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Complexity Theory and Chaos
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== <span style="color: #FFFFFF;">Remembering</span> == * '''Chaos Theory''' β The "Study" of "Dynamical Systems" that are "Highly Sensitive" to "Initial Conditions." * '''The Butterfly Effect''' β (Edward Lorenz, 1963). The "Metaphor" that a "Butterfly Flapping its Wings" in Brazil could "Cause" a "Tornado" in Texas "Weeks Later." * '''Nonlinear System''' β A "System" where the "Output" is "Not Proportional" to the "Input" (e.g., 'Double the force' does 'not' 'double the result'). * '''Fractal''' β (Benoit Mandelbrot). A "Geometric Shape" that "Repeats" its "Complexity" at "Every Scale" (**Self-Similarity**) (e.g., 'Coastlines,' 'Lungs,' 'Romanesco Broccoli'). * '''Self-Organization''' β (See Article 630). When a "System" "Develops" "Order" and "Structure" "Spontaneously" "Without" an "External Leader" (e.g., 'Bird Flocks,' 'Market Prices'). * '''Attractor''' β A "State" or "Pattern" toward which a "Dynamical System" "Tends to Evolve" (The 'Strange Attractor' is the signature of chaos). * '''Feedback Loop''' β (See Article 602). When the "Output" of a system "Becomes" the "Input" for the next step (**Recursive**). * '''Bifurcation''' β A "Tipping Point" where a "Small Change" causes a system to "Split" into "Two Different Possible Futures." * '''Emergence''' β (See Article 578). When "Simple Parts" "Interact" to "Create" a "Wholly New" "High-Level Property" (e.g., 'Water' being 'Wet' when 'Hydrogen and Oxygen' are not). * '''Entropy''' (in Information) β (See Article 123). The "Measure" of "Disorder" or "Uncertainty" in a system. </div> <div style="background-color: #006400; color: #FFFFFF; padding: 20px; border-radius: 8px; margin-bottom: 15px;">
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