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Chaos Theory and the Financial Markets Why Do Fractals Matter ?

Chaos Theory and the Financial Markets Why Do Fractals Matter ?. Why Do Fractals Matter ?. Fractals are important because they reveal a new mathematical discipline of study related directly towards the study of nature and the world

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Chaos Theory and the Financial Markets Why Do Fractals Matter ?

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  1. Chaos Theory and the Financial MarketsWhy Do Fractals Matter ?

  2. Why Do Fractals Matter ? • Fractals are important because they reveal a new mathematical discipline of study related directly towards the study of nature and the world • This in turn offers a revolutionary breakthrough in our “comprehension of reality.” • A scientific study or analysis to be valid must include fractals.

  3. Our Perception of Reality • Uniform Rectangular Objects like Boxes and Buildings do not exist in nature. They are all man made. • The world is not naturally smooth-edged rather it is filled with rough edges. • Smooth shapes are the exception in nature. • Yet we use a geometry that describes shapes rarely found in the real world.

  4. An Organized Approach to Chaos • What is Chaos? • Why Euclidean Geometry Doesn’t Work for Traders • What are Fractals • Market Applications • Trading with Fractals

  5. Examples of Chaos • Lightning • Weather Patterns • Earthquakes • Financial Markets • Social and Natural Systems • Governmental and Financial Institutions

  6. Constant Bewilderment • Chaos Theory is a way to describe or quantify nonlinear, random events or systems • Analyze events or systems that are influenced by their own outcomes, taking on a life of their own • Order and randomness can coexist allowing predictability

  7. Why is Chaos so Confusing? • Euclidean Geometry assumes a symmetrical world • Mountains are not cones • Clouds are not spheres • Coastlines are not circles • Lightning doesn’t travel in a straight line • Markets chop and correct

  8. The Texture of Reality • Nature deals in non-uniform shapes and rough edges. There is an inherent similarity within the shapes yet one can not fully describe the patterns with traditional geometry and analysis. • What has been missing from science is a method of describing the shapes and objects of the real world.

  9. Fractal Geometry • Unlike Euclid’s Ideal Forms, the broken, wrinkled and uneven shapes found in nature are not smooth. For example a tree or arteries in the human body. • Fractal Geometry is the real geometry of the natural world : Man, Animal, Vegetable, mineral and the galaxies.

  10. General Fractal Characteristics • Infinite Detail • Infinite Length • Absences of Smoothness • Absences of Derivatives • Fractal Geometry is the geometry one finds in irregular shapes in nature. • Fractal Geometry is an Extension of Classical Geometry ---- it is a new scientific language.

  11. Fractals – Bringing Order to Chaos • Assumes an infinite complexity in everything • Worldly objects are a collection of many similar curves combined • Each curve is made up of identical smaller curves making for infinite length • Each curve has “self-similar” smaller curves or “Fractal Dimensions” within it • Fractals identify order in apparent randomness • Patterns exist within a market’s underlying “noise”

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