Entropy can help distinguish Wolfram's four classes (i.e., equilibrium, cyclic (periodic), random, and complex). To do so, the information entropy must be calculate for different sub-sequences of the time-series data.

Distinguishing Wolfram's 4 classes of outcomes using entropy

Perfectly random, maximal entropy. A sequence of fair coin flips or the stock prices (approximately) are random outcomes.

University of Michigan - Ann Arbor

- 1) Equilibrium
- 2) Cyclic (periodic)
- 3) Random 
- 4) Complex

Wolfram's four classes of empirical data

Page, Scott. The Model Thinker. https://doi.org/10.1017/mag.2019.84

The Model Thinker

An outcome with no uncertainty, entropy = 0. A pencil sitting stationary on a desk is considered an equilibrium outcome.

Equilibrium ( classes of outcomes )

Somewhat predictable, low entropy. A planet orbiting a star is a cyclic/periodic outcome.

Cyclic / Periodic ( classes of outcomes )

Not completely certain or uncertain (somewhere in-between), intermediate entropy. Neuronal firings are a complex outcome (they fire neither randomly nor in a fixed pattern).

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