Social systems are characterized by an enormous network of connections and factors that can influence the structure and dynamics of these systems. Among them the whole economical sphere of human activity seems to be the most interrelated and complex. All financial markets, including the youngest one, the cryptocurrency market, belong to this sphere. The complexity of the cryptocurrency market can be studied from different perspectives. First, the dynamics of the cryptocurrency exchange rates to other cryptocurrencies and fiat currencies can be studied and quantified by means of multifractal formalism. Second, coupling and decoupling of the cryptocurrencies and the conventional assets can be investigated with the advanced cross-correlation analyses based on fractal analysis. Third, an internal structure of the cryptocurrency market can also be a subject of analysis that exploits, for example, a network representation of the market. In this work, we approach the subject from all three perspectives based on data from a recent time interval between January 2019 and June 2020. This period includes the peculiar time of the Covid-19 pandemic; therefore, we pay particular attention to this event and investigate how strong its impact on the structure and dynamics of the market was. Besides, the studied data covers a few other significant events like double bull and bear phases in 2019. We show that, throughout the considered interval, the exchange rate returns were multifractal with intermittent signatures of bifractality that can be associated with the most volatile periods of the market dynamics like a bull market onset in April 2019 and the Covid-19 outburst in March 2020. The topology of a minimal spanning tree representation of the market also used to alter during these events from a distributed type without any dominant node to a highly centralized type with a dominating hub of USDT. However, the MST topology during the pandemic differs in some details from other volatile periods.

This contribution addresses the question commonly asked in the scientific literature about the sources of multifractality in time series. Two primary sources are typically considered. These are temporal correlations and heavy tails in the distribution of fluctuations. Most often, they are treated as two independent components, while true multifractality cannot occur without temporal correlations. The distributions of fluctuations affect the span of the multifractal spectrum only when correlations are present. These issues are illustrated here using series generated by several model mathematical cascades, which by design build correlations into these series. The thickness of the tails of fluctuations in such series is then governed by an appropriate procedure of adjusting them to q-Gaussian distributions, and q is treated as a variable parameter that, while preserving correlations, allows for tuning these distributions to the desired functional form. Multifractal detrended fluctuation analysis (MFDFA), as the most commonly used practical method for quantifying multifractality, is then used to identify the influence of the thickness of the fluctuation tails in the presence of temporal correlations on the width of multifractal spectra. The obtained results point to the Gaussian distribution, so $q=1$, as the appropriate reference distribution to evaluate the contribution of fatter tails to the width of multifractal spectra. An appropriate procedure is presented to make such estimates.

Multifractality is a concept that helps compactly grasp the most essential features of financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded on centralized exchanges. A new element that adds complexity to cryptocurrency markets is the possibility of decentralized trading. Based on the extracted tick-by-tick transaction data from the Universal Router contract of the Uniswap decentralized exchange, from 6 June 2023 to 30 June 2024, the present study using multifractal detrended fluctuation analysis (MFDFA) shows that even though liquidity on these new exchanges is still much lower compared to centralized exchanges, convincing traces of multifractality are already emerging in this new trading as well. The resulting multifractal spectra are, however, strongly left-side asymmetric, which indicates that this multifractality comes primarily from large fluctuations, and small ones are more of the uncorrelated noise type. What is particularly interesting here is the fact that multifractality is more developed for time series representing transaction volumes than rates of return. On the level of these larger events, a trace of multifractal cross-correlations between the two characteristics is also observed.

As the recent studies indicate, the structure imposed onto written texts by the presence of punctuation develops patterns which reveal certain characteristics of universality. In particular, based on a large collection of classic literary works, it has been evidenced that the distances between consecutive punctuation marks, measured in terms of the number of words, obey the discrete Weibull distribution—a discrete variant of a distribution often used in survival analysis. The present work extends the analysis of punctuation usage patterns to more experimental pieces of world literature. It turns out that the compliance of the the distances between punctuation marks with the discrete Weibull distribution typically applies here as well. However, some of the works by James Joyce are distinct in this regard—in the sense that the tails of the relevant distributions are significantly thicker and, consequently, the corresponding hazard functions are decreasing functions not observed in typical literary texts in prose. Finnegans Wake—the same one to which science owes the word quarks for the most fundamental constituents of matter—is particularly striking in this context. At the same time, in all the studied texts, the sentence lengths—representing the distances between sentence-ending punctuation marks—reveal more freedom and are not constrained by the discrete Weibull distribution. This freedom in some cases translates into long-range nonlinear correlations, which manifest themselves in multifractality. Again, a text particularly spectacular in terms of multifractality is Finnegans Wake.