Attractors

What is it?

Formulas

$$\dot x = \sigma(y - x), \quad \dot y = x(\rho - z) - y, \quad \dot z = xy - \beta z$$

Lorenz system ($\sigma = 10$, $\rho = 28$, $\beta = 8/3$)

Where it shows up in computing

• Weather and climate modelling★★★★★frequentPhysics and simulation

  Lorenz found his attractor in a toy convection model; climate can be seen as the statistics of the attractor, weather as a point on it.

Where it shows up in AI

• Neural networks★★★★★historicalAI and machine learning

  Hopfield networks store memories as point attractors of an energy-descending dynamics (Nobel Prize in Physics 2024).

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

What depends on it

• Chaos and sensitivity to initial conditions