Applying Chaos Theory to Perceive Order in Real life Scenarios

NCL-RSM Tech Exhibition�(Team- Indranil Saha, Siddharth Ghule)�

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Topics of Discussion

1. Introduction to Chaos (vs. Randomness).
2. History and Overview of the Chaos Theory.
3. Applications of the theory.
4. Lorenz system in a nutshell.
5. Study of reaction-diffusion system on a screen.
6. Observing chaos in collective motion.
7. Simulating crowd evacuation techniques.
8. Conclusion.

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Chaos vs. randomness

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• Chaos theory has shown that deterministic systems can produce results which are chaotic and appear to be random.

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• But they are not technically random because the events can be modelled by a (non-linear) formula.
• Thus, there is no definition of what randomness is, only definitions of what it isn't.

Chaos Game (Order in randomness)

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Sierpinski Triangle

Barnsley Fern

Abbreviated History of the Chaos Theory

• Kepler (1605).
• Newton (1687).

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• Poincare (1890).
• Lorenz (1963).

Conditions to make a Chaos

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• It must be sensitive to initial conditions.
• It must be topologically mixing.

Game of Life- Sensitivity_1

Game of Life- Sensitivity_2

Applications of the theory

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• Cryptography.
• Robotics.
• Biology.
• Meteorology.
• Economics.
• Sociology.
• Physics.

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• The equations relate the properties of a two-dimensional fluid layer uniformly warmed from below and cooled from above.
• The Lorenz equations also arise in simplified models for lasers, dynamos, electric circuits, chemical reaction and forward osmosis.
• Chaotic behaviors can only be observed in deterministic continuous systems with a phase space of dimension 3.

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Simulating Lorenz System

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• This is a system of ordinary differential equations. It is notable for having chaotic solutions for certain parameter values and initial conditions.
• Parameters of the solution ρ = 28, σ = 10, and β = 8/3

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Reaction-Diffusion System

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• In recent times, reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. Interesting patterns (fronts, spirals, targets, hexagons, stripes and dissipative solitons) can be found in various types of reaction-diffusion systems.

Visualizing Types Of It

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• Set parameters for spots (k = 0.0625, f = 0.035)
• Set parameters for stripes (k = 0.06, f = 0.035)
• Set parameters for spiral waves (k = 0.0475, f = 0.0118)

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Spots

Stripes

Spiral waves

Visualizing B-Z Reaction

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A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator. The only common element in these oscillators is the inclusion of bromine and an acid

Chaos in collective motion

• It is defined as the spontaneous emergence of ordered movement in a system consisting of a large number of self-propelled agents. It can be observed in everyday life, for example in flocks of birds, schools of fish, herds of animals and also in crowds and car traffic.

Simulating crowd evacuation

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• Evacuation simulation is a method to determine evacuation times for areas, buildings, or vessels.
• Modelling approaches are classified based on the details of evacuation simulation.

Thank You

‘‘The present determines the future, but the approximate present does not approximately determine the future.’’ -Dr. Edward Lorenz