{"id":268321,"date":"2020-02-18T15:10:42","date_gmt":"2020-02-18T20:10:42","guid":{"rendered":"https:\/\/mymodernmet.com\/robert-bosch-optimization-art\/"},"modified":"2020-02-18T13:15:25","modified_gmt":"2020-02-18T18:15:25","slug":"robert-bosch-arte-optimizacion","status":"publish","type":"post","link":"https:\/\/mymodernmet.com\/es\/robert-bosch-arte-optimizacion\/","title":{"rendered":"Matem\u00e1tico crea complejos dibujos usando una sola l\u00ednea continua"},"content":{"rendered":"<p><noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267760\" src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-11.jpg\" alt=\"Robert Bosch arte de optimizacion\" width=\"750\" height=\"749\" srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-11.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-11-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-11-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267760\" src=\"data:image\/svg+xml,&lt;svg xmlns=&quot;http:\/\/www.w3.org\/2000\/svg&quot; viewBox=&quot;0 0 750 749&quot;&gt;&lt;\/svg&gt;\" data-src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-11.jpg\" alt=\"Robert Bosch arte de optimizacion\" width=\"750\" height=\"749\" data-srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-11.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-11-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-11-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<p>El matem&aacute;tico y artista <a href=\"http:\/\/www2.oberlin.edu\/math\/faculty\/bosch.html\" target=\"_blank\" rel=\"noopener noreferrer\">Robert Bosch<\/a> combina sus dos disciplinas en una serie de complejos dibujos laber&iacute;nticos que &eacute;l llama &#8220;arte de optimizaci&oacute;n&#8221;. Esto quiere decir que fueron hechos con la ayuda de t&eacute;cnicas de optimizaci&oacute;n matem&aacute;ticas y computacionales para ajustarse a ciertas restricciones hechas por el artista.<\/p>\n<p>En particular, a Bosch le interesa producir arte que resuelve lo que se conoce como el problema del vendedor ambulante. Este problema de optimizaci&oacute;n consiste en que un vendedor debe visitar varios otros lugares sin visitar el mismo lugar dos veces. El objetivo es encontrar la ruta m&aacute;s corta y eficiente que pasa por cada punto una sola vez. Bosch resuelve este escenario en sus obras de arte usando la restricci&oacute;n de que la ruta del vendedor debe ser un ciclo largo y conectado. Lo que significa que cada uno de sus dibujos es una sola l&iacute;nea tortuosa.<\/p>\n<p>&#8220;Al matem&aacute;tico en m&iacute; le fascinan los varios roles que juegan las restricciones en problemas de optimizaci&oacute;n&#8221;, explica Bosch. &#8220;A veces los hacen mucho m&aacute;s dif&iacute;ciles de resolver; otras veces, mucho m&aacute;s f&aacute;ciles. Y al artista en m&iacute; le fascinan los roles que juegan las restricciones en el arte. Todos los artistas deben lidiar con restricciones, y muchos artistas optan por poner restricciones sobre s&iacute; mismos&#8221;.<\/p>\n<p>La complejidad del arte de Bosch es determinada por el n&uacute;mero de lugares que usa en cada escenario. Por ejemplo, la versi&oacute;n de este artista del autorretrato de <a href=\"https:\/\/mymodernmet.com\/van-gogh\" title=\"van Gogh\" class=\"pretty-link-keyword\"rel=\"\">Van Gogh<\/a> usa una soluci&oacute;n para 120,000 lugares, mientras que <em>La joven de la perla<\/em> usa 200,000. Al compararlos visualmente, queda claro en el fondo de la obra maestra de Vermeer que la l&iacute;nea sinuosa est&aacute; m&aacute;s enrevesada debido al alto n&uacute;mero de lugares que debe transitar.<\/p>\n<p>Contin&uacute;a hacia abajo para ver m&aacute;s ejemplos de arte de Bosch. Si quieres conocer m&aacute;s sobre est&aacute; pr&aacute;ctica, adquiere una copia de su libro, <a href=\"https:\/\/amzn.to\/37q3ann\" target=\"_blank\" rel=\"nofollow\"><em>Opt Art: From Mathematical Optimization to Visual Design (&#8220;Arte de optimizaci&oacute;n: De optimizaci&oacute;n matem&aacute;tica a dise&ntilde;o visual&#8221;)<\/em><\/a>.<\/p>\n<h2>El matem&aacute;tico Robert Bosch crea complejos dibujos con una sola l&iacute;nea continua.<\/h2>\n<p><noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267762\" src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-12.jpg\" alt=\"Robert Bosch dibujos de una sola linea\" width=\"750\" height=\"750\" srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-12.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-12-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-12-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267762\" src=\"data:image\/svg+xml,&lt;svg xmlns=&quot;http:\/\/www.w3.org\/2000\/svg&quot; viewBox=&quot;0 0 750 750&quot;&gt;&lt;\/svg&gt;\" data-src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-12.jpg\" alt=\"Robert Bosch dibujos de una sola linea\" width=\"750\" height=\"750\" data-srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-12.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-12-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-12-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<h2>Este &#8220;arte de optimizaci&oacute;n&#8221; se basa en el problema del vendedor ambulante.<\/h2>\n<p><noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267736\" src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-1.jpg\" alt=\"Robert Bosch dibujos de una sola linea\" width=\"750\" height=\"750\" srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-1.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-1-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-1-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267736\" src=\"data:image\/svg+xml,&lt;svg xmlns=&quot;http:\/\/www.w3.org\/2000\/svg&quot; viewBox=&quot;0 0 750 750&quot;&gt;&lt;\/svg&gt;\" data-src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-1.jpg\" alt=\"Robert Bosch dibujos de una sola linea\" width=\"750\" height=\"750\" data-srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-1.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-1-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-1-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<h2>Esto significa que cada imagen est&aacute; formada por una l&iacute;nea continua que sigue la ruta m&aacute;s corta posible sin visitar ning&uacute;n punto dos veces.<\/h2>\n<p><noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267764\" src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-13.jpg\" alt=\"Robert Bosch arte y matematicas\" width=\"750\" height=\"750\" srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-13.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-13-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-13-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267764\" src=\"data:image\/svg+xml,&lt;svg xmlns=&quot;http:\/\/www.w3.org\/2000\/svg&quot; viewBox=&quot;0 0 750 750&quot;&gt;&lt;\/svg&gt;\" data-src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-13.jpg\" alt=\"Robert Bosch arte y matematicas\" width=\"750\" height=\"750\" data-srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-13.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-13-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-13-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<p><noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267758\" src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-10.jpg\" alt=\"Robert Bosch arte y matematicas\" width=\"750\" height=\"750\" srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-10.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-10-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-10-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267758\" src=\"data:image\/svg+xml,&lt;svg xmlns=&quot;http:\/\/www.w3.org\/2000\/svg&quot; viewBox=&quot;0 0 750 750&quot;&gt;&lt;\/svg&gt;\" data-src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-10.jpg\" alt=\"Robert Bosch arte y matematicas\" width=\"750\" height=\"750\" data-srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-10.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-10-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-10-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<p><noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267750\" src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-8.jpg\" alt=\"Robert Bosch arte y matematicas\" width=\"750\" height=\"750\" srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-8.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-8-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-8-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267750\" src=\"data:image\/svg+xml,&lt;svg xmlns=&quot;http:\/\/www.w3.org\/2000\/svg&quot; viewBox=&quot;0 0 750 750&quot;&gt;&lt;\/svg&gt;\" data-src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-8.jpg\" alt=\"Robert Bosch arte y matematicas\" width=\"750\" height=\"750\" data-srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-8.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-8-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-8-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<p><noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267746\" src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-6.jpg\" alt=\"Robert Bosch arte de optimizacion\" width=\"750\" height=\"309\" srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-6.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-6-300x124.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267746\" src=\"data:image\/svg+xml,&lt;svg xmlns=&quot;http:\/\/www.w3.org\/2000\/svg&quot; viewBox=&quot;0 0 750 309&quot;&gt;&lt;\/svg&gt;\" data-src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-6.jpg\" alt=\"Robert Bosch arte de optimizacion\" width=\"750\" height=\"309\" data-srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-6.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-6-300x124.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<p><noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267748\" src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-7.jpg\" alt=\"Robert Bosch arte de optimizacion\" width=\"750\" height=\"750\" srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-7.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-7-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-7-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/noscript><img decoding=\"async\" class=\"lazyload alignnone size-full wp-image-267748\" src=\"data:image\/svg+xml,&lt;svg xmlns=&quot;http:\/\/www.w3.org\/2000\/svg&quot; viewBox=&quot;0 0 750 750&quot;&gt;&lt;\/svg&gt;\" data-src=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-7.jpg\" alt=\"Robert Bosch arte de optimizacion\" width=\"750\" height=\"750\" data-srcset=\"https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-7.jpg 750w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-7-150x150.jpg 150w, https:\/\/mymodernmet.com\/wp\/wp-content\/uploads\/2020\/02\/bob-bosch-optimization-art-7-300x300.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/p>\n<p><strong>Robert Bosch: <a href=\"http:\/\/www2.oberlin.edu\/math\/faculty\/bosch.html\" target=\"_blank\" rel=\"noopener noreferrer\">Sitio web<\/a><\/strong><\/p>\n<h4><em>My Modern Met obtuvo permiso de Robert Bosch para reproducir estas im&aacute;genes.<\/em><\/h4>\n<h2><span style=\"text-decoration: underline;\">Art&iacute;culos relacionados:<\/span><\/h2>\n<p><a href=\"https:\/\/mymodernmet.com\/es\/enrique-bernal-ilustraciones-fluorescentes\/\" target=\"_blank\" rel=\"noopener noreferrer\">Este artista crea ilustraciones a l&aacute;piz que parecen estar iluminadas por luces fluorescentes<\/a><\/p>\n<p><a href=\"https:\/\/mymodernmet.com\/es\/anton-thomas-mapa-norteamerica\/\" target=\"_blank\" rel=\"noopener noreferrer\">Entrevista: Este artista pas&oacute; 5 a&ntilde;os dibujando un enorme mapa de Am&eacute;rica del Norte con l&aacute;pices de colores<\/a><\/p>\n<p><a href=\"https:\/\/mymodernmet.com\/es\/randa-haddadin-arte-corporal\/\" target=\"_blank\" rel=\"noopener noreferrer\">Esta artista usa su propia pierna como lienzo para crear hermosas ilustraciones<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>El matem&aacute;tico y artista Robert Bosch combina sus dos disciplinas en una serie de complejos dibujos laber&iacute;nticos que &eacute;l llama &#8220;arte de optimizaci&oacute;n&#8221;. Esto quiere decir que fueron hechos con la ayuda de t&eacute;cnicas de optimizaci&oacute;n matem&aacute;ticas y computacionales para ajustarse a ciertas restricciones hechas por el artista. En particular, a Bosch le interesa producir [&hellip;]<\/p>\n","protected":false},"author":320,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"om_disable_all_campaigns":false,"footnotes":""},"categories":[168388],"tags":[180805,317803,317804,317762,317807,183383,317806,317763,317764,317805,317767,317768,317769,317771],"class_list":["post-268321","post","type-post","status-publish","format-standard","hentry","category-arte","tag-arte-digital","tag-arte-matematico","tag-arte-y-matematicas","tag-bosch-artist-es","tag-dibujo-de-una-sola-linea","tag-dibujo-digital","tag-matematicas-y-arte","tag-mathematical-art-es","tag-optimisation-art-es","tag-problema-del-vendedor-ambulante","tag-travel-salesman-problem-es","tag-traveling-salesman-problem-es","tag-traveling-salesman-problem-art-es","tag-use-of-mathematics-in-art-es"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.6 (Yoast SEO v26.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matem\u00e1tico crea complejos dibujos hechos con una sola l\u00ednea continua<\/title>\n<meta name=\"description\" content=\"El matem\u00e1tico Robert Bosch resuelve el problema del vendedor ambulante con su arte laber\u00edntico. 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