2. C T H H A E O O S R Y PatternsOfLife

3. Chaos What is Chaos? Chaos, from a static view, is “pieces waiting to come together,” an inchoate pattern about to happen. Chaos, from a dynamic view, is a process. It has a consistency to it. From a scientific standpoint chaos has a pattern, a kind of rhythm, ebbs and flows. Real “scientific” chaos isn’t just a mish-mash, a dissolution of a pattern, but also a new pattern coming together.

4. Chaos Theory What is Chaos Theory? Chaos Theory (ChT) is a mathematical approach to modeling patterns of non-linear, non- independent behaviors of dynamical systems. It is not, per se, a philosophical system or paradigm. ChT is about the fracturing of patterns, but it is also about how that collection of pieces sorts itself out. That coming back together again is what makes Chaos so interesting—and why it and ChT is so import to you.

5. The Generation of Chaos From Simplicity x n+1 = k x n (1-x n )

6. Complexity

7. Chaos Theory Constructs Phase Space Strange Attractors and Basins of Attraction Self-Affinity Fractals (Dis)Equilibrium Control and Order (Parameters) Bifurcation and Bifurcation Cascade Unpredictability—The Butterfly Effect and others Recursivity Resonance Self-Organization (Emergence)

8. Phase Spaces: Maps and Mappings The Phase Space: a conceptualization (often pictorial or geometric) of the possible states a system might take. Conveys that, at best, we see only a portion of “reality” at one time— that part on which we choose to focus.

9. Phase Space: Points to Remember The map is not the territory. The territory-- reality--is unknowable. You see what you look for.

10. Strange Attractors and Basins of Attraction Strange attractors are focal points for many-- the most challenging - - patterns generated by dynamical, chaotic systems. Basins of attraction are the areas containing those patterns within their boundaries.

11. Self-Affinity Self-affinity denotes the tendency for phenomena to evidence recurring patterns. The affinity can be over size, time, different angles, or other ways more difficult to see or to grasp, for example, by the process that generates them or probabilistically.

12. Fractals Fractal boundaries (or simply fractals) are mathematical representations of the irregular "lines" of demarcation between separate units. Fractals convey that reality is rarely as clear/clean cut as we picture it.

13. (Dis)Equilibrium Equilibrium relates to the possibility for change—types of pattern attractors Change occurs with disequilibrium (far from equilibrium states

14. Control and Order (Parameters) Control Parameters- determine the degree of sensitivity/disequilibrium Order Parameters-reflect the “bigger” picture of the system patterns Order parameters at one level can be the control parameters at another (and vice versa)

15. Bifurcation/Cascade Bifurcation is a scientific way to say something splits in two—branches. If patterns bifurcate quickly enough, they can become complex very fast, leading to bifurcation cascade and chaos.

16. Unpredictability is the inability to state with certainty the next state (or, for that matter, the previous state) of a system given knowledge of its present state.

17. Unpredictability is the inability to state with certainty the next state (or, for that matter, the previous state) of a system given knowledge of its present state.

18. Unpredictability Unpredictability is the inability to state with certainty the next state (or, for that matter, the previous state) of a system given knowledge of its present state.

19. Types of Unpredicability Heisenberg-the more/the less. Schroedinger’s Cat-both/and. Goedel-inside/outside. Lorenz (The “Butterfly Effect”)-left/right?

20. Experiences of Unpredictability

21. Types of Unpredicability Heisenberg-the more/the less. Schroedinger’s Cat-both/and. Goedel-inside/outside. Lorenz (The “Butterfly Effect”)-left/right?

22. Recursivity Recursivity is self- reflexiveness, and self- relectiveness, feeding information from one’s patterns back into the process of producing them. In mathematical language it is non-linearity and non-independence. Because of recursivity, change depends on the tuning constant, k, which determines the sensitivity of the system.

23. Resonance Resonance is when two or more separate entities find their patterns in synch and that synchronicity reappears or continues over time and changes

24. Self-Organization (Emergence) Self-organization is the inherent tendency for systems in a chaotic state to form a new coherent pattern (i.e., for it to emerge). Their innate ability to reorganize is based only on the interactions of their components.

25. The Key to Chaos SPONTANEITY

26. SPONTANEITY Prepared Adaptability Producing a novel response to an old stimulus/situation…or an adequate response to a new one.

27. A Recipe for Spontaneity Spontaneity is: Parameter bound—appropriate to the situation, aimed at staying in the basin of attraction or creating a new one; Adequate--meeting situational demands, applying apt phase mappings and self-affine; Novel—fractal and bifurcating--new, at least somewhat--and imbued with energy; Immediate—done, that is enacted, in the “here and now” of the circumstances; and Creative—generating and providing a new “map” for the next similar situation, self-organizing.

28. Points to Remember Chaos is not Havoc (a violent disruption of a pattern). Chaos is crisis with opportunity to change. Take the “v” (violence) out of havoc; replace it with the “s” for spontaneity—hasoc; allow some self- organization; and … CHAOS

29. So what do you do when you meet Chaos? Take a new perspective. Don’t panic!! P A N I C

30. Chaos doesn’t have to be scary! Chaos can be BEAUTIFUL Take a Peek Final Thoughts