Cryptocurrencies have attracted the attention of media, investors, lawmakers, and universities in recent years. Despite some doubts in the financial sector, understanding the price behavior of cryptocurrencies is an area of interest for researchers. It is considered as one of the seemingly unpredictable processes in the financial sector, and several methods have been proposed to understand their trends and make predictions. The present study aims to find fractal properties in the cryptocurrency market. So far, there is substantial evidence indicating the complexity and volatility of cryptocurrency prices, similar to stock market prices, and their random nature makes them unpredictable. However, it is possible that these time series exhibit dynamic nonlinear processes or, in other words, chaos, and as a result, they may have predictability. Therefore, in this study, the prices of ten cryptocurrencies with the highest market cap from 2018 to 2023 were selected as the statistical sample. By employing the R/S method, this method's assumptions, the fractal market hypothesis, and its effectiveness can be demonstrated. The study's results indicate that the fractal market hypothesis can be considered as an alternative to the efficient market hypothesis in the financial sector.