{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:58:46Z","timestamp":1760057926206,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,2]],"date-time":"2025-03-02T00:00:00Z","timestamp":1740873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study introduces a novel approach to chess analysis based on center-of-mass dynamics and discrete fractal derivatives, offering an alternative framework for evaluating gameplay strategies. Unlike conventional methods that rely on exhaustive search and statistical simulations, our model provides a macroscopic perspective by analyzing the collective motion of pieces over time. By representing chess positions as a dynamic system in R2, we identify key movement patterns\u2014such as oblique, parallel, and orthogonal trends\u2014revealing strategic tendencies throughout the game. Additionally, fractal derivatives enable the detection of subtle momentum shifts and long-term imbalances, enhancing the understanding of decision-making processes. This approach is computationally efficient and adaptable, extending beyond chess to applications in sports analytics and real-time strategy games. These findings highlight the potential of interdisciplinary techniques in capturing complex strategic behavior within dynamic environments.<\/jats:p>","DOI":"10.3390\/sym17030381","type":"journal-article","created":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T09:04:49Z","timestamp":1740992689000},"page":"381","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Determination of Centers of Mass via Fractal Calculus and Its Applications in Board Games"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1765-3206","authenticated-orcid":false,"given":"Josu\u00e9 N.","family":"Guti\u00e9rrez-Corona","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad Iberoamericana, Prolongaci\u00f3n Paseo de Reforma 880, Lomas de Santa Fe, Mexico City 01219, Mexico"},{"name":"Departamento de Matem\u00e1ticas y F\u00edsica, Universidad Aut\u00f3noma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5395-1369","authenticated-orcid":false,"given":"Israel","family":"Gardu\u00f1o-Bonilla","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad Iberoamericana, Prolongaci\u00f3n Paseo de Reforma 880, Lomas de Santa Fe, Mexico City 01219, Mexico"},{"name":"Facultad de Estudios Superiores Arag\u00f3n (FES Arag\u00f3n), Universidad Nacional Aut\u00f3noma de M\u00e9xico, Avenida Hacienda de Rancho Seco s\/n, Impulsora Popular Av\u00edcola, Nezahualc\u00f3yotl 57130, Estado de M\u00e9xico, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9262-9951","authenticated-orcid":false,"given":"Luis A.","family":"Quezada-T\u00e9llez","sequence":"additional","affiliation":[{"name":"Escuela Superior de Apan, Universidad Aut\u00f3noma del Estado de Hidalgo, Carretera Apan-Calpulalpan Km. 8, Colonia Chimalpa Tlalayote, Apan 43900, Hidalgo, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9695-3409","authenticated-orcid":false,"given":"Guillermo","family":"Fern\u00e1ndez-Anaya","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad Iberoamericana, Prolongaci\u00f3n Paseo de Reforma 880, Lomas de Santa Fe, Mexico City 01219, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7580-7533","authenticated-orcid":false,"given":"Jorge E.","family":"Mac\u00edas-D\u00edaz","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y F\u00edsica, Universidad Aut\u00f3noma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico"},{"name":"Department of Mathematics and Didactics of Mathematics, Tallinn University, Narva mnt 25, 10120 Tallinn, Estonia"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sanjaya, R., Wang, J., and Yang, Y. 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