James Joyce, Julio Cortazar, Marcel Proust or Umberto Eco. Regardless of their language of expression, the world's greatest writers seem to be, in some way, fractal builders. However, statistical analysis carried out at the Institute of Nuclear Physics of the Polish Academy of Sciences shows something even more intriguing. The composition of works in a certain genre - internal monologue - is characterized by the exceptional dynamics of a cascading narrative structure. This type of storytelling turns out to be multifractal.

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That is, fractal fractals are created. Researchers from the Institute of Nuclear Physics of the Polish Academy of Sciences carried out a detailed statistical analysis of more than a hundred works of universal literature, written in several languages ​​and representing various literary genres.

Books that were examined for correlations in sentence length variations were found to be influenced by cascade dynamics. This means that the pattern of these books is actually a fractal. In the case of several works, their mathematical complexity turned out to be exceptional, comparable to the structure of complex mathematical objects that are considered multifractals.

Fractals are self-similar mathematical objects. When we begin to expand one or more fragments, a structure finally emerges that resembles the original object. Typical fractals, especially those commonly known as the Sierpinski triangle and Mandelbrot set, are monofractals, meaning that the rate of increase in any fractal is the same, linear.

Multifractals are highly developed mathematical structures: fractal fractals. They arise from fractals that “intertwine” with each other in appropriate ways and in correct proportions. They are not simply the sum of fractals and cannot be separated back into their original components, due to the way they are woven fractal in nature. As a result, in order to see a similar structure to the original, different parts of the multifractal need to be expanded with at different speeds. Therefore, a multifractal is nonlinear in nature.

Multiscale analysis using fractals allows us to capture information about correlations between data at different levels of complexity of the systems under test. As a result, they indicate a hierarchical organization of phenomena and structures in nature. Therefore, natural language, which represents an important evolutionary leap in the natural world, can also expect such correlations. However, its existence in literary works has not yet been convincingly documented. when we look at these works from the right point of view, these correlations not only seem ordinary, but in some works they acquire particularly complex mathematical complexity, says Professor Stanislav Drozd.

To convert texts into number sequences, sentence length is measured by the number of words. The researchers then looked for relationships in the data that started at the simplest, which is linear. However, the correlations were obvious, and therefore these texts built a fractal, says Dr. Pavel Oswiecimka, who also noted that the fractal nature of a literary text in practice will never be as perfect as in the world of mathematics.

It is possible to expand mathematical fractals to infinity, whereas the number of sentences in each book is finite, and at some stage of expansion there will always be a final cut of the data set. Things took a particularly interesting turn when physicists began to track a nonlinear relationship, which was present to a mild to moderate extent in most of the papers examined. However, more than a dozen works show a very clear multifractal structure, and almost all of them turned out to be representative of the genre: internal monologue.