A little organized chaos

I remember Blake Madill introducing us to chaos theory in MATH 147. What stayed with me was the coexistence of structure and unpredictability: tiny differences in where you begin can lead to very different paths, even under exactly the same rules.

The Thomas attractor, shown first here, comes from three equations describing how a point moves in three dimensions:

Each coordinate influences another in a cycle, while b controls the damping. Here b = 0.208186. The drawing traces a two-dimensional view of that motion; its intricate shape emerges as the path accumulates.

I think life can feel that way too. Your efforts can feel scattered from one day to the next, while a longer view reveals what they have been adding up to. A pattern can become clearer without the future becoming certain.

For more on the mathematics behind chaos, read this essay in Quanta (opens in a new tab).