The consideration of topics related to quantum and fractal information science is now highly crucial. For this reason, several efforts made to studying approaches addressed to the basic fundamentals issues of the functioning of quantum and fractal information reality are extremely relevant. The book are welcomed and supported theoretical background, topics and applications for quantum fractals communications, fractal algorithms, fractal complexity, and fractality of the self-organized information structures. Also physical and software their implementations, including fractal information topics of the business, cybersecurity, technology and society are considered. This book, while preserving the integrity of the information statement, presents the vision and perception of self-organized fractal systems as a "simple algorithm" that can create all the uniqueness and completeness of nature. The monograph may be interesting both for specialists in the field of synergetics, research of structured levels for the non-crystalline and intelligent materials of artificial intelligence, contribute to the formation of a new the areas of the research, as well for the general public of readers.