The collection includes articles by foreign mathematicians and fractal artists, many of whom are well known in scientific and artistic circles. The problems of the book are connected with the philosophical and aesthetic meanings of fractal art, which is a special artistic phenomenon of the late 20th - early 21st centuries. A selection of articles is an attempt to look at digital fractal art from several angles: mathematical, technological, aesthetic and philosophical. Most of the texts are not of a special mathematical nature and rather belong to the field of digital humanities (digital humanities).Many articles of the collection are published in Russian for the first time.The book is of interest to experts in the field of aesthetics, philosophy of art, cultural studies and art history, teachers and students of art specialties, a wide range of readers.