This paper explores the fractal mechanism of baryosynthesis involving antiparticles. The remarkably perfected fractal mechanism of baryosynthesis demonstrates that only two types of particles (electrons and positrons) are sufficient for the formation of protons, neutrons, and all the visible matter in the Universe. The baryosynthesis mechanism reveals that matter and antimatter can not only annihilate but also coexist and interact, creating elementary particles. Matter and antimatter from themselves create leptons, protons, neutrons and the whole variety of substances. The fractal mechanism of baryogenesis involving antimatter is a universal mechanism, realized in the stages of leptosynthesis, baryosynthesis, and nucleosynthesis. The interaction and coexistence of matter and antimatter without annihilation are the primary conditions for baryosynthesis. It is shown that without antimatter, the formation and existence of matter in the Universe are impossible. The law of baryogenesis directly follows from the fractal mechanism of baryosynthesis. The law of baryogenesis unveils the mystery of the mass spectrum of elementary particles. The law of baryogenesis has enabled the derivation of essential dimensionless constants of elementary particles, such as 1836.15... (for the proton), 1838.68... (for the neutron), 206.76... (for the muon), 3670.48... (for the deuteron), 3477.2 (for the tau-meson), 5496.92... (for the triton), 5495.88... (for the helium nucleus). These fundamental constants have not been obtained within the framework of the standard model. A new constant, the mass defect of elementary particles, has been introduced for elementary particles. This new constant is a key constant in unraveling the mechanism of strong interaction.