Chaos Theory Chaos Theory and the Financial and the Financial

MarketsMarketsWhy Do Fractals Why Do Fractals

Matter ?Matter ?

Why Do Fractals Matter ?Why Do Fractals Matter ?

Fractals are important because they Fractals are important because they reveal a new mathematical discipline reveal a new mathematical discipline of study related directly towards the of study related directly towards the study of nature and the worldstudy of nature and the world

This in turn offers a revolutionary This in turn offers a revolutionary breakthrough in our “comprehension breakthrough in our “comprehension of reality.”of reality.”

A scientific study or analysis to be A scientific study or analysis to be valid must include fractals.valid must include fractals.

Our Perception of RealityOur Perception of Reality

Uniform Rectangular Objects like Boxes Uniform Rectangular Objects like Boxes and Buildings do not exist in nature. and Buildings do not exist in nature. They are all man made.They are all man made.

The world is not naturally smooth-edged The world is not naturally smooth-edged rather it is filled with rough edges.rather it is filled with rough edges.

Smooth shapes are the exception in Smooth shapes are the exception in nature.nature.

Yet we use a geometry that describes Yet we use a geometry that describes shapes rarely found in the real world.shapes rarely found in the real world.

An Organized Approach An Organized Approach to Chaosto Chaos

What is Chaos?What is Chaos? Why Euclidean Geometry Why Euclidean Geometry

Doesn’t Work for TradersDoesn’t Work for Traders What are FractalsWhat are Fractals Market ApplicationsMarket Applications Trading with FractalsTrading with Fractals

Examples of ChaosExamples of Chaos LightningLightning Weather PatternsWeather Patterns EarthquakesEarthquakes Financial MarketsFinancial Markets Social and Natural SystemsSocial and Natural Systems Governmental and Governmental and

Financial InstitutionsFinancial Institutions

Constant BewildermentConstant Bewilderment Chaos Theory is a way to describe or Chaos Theory is a way to describe or

quantify nonlinear, random events or quantify nonlinear, random events or systemssystems

Analyze events or systems that are Analyze events or systems that are influenced by their own outcomes, influenced by their own outcomes, taking on a life of their owntaking on a life of their own

Order and randomness can coexist Order and randomness can coexist allowing predictabilityallowing predictability

Why is Chaos so Why is Chaos so Confusing?Confusing?

Euclidean Geometry assumes Euclidean Geometry assumes a symmetrical worlda symmetrical world

Mountains are not conesMountains are not cones Clouds are not spheresClouds are not spheres Coastlines are not circlesCoastlines are not circles Lightning doesn’t travel in a Lightning doesn’t travel in a

straight linestraight line Markets chop and correctMarkets chop and correct

The Texture of RealityThe Texture of Reality

Nature deals in non-uniform shapes Nature deals in non-uniform shapes and rough edges. There is an inherent and rough edges. There is an inherent similarity within the shapes yet one similarity within the shapes yet one can not fully describe the patterns can not fully describe the patterns with traditional geometry and analysis.with traditional geometry and analysis.

What has been missing from science is What has been missing from science is a method of describing the shapes and a method of describing the shapes and objects of the real world.objects of the real world.

Fractal GeometryFractal Geometry

Unlike Euclid’s Ideal Forms, the Unlike Euclid’s Ideal Forms, the broken, wrinkled and uneven shapes broken, wrinkled and uneven shapes found in nature are not smooth. For found in nature are not smooth. For example a tree or arteries in the example a tree or arteries in the human body.human body.

Fractal Geometry is the real Fractal Geometry is the real geometry of the natural world : Man, geometry of the natural world : Man, Animal, Vegetable, mineral and the Animal, Vegetable, mineral and the galaxies.galaxies.

General Fractal General Fractal CharacteristicsCharacteristics

Infinite DetailInfinite Detail Infinite LengthInfinite Length Absences of SmoothnessAbsences of Smoothness Absences of DerivativesAbsences of Derivatives Fractal Geometry is the geometry one Fractal Geometry is the geometry one

finds in irregular shapes in nature.finds in irregular shapes in nature. Fractal Geometry is an Extension of Fractal Geometry is an Extension of

Classical Geometry ---- it is a new Classical Geometry ---- it is a new scientific language.scientific language.

Fractals – Bringing Order to Fractals – Bringing Order to ChaosChaos

Assumes an infinite complexity in everythingAssumes an infinite complexity in everything Worldly objects are a collection of many Worldly objects are a collection of many

similar curves combinedsimilar curves combined Each curve is made up of identical smaller Each curve is made up of identical smaller

curves making for infinite lengthcurves making for infinite length Each curve has “self-similar” smaller curves Each curve has “self-similar” smaller curves

or “Fractal Dimensions” within itor “Fractal Dimensions” within it Fractals identify order in apparent Fractals identify order in apparent

randomnessrandomness Patterns exist within a market’s underlying Patterns exist within a market’s underlying

“noise”“noise”