1. Stochasticity 1 Incommensurate periodsPractically unpredictable Fundamentally indeterministicIllustrating memory-free processes

2. 2 Deterministic dynamics with incommensurate periods 2345678901 10 + ++++ + 50 Time interval Prevalence Sampling (explore different arrangements)

3. Stochasticity 3 Incommensurate periodsPractically unpredictable Fundamentally indeterministicIllustrating memory-free processes

4. Sampling (explore different arrangements) Unpredictability (in a practical sense) 4 Deterministic systems with practically unpredictable dynamics 2345678901 10 + ++++ +

5. Stochasticity 5 Incommensurate periodsPractically unpredictable Fundamentally indeterministicIllustrating memory-free processes

6. 6 Unpredictability and indeterminism at a fundamental level 12340 5 When heterogeneous outcomes result from an initially homogeneous population of individually isolated fundamental objects, the systems are indeterministic.

7. 7 Unpredictability and indeterminism at a fundamental level 12340 5

8. 8 Aspects of stochasticity can manifest to varying degrees Indeteminism: Heterogeneous outcomes from an initially homogeneous population Practically unpredictable: Sensitive to initial conditions. Sampling: Both systems explore a variety of configurations

9. 9 Depicting the independent sampling of possibilities over time Memory-free (Markov) process: A variety of behaviors or “events” is possible in the upcoming short time interval, and the distribution of possible behaviors is not influenced by the time-sequence of configurations the system explored before the immediate present.

10. 10 Depicting the independent sampling of possibilities over time Memory-free (Markov) process: A variety of behaviors or “events” is possible in the upcoming short time interval, and the distribution of possible behaviors is not influenced by the time-sequence of configurations the system explored before the immediate present.

11. 11 Depicting the independent sampling of possibilities over time Memory-free (Markov) process: A variety of behaviors or “events” is possible in the upcoming short time interval, and the distribution of possible behaviors is not influenced by the time-sequence of configurations the system explored before the immediate present.