# Fractal

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Related to Fractals: Mandelbrot set, Mandelbrot

## Fractal

An object in which the parts are in some way related to the whole. That is, the individual components are "self-similar." An example is the branching network in a tree. While each branch, and each successive smaller branching is different, they are qualitatively similar to the structure of the whole tree.

## Fractal

1. In technical analysis, an indicator of the reversal of the previous trend. It is shown on a candlestick chart as a series of five candles, representing five trading days. A bullish fractal occurs when the lowest low of any trading day is represented by the middle candle, with two successively less low trading days on each side. This is seen as a buy signal. A bearish fractal occurs when the highest high of the five days is represented by the middle candle, with two successively less high trading days on each side. This is seen as a sell signal.

2. Any whole made up of parts that are self-similar.
References in periodicals archive ?
However, for a better performance of economic and financial forecasts, predictions and the impact of decisions throughout the economy, we argue that fractals pattern are more than helpful be taken into account, fractals can let financial experts to be aware or prepared for periods of cyclical recession and take better and less risky business decisions.
The newest intelligent financial decision tool: fractals. A smart approach to assess the risk.
Then fractal dimension [D.sub.f] can be calculated from the lg [S.sub.Hg]-lg [p.sub.c] plot.
Method I reflects the fractal characteristics of the capillary tube distribution in the cross-section of core samples, which is in two-dimensional space, and the range of the calculated fractal dimension using method I is 1 < [D.sub.f] < 2.
In fractal geometry, the fractal dimension is the objective tool used to measure the degree of "irregularity" and "complexity" in two fractal sets.
where [phi] is porosity, De is the Euclidean space dimension, and [D.sub.f] is the fractal dimension.
The fractal dimension D was determined in terms of the parameters that characterize thermofractals  and is given by
Equation (9) represents the fundamental properties of the fractal structure under scale transformation.
The notion of "fractal" was introduced by Mandelbrot (1983) and comes from the Latin term "fractus", meaning irregular and fragmented; this term is a general expression for self-similarity (Hirata et al.
Fractal objects develop via the repetition of the same principles from small scales to large scales.
where [sigma] is the standard deviation (rms height), C is the amplitude control factor, N is the number of tones, [b.sub.1] and [b.sub.2] ([b.sub.1] > 1, [b.sub.2] > 1) are the spatial-frequency scaling parameters, b is a constant (b > 1), D (2 < D < 3) is the roughness fractal dimension, [K.sub.1] and [K.sub.2] are the fundamental spatial wave numbers in the direction of x and y respectively, and [[phi].sub.n1], [[phi].sub.n2] are arbitrary phases with uniform distribution over the interval [-[pi], [pi]].
where M([epsilon]) means the length of a line, the area of a surface, the volume of a cube, or the weight of an object; D is the fractal dimension.

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