ show dangerously slow convergence before divergence occurs.