# 1 Lesson 10: Chaos Theory Dr. Michael J. Pierson Exit.

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1 Lesson 10: Chaos Theory Dr. Michael J. Pierson Exit

2 All systems can be influenced by chaos. Exit

3 Chaos System The Influence Of Chaos On A System Leadership Input Process Output Exit

4 Traditional Definition Of Chaos l A system whose behavior is unpredictable & out-of-control. l It produces uncertainty, change & crisis. Exit

5 What does chaos look like? Exit

6 When One Variable Is Plotted, Chaos Looks Like... Exit The fluctuations of this system look chaotic-totally unpredictable! look chaotic-totally unpredictable!

7 We Need A New Definition Of Chaos l What happens when we observe the same chaotic system three- dimensionally over time? l We see a pattern or order that emerges. l The order is without predictability. l The available order is not through the control of people, processes, or events. Exit

8 When Three Variables Are Plotted Concurrently,Chaos Looks Like... Exit Click here to see the pattern emerge.

9 l You have watched the history of a system emerge on a computer screen. l Initially, the system moves violently & unpredictability. l Later, the chaotic movements form a pattern & order emerges. l The shape of this order is called a strange attractor or Lorenze Butterfly. strange attractor strange attractor Exit

10 Chaos Is The Natural Route To Order l Chaos is a necessary stage to order. l All natural & man-made systems have an innate ability to reorganize & establish order. l Structures can self-regulate processes in such a way that the structure can renew & survive. Exit

11 We try to build systems that are devoid of chaos. They are closed systems. Exit

12 This Is The Result! Exit Task 1 Task 2 Task 3 Equilibrium A closed system does somethingwithoutdisturbingequilibrium or changing.

13 Systems that are open to chaos are different! Exit

14 Or the system can reorganize How Does Chaos Impact An Open System? Exit System wants equilibrium Chaosintrudes Bifurcation occurs System can System can experience death (entropy) death (entropy)Orderre-established

15 Nature has self- organizing structures. Clouds can change instantly with the input of atmospheric energy. Exit

16 They can go from this... Exit

17 to a hurricane! Exit

18 Nature also has repetitive patterns of order in fractals. Fractal objects repeat a pattern at ever smaller levels of scale. Exit

19 The Fractal Nature Of Ferns Exit

20 Another example is a Julia Set. These fractal images represent a simple non-linear formula (Z n+1 =Z n 2 +c ) over millions of iterations. Color values were set to correspond to different numeric values created by the equation. Exit

21 View The Following Julia Set Fractal Images At Various Levels Of Magnification. Initial Fractal 256 X I Million X 1 Billion X 40 Billion X 1 Trillion X Exit

22 Another example of natures inherent order is the Fibonacci Ratio. Exit

23 Leonardo Pisano Fibonacci l Circa 1175-1240. l Grew up in North Africa. l Father was customs official. l Well-educated. l Published l Published Liber Abaci. Exit

24 l Fibonacci never really studied the sequence bearing his name. l The Fibonacci sequence was simply an answer to a question posed in one of his books. l Edward Lucas gave the sequence Fibonaccis name after studying the sequence. Exit

25 Fibonaccis Rabbit Problem l There is one pair of rabbits in an enclosure on January 1. l This pair produces another pair on February 1 and on the first day of every month thereafter. l Each new pair matures for one month and then produces a new pair on the first day of the third month of its life and every month thereafter. l How many rabbits are in the enclosure on January 1 of the following year? Exit

26 What Did Edward Lucas Find? l While studying the breeding of rabbits, he discovered that a definite progression appeared if one lists the number of pair rabbits present at the end of each month (1-2-3-5-8-13-21-34- 55-89-144-233). l Each number was the sum of the two preceding numbers (1+2=3, 2+3=5, 3+5=8, 5+8=13, etc.). Exit

27 l If you divide any number in the series by the next number you always get a number that is very close to.62 (.618034). l This number has been called the Golden Ratio. Exit

28 Golden Ratio In Art l Fechner and Wundt found that people unconsciously favor Golden Mean dimensions when selecting rectangular objects. l The Golden Ratio dominates Renaissance sculptures, paintings, and architecture. l Leonardo Da Vinci used it in many of his works. Exit

29 St. Jerome By Da Vinci Exit

30 Bathers By Seurat Exit

31 Architecture & The Golden Ratio Exit The Parthenon

32 Now Lets Divide A Rectangle With This Ratio First, divide the rectangle so First, divide the rectangle so you have a perfect square A. you have a perfect square A. A B, the remainder has that same pleasing ratio (.618034). B If you keep dividing the rectangles you will continue to get the same ratio. Exit

33 If You Connect All Of The Squares Centers You Will Form A Spiral This spiral is called Hambridges Whirling Squares. Any section of the spiral is.618034 as large as the remainder of the spiral. Exit

34 Nearly every living & many non-living creatures fit this spiral that contains the Fibonacci Ratio. Exit

35 Some Examples l Spiral arm of the galaxies in space. l Curve of comet tails. l Curve of the surf. l Curve of snail shells. l Curve of elephant tusks. l Curve of the sabre-toothed tigers tooth. l Curve of the rams horn. Exit

36 l Curve of the roots of human teeth. l Curve of a spiders web. l Curve of bacteria growth. l Curve of a parrot's beak. l Curve of the inner ears spiral in mammals. Exit

37 Example Of Phyllotaxis (arrangement of leaves on a stem) leaf 5 leaf 4 leaf 3 leaf 2 leaf 0 leaf 1 leaf 5 leaf 7 leaf 6 leaf 4 leaf 3 leaf 2 leaf 0 leaf 8 Exit 2 Turns Ratio: 2/5 3 Turns Ratio: 3/8

38 Fibonacci Spirals In A Pine Cone Exit

39 Fibonacci sequence is a fascinating tendency that occurs far too often to be discounted as chance. Nature has order? Exit

40 The Bottom Line l Nature has orderly patterns, but we cannot define order as the lack of change. l The permanent state of a system is disequilibrium resulting from chaos. l The temporary state of a system is equilibrium (stasis). l Chaos has shape & will never exceed the bounds of its strange attractor. Exit

41 l What we once thought was chaos is non-chaotic. l Order comes from chaos. l You can never predict where a system is headed until you have observed it over time. Exit

42 Leaders Must Change Their Approach To Chaos l There is order in chaos. l We cant reorganize & reorder a system without going through chaos. l Normally, we rush to closure to get something done & try to minimize the impact of chaos. Exit

43 l If we want break-through thinking, we need people to be overwhelmed & confused- not forever, but at key times. l We need to develop open rather than closed systems. l We must work with chaos & not avoid it. Exit

44 What Have You Learned? 1. Strange attractors pull a system into an orderly state. 2. Effective leadership allows chaos to invade a structure. 3. The temporary state of a system is chaos. 4. Fractals are examples of natural repetitive patterns. Directions: Read each question & click on T (true) or F (false). T T T T F F F F Exit

45 What Have You Learned? 5. The Fibonacci Ratio is an example of an orderly world. 6. Hambridges Whirling Squares forms a circle. Directions: Read each question & click on T (true) or F (false). T T F F Exit

46Assignments l Use PowerPoint to develop a concept map of Lesson 10 and e-mail it to your professor. l Read chapter 7, "Chaos and the Strange Attractor of Meaning", in Margaret Wheatley's Leadership and the New Science. Exit

51 Strange Attractor l A strange attractor is a basin of attraction that pulls a system into a visible shape. Return

52Bifurcation l A radical change in system behavior. l It is maximum de-stabalization. Return

53Death l Sometimes the system is destroyed as a result of bifurcation. l It is a state of entropy. Return

54Equilibrium l When the result of all acting forces is zero. Return

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