International Journal of Research & Methodology in Social Science Vol. 5, No. 4, p.- 1 - (Oct. – Dec. 2019). ISSN 2415-0371 (online). DOI: 10.5281/zenodo.3877594 - 1 - The Intrinsic Beauty of the Penrose's Mosaics Dante Roberto Salatino About the author Dante Roberto Salatino is a researcher of the Institute of Philosophy and of the Institute of Linguistics - Lecturer in the General Psychology Department – Lecturer in the Philosophical Aspects of Physical-Mathematical Science Department - Faculty of Philosophy and Letters - Teacher and Researcher in Artificial Intelligence in the Mechatronics Career - Faculty of Engineering - National University of Cuyo - Email for correspondence: dantesalatino@gmail.com ABSTRACT The reason for this work was to reconsider our intuitive vision of the Penrose's mosaics, addressing them from Transcurssive Logic (TL). The aesthetic, and even artistic-decorative effects that these geometric developments generate, it is said, depend on their aperiodicity, being understood by it, the possibility of expressing their structure through functions that are repeated indefinitely, but not keeping the symmetry they have defined during over 170 years, for example, the crystalline structure of matter. In these mosaics, the existence of an "intrinsic beauty" is the product of sticking to a universal pattern, as the first cause of its particular appeal, beyond constituting a recreational application of mathematics, or a source of inspiration for the discovery of quasicrystals. Keywords: Roger Penrose, recreational math, quasicrystals, Transcurssive Logic. CITATION: Salatino, D. R. (2020). “The Intrinsic Beauty of the Penrose’s Mosaics” Inter. J. Res. Methodol. Soc. Sci., Vol., 6, No. 1: pp. 1-14. (Oct. – Dec. 2019); ISSN: 2415-0371. DOI: 10.5281/zenodo.3877594 1.0 INTRODUCTION One could say, without fear of being wrong, that Roger Penrose is, today at 88 years old, one of the most original thinkers of our time. English physicist and mathematician, currently Emeritus Professor of Mathematics at the University of Oxford. Member of the Royal Society of London since 1972. Wolf Prize in Physics in 1988. Aventis Award, for the best scientific dissemination book (The Emperor’s New Mind), in 1990. A detailed examination of Penrose's work allows us to see how he manages to combine the genuine aspects of physics with refined mathematical techniques. The contributions of this particular scientist have been numerous. Thus, in the Theory of Relativity, through its Theory of the Twistors of 1967, useful for mapping geometric objects in a tetra- dimensional Minkowski space. In this way, he opened a window to explore non-linear, coherent and non-disturbing phenomena, in an accessible, beautiful and geometric way, which allowed dealing with non-linear problems while working with explicit solutions (Ward, 1998, p. 99 ). The purpose of this attempt was to find a