In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The popular example is a butterfly flapping its wings in New Mexico causes a hurricane in China, because everything in-between the two events happens as a result of them. While the butterfly effect is not the main focus of Run Lola Run (1998), it's a component in a film depicting the balance between chance and order.
Run Lola Run is an experimental film showing the very different consequences of seemingly minor variances in action. While Lola’s (Franka Potente) own narrative shows this in action, the film also details the futures of the people she briefly encounters through butterfly effect-type situations. The most powerful example is Lola’s split-second encounters with the old lady she bumps into on the sidewalk. In one sequence, Lola runs almost directly into the woman. In another, she nudges her slightly, and in the final sequence, avoids her entirely. The woman’s frustration (and level of expletives) changes in severity depending on how forcefully Lola interrupts her stride. We then see what happens to the woman in a quick montage of still-frame photographs.
The film wants to show that everyone, not just its main characters, has very different outcomes. Small changes turn into big differences for everyone.
In the first sequence, Lola full-on bumps into her. We then see the woman and her husband becoming alcoholics and losing custody of their kid. In the second sequence, Lola brushes by the her gently. Her and her husband win the lottery in the future. Finally, in the third sequence, Lola runs past her without direct interaction. The woman joins the Jehovah’s Witnesses and leaves her husband and child behind.
While we have no way of knowing how Lola’s minor interactions with the woman changed the course of her life, the butterfly effect maintains the relation is there. Perhaps bumping into the woman in the first sequence caused her to lose her train of thought, and she forgot to buy a lottery ticket she was intending to buy. In the second sequence, she wasn’t as directly impacted by Lola, remembers she wants the lottery ticket, buys it, and wins. In the third, Lola running freely past her inspires the woman to find freedom herself, and she lets go of her life and joins the Jehovas. It’s impossible to follow the path, but it’s the butterfly effect at work.
The film counteracts this theory with the concept of equifinality, in that she still encounters the same people most of the time regardless of her earlier interactions. Equifinality is the idea that certain outcomes will happen eventually despite what happened before them. The use of the butterfly effect and equifinality's recurring situations stresses the film's themes of chance and order, human will and circumstance.