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

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2 All systems can be influenced by chaos. Exit

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

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

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5 What does chaos look like? Exit

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

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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

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

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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

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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

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

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

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13 Systems that are open to chaos are different! Exit

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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

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

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16 They can go from this... Exit

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17 to a hurricane! Exit

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

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19 The Fractal Nature Of Ferns Exit

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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

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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

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

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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

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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

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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

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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

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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

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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

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29 St. Jerome By Da Vinci Exit

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30 Bathers By Seurat Exit

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31 Architecture & The Golden Ratio Exit The Parthenon

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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

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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

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

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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

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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

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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

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38 Fibonacci Spirals In A Pine Cone Exit

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

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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

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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

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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

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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

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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

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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

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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

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47 Your answer was correct! Return

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48 Your answer was incorrect! Please review the material. Return

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49 Your answer was correct! Return

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50 Your answer was incorrect! Please review the material. Return

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

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

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

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

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