1. Chaos Theory and the Financial Markets Why 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 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.” This in turn offers a revolutionary breakthrough in our “comprehension of reality.” A scientific study or analysis to be valid must include fractals. 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. 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. The world is not naturally smooth-edged rather it is filled with rough edges. Smooth shapes are the exception in nature. Smooth shapes are the exception in nature. Yet we use a geometry that describes shapes rarely found in the real world. 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 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 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 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. 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. 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. 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. Fractal Geometry is the real geometry of the natural world : Man, Animal, Vegetable, mineral and the galaxies.

10. General Fractal Characteristics Infinite Detail Infinite Detail Infinite Length Infinite Length Absences of Smoothness Absences of Smoothness Absences of Derivatives Absences of Derivatives Fractal Geometry is the geometry one finds in irregular shapes in nature. 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. 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 Assumes an infinite complexity in everything Worldly objects are a collection of many similar curves combined 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 is made up of identical smaller curves making for infinite length Each curve has “self-similar” smaller curves or “Fractal Dimensions” within it Each curve has “self-similar” smaller curves or “Fractal Dimensions” within it Fractals identify order in apparent randomness Fractals identify order in apparent randomness Patterns exist within a market’s underlying “noise” Patterns exist within a market’s underlying “noise”