C T C T H H H H A E A E O O O O S R S R Y Y

PatternsPatterns

OfOf

LifeLife

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.

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.

The Generation of Chaos

From Simplicity xn+1 = k xn (1-xn)

Complexity

Chaos Theory Constructs

Phase Space Strange Attractors and Basins of AttractionSelf-AffinityFractalsBifurcation and Bifurcation CascadeUnpredictability—The Butterfly Effect et al.RecursivityResonanceFar-from-Equilibrium (Disequilibrium)Self-Organization

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.

Phase Space: Points to Remember

The map is not the territory.

The territory-- reality--is unknowable.

You see what you look for.

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.

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.

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.

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.

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.

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.

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.

Types of Unpredictability

Heisenberg-the more/the less.

Schroedinger’s Cat-both/and.

Goedel-inside/outside.

Lorenz (The “Butterfly Effect”)-left/right?

Experiencesof

Unpredictability“ T h r e e D im e n s i o n a l” C u b e F i g u r e

Types of Unpredictability

Heisenberg-the more/the less.

Schroedinger’s Cat-both/and.

Goedel-inside/outside.

Lorenz (The “Butterfly Effect”)-left/right?

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.

Human Dynamical System

Behaviors

FeelingsThoughts

Behaviors

Thoughts Feelings

Person A Person B

Resonance

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

Far-from-Equilibrium

Equilibrium is the tendency or inertia of system not to change its patterns by staying near or returning to points of attraction (homeostasis). Patterns change significantly and most unpredictably in far-from-equilibrium (chaotic) systems, those whose sensitivity (tuning constant) has exceeded a threshold of stability, thus producing disequilibrium.

Self-Organization

Self-organization is the inherent tendency for systems in a chaotic state to form a new coherent pattern.

Their innate ability to reorganize is based only on the interactions of their components.

The Key to Chaos

SPONTANEITY

SPONTANEITY

Prepared Adaptability

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

A Recipe for SpontaneitySpontaneity 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; andCreative—generating and providing a new “map” for the next similar situation, self-organizing. 

Points to RememberChaos 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

So what do you do when you meet Chaos?

Take a new perspective. Don’t panic!!

PANIC

Chaos doesn’t have to be scary!

Chaos can be BEAUTIFUL

Take a Peek

Final Thoughts