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What are Fractals? – Fractal Foundation

Bill Williams also gives us his approach to using fractals in trading, which we are going to highlight here as well. But before that, let’s touch

One of the earliest applications of fractals came about well before the term was even used. Lewis Fry Richardson was an English mathematician in the early 20th century studying the length of the English coastline. He reasoned that the length of a coastline depends on the length of the measurement tool. Measure with a yardstick, you get one number, but measure with a more detailed foot-long ruler, which takes into account more of the coastline's irregularity, and you get a larger number, and so on.

The word "fractal" often has different connotations for laypeople than for mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. The mathematical concept is difficult to define formally even for mathematicians, but key features can be understood with little mathematical background.

Fractals are  indicators   on candlestick charts  that identify reversal points in the market. Traders often use fractals to get an idea about the direction in which the price will develop. A fractal will form when a particular price pattern happens on a chart. The pattern itself comprises five candles and the pattern indicates where the price has struggled to go higher, in which case an up fractal appears or lower, in which case a down fractal appears.

The fractals shown below are two examples of perfect patterns. Note that many other less perfect patterns can occur, but this basic pattern should remain intact for the fractal to be valid.

Fractal edges shown to be key to imagery seen in Rorschach inkblots Science Daily - February 14, 2017 Researchers have unlocked the mystery of why people ...

They are tricky to define precisely, though most are linked by a set of four common fractal features: infinite intricacy, zoom symmetry, complexity from simplicity and fractional dimensions – all of which will be explained below.

φ = ( 1 + 5 ) / 2 {\displaystyle \varphi =(1+{\sqrt {5}})/2} ( golden ratio ).

These complex images of extraordinary beauty can arise out of fairly simple mathematical formulas, and then by selectively modifying these formulas, changing coloring algorithms, etc. one can create unique compositions previously unseen to the human eye.

To create a fractal, you can start with a simple pattern and repeat it at smaller scales, again and again, forever. In real life, of course, it is impossible to draw fractals with “infinitely small” patterns. However we can draw shapes which look just like fractals. Using mathematics, we can think about the properties a real fractal would have – and these are very surprising.

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.

Fractal - Wikipedia

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