The Theory of Dynamical Systems studies how systems evolve over time,
often through differential equations or iterated transformations. Even
deterministic systems governed by simple laws can display chaotic
behaviour, marked by extreme sensitivity to initial conditions — tiny
changes in the starting state may lead to dramatically different
outcomes. Using the Lorenz attractor as an example, we illustrate this
unpredictability, popularly known as the butterfly effect. We then
show how a probabilistic approach provides the appropriate framework
for analysing chaotic systems, offering the right tools to make
meaningful predictions precisely where a purely deterministic
description proves inadequate.