One sample path of $X_t = b\,t + \sigma W_t + J_t$. Slide the three ingredients of the Lévy–Itô decomposition — the drift $b$, the diffusion strength $\sigma$, and the jump rate $\lambda$ (with a jump-size scale) — and watch how the path changes. Press New path to resample.
The blue curve is $X_t$. The dashed gray line is the pure drift $b\,t$; the red dots mark individual jumps. Turn the diffusion off ($\sigma = 0$) to see a pure-jump path, or the jumps off ($\lambda = 0$) to see a drifted Brownian motion.