Through the study of fractal geometry and Bionic we have been able to find out the expression of infinite in the nature structure, and to realize that there is an internal order, which is a law. A law whose expression is also the infinite. This discovery has allowed us to study Art history from a more global perspective. We have been able to see that almost every cultural manifestation has the expression of infinite as its goal. We have conclude that the searching for the infinite is what artists have called beauty and have found as something unreachable. Fractal geometry open new ways and gives us the tools to propose a new beauty canon to answer to the cultural and artistic needs of the XXI century.