This paper, titled How Long Is the Coast fraktale forex exchange Britain? Statistical Self-Similarity and Fractional Dimension, discussed what is known as the coastline paradox, first posited by mathematician Lewis Fry Richardson: if you were to measure the coastline of Britain with a yardstick, you would get a value less than if you were to measure the coastline with a one-foot ruler.
1975 book Les Objects Fractals: Forme, Hasard et Dimension. When looking at the market from a perspective of several years, the period from one month to the next may look relatively smooth. When the focus is narrowed to a particular year, the prices from month to month look increasingly rough. Peters published Chaos and Order in the Capital Markets and Fractal Market Analysis: Applying Chaos Theory to Investment and Economics, respectively, expanding upon this fractal market hypothesis. Hudson explore the world of finance from a fractal perspective in The Misbehavior of Markets: A Fractal View of Financial Turbulence.
Knowing the support and resistance levels is arguably the most valuable knowledge a spot trader can have, as they represent prices where the supply meets the demand. When the price breaks these levels, it is known as a breakout, and traders may expect that the price will continue in that direction. Figure 1: EURUSD M15 chart with the Fractals indicator applied. The fractal indicator is a powerful tool to identify where these support and resistance levels are located. Many existing indicators augment the standard fractal indicator and draw line placements for traders to more easily relate the price to previous fractals marked on the chart.
A common issue with fractal trading, however, is knowing which fractal levels continue to be relevant to the most recent market conditions. A source fractal is the previous fractal in the opposing direction. For example, if there were a buy fractal at some arbitrary location on the chart, then its source fractal would be the most recent sell fractal prior to said buy fractal. Figure 2: USDCHF M15 with the Fractals indicator applied.
Figure 3: USDCHF M15 with only the relevant fractals visible. USDCHF pair on the M15 timeframe. As the short-term trend is up, the majority of the relevant fractals are buy fractals, where the resistance has become the support. Taking this concept one step further, relevant fractals located within the same region of each other suggest that this price zone is a significant area of support or resistance, more so than a fractal found at a price distant from other relevant fractals. Identification of these regions is of great use to a trader, as it suggests that the region is of greater significance and, subsequently, more likely to indicate where breakouts are likely to occur. The last step to the process is determining what distance should be used when seeking neighboring fractals. Again, no subjectivity here, as the standard deviation of the price provides that distance for us.