{"id":13865,"date":"2021-03-25T08:00:00","date_gmt":"2021-03-25T12:00:00","guid":{"rendered":"https:\/\/mathemalchemy.org\/2021\/03\/25\/copos-de-nieve-y-laseres\/"},"modified":"2025-05-03T11:55:41","modified_gmt":"2025-05-03T15:55:41","slug":"copos-de-nieve-y-laseres","status":"publish","type":"post","link":"https:\/\/mathemalchemy.org\/es\/2021\/03\/25\/copos-de-nieve-y-laseres\/","title":{"rendered":"Copos de nieve y l\u00e1seres"},"content":{"rendered":"\n<div class=\"wp-block-cover alignfull has-background-dim-10 has-background-dim\"><video class=\"wp-block-cover__video-background intrinsic-ignore\" autoplay muted loop playsinline src=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/Snow-5182.mp4\" data-object-fit=\"cover\"><\/video><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Siempre nieva sobre la colina de Riemann-Lebesgue. Es probable que esta nieve sea un poco distinta de la que ves caer en tu barrio. Esa nieve se forma a partir de la condensaci\u00f3n del vapor de agua en gotitas que luego se congelan en una semilla cristalina sobre la que se congela m\u00e1s vapor de agua. Una y otra vez hasta que, <em>\u00a1voil\u00e1<\/em>! <strong>Los copos de nieve <\/strong>de la exposici\u00f3n Mathemalchemy se forman utilizando <strong>las matem\u00e1ticas y el l\u00e1ser. <\/strong>    <\/p>\n<\/div><\/div>\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<h2 class=\"wp-block-heading\">Dise\u00f1o de copos de nieve<\/h2>\n\n<h3 class=\"has-large-font-size wp-block-heading\">Serpientes en el plano (Del tipo geom\u00e9trico)<\/h3>\n\n<p class=\"wp-block-paragraph\">Primero se genera un dise\u00f1o mediante un programa inform\u00e1tico compuesto en <a href=\"https:\/\/www.mathworks.com\/products\/matlab.html\" target=\"_blank\" rel=\"noreferrer noopener\">MATLAB<\/a>, <a href=\"https:\/\/www.wolfram.com\/mathematica\/\" target=\"_blank\" rel=\"noreferrer noopener\">Mathematica<\/a>, <a href=\"https:\/\/www.sagemath.org\/\" target=\"_blank\" rel=\"noreferrer noopener\">SAGE<\/a> o podemos contar con la ayuda de una simp\u00e1tica serpiente: <a href=\"https:\/\/www.python.org\/\" target=\"_blank\" rel=\"noreferrer noopener\">Python<\/a>. Puedes encontrar una buena introducci\u00f3n a la generaci\u00f3n de <a href=\"https:\/\/en.wikipedia.org\/wiki\/Koch_snowflake\" target=\"_blank\" rel=\"noreferrer noopener\">Copos de Nieve de<\/a> Koch en <a href=\"https:\/\/trinket.io\/python\/8c8b7f567e\" target=\"_blank\" rel=\"noreferrer noopener\">Trinket<\/a> &#8211; # Tu tri\u00e1ngulo de Koch b\u00e1sico. <\/p>\n\n<iframe loading=\"lazy\" src=\"https:\/\/trinket.io\/embed\/python\/3f24c7d716?start=result\" width=\"100%\" height=\"356\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" allowfullscreen=\"\"><\/iframe>\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Esta es una bonita introducci\u00f3n a Python y a la iteraci\u00f3n con un poco de ayuda de una tortuga. La exposici\u00f3n cuenta con <a href=\"https:\/\/mathemalchemy.org\/2020\/10\/29\/tess-the-tortoises-story\/\">una tortuga llamada Tess<\/a> en un viaje al infinito, as\u00ed que es l\u00f3gico que una tortuga nos aconseje para ver c\u00f3mo las matem\u00e1ticas pueden dar esta bella forma. <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\"><\/div>\n<\/div>\n\n<div style=\"height:75px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<h2 class=\"wp-block-heading\">Todo empieza con un tri\u00e1ngulo<\/h2>\n\n<p class=\"wp-block-paragraph\">Nuestros dise\u00f1os de copos de nieve han sido generados por <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/#Ingrid-Daubechies\">Ingrid Daubechies<\/a>. Los ejemplos con los que voy a trabajar empiezan con un tri\u00e1ngulo equil\u00e1tero, tal como lo describi\u00f3 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Helge_von_Koch\" target=\"_blank\" rel=\"noreferrer noopener\">Helge von Koch<\/a> en su art\u00edculo de 1904 <em>\u00abSur une courbe continue sans tangente, obtenue par une construction g\u00e9om\u00e9trique \u00e9l\u00e9mentaire<\/em>\u00bb o, en espa\u00f1ol,<em>\u00abSobre una curva continua sin tangentes construida a partir de la geometr\u00eda elemental\u00bb<\/em>. Tenga en cuenta que el franc\u00e9s era la lengua internacional de las ciencias en aquella \u00e9poca.  <\/p>\n\n<div class=\"wp-block-cover alignfull has-background-dim has-parallax\" style=\"background-image:url(https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/sergey-zolkin-32YLLwBI8Q4-unsplash.jpg)\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<figure class=\"wp-block-image size-large coblocks-animate\" data-coblocks-animation=\"fadeIn\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"652\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/On-a-continuous-curve-without-tangents-constructible-from-elementary-geometry.jpg?resize=900%2C652&#038;ssl=1\" alt=\"\" class=\"wp-image-2347\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/On-a-continuous-curve-without-tangents-constructible-from-elementary-geometry.jpg?resize=1024%2C742&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/On-a-continuous-curve-without-tangents-constructible-from-elementary-geometry.jpg?resize=300%2C217&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/On-a-continuous-curve-without-tangents-constructible-from-elementary-geometry.jpg?resize=768%2C556&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/On-a-continuous-curve-without-tangents-constructible-from-elementary-geometry.jpg?w=1200&amp;ssl=1 1200w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size wp-block-paragraph\">No estoy seguro de si utiliz\u00f3 una regla o un comp\u00e1s, pero fue capaz de trazar y triseccionar unas l\u00edneas muy bonitas.<\/p>\n<\/div><\/div>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-paragraph\">Ingrid me proporcion\u00f3 cinco iteraciones de copos de nieve Koch que import\u00e9 a una aplicaci\u00f3n gr\u00e1fica gratuita llamada <a href=\"https:\/\/inkscape.org\/\" target=\"_blank\" rel=\"noreferrer noopener\">Inkscape<\/a>. Puede hacer casi lo mismo que programas por los que se pagan cientos de d\u00f3lares. Tambi\u00e9n hay muchos <a href=\"https:\/\/www.youtube.com\/playlist?list=PLqazFFzUAPc5lOQwDoZ4Dw2YSXtO7lWNv\">v\u00eddeos \u00fatiles en YouTube<\/a>.  <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-image size-large coblocks-animate\" data-coblocks-animation=\"slideInRight\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"488\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/fift-iteration-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=900%2C488&#038;ssl=1\" alt=\"Copos de nieve Koch en Inkscape\" class=\"wp-image-2290\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/fift-iteration-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=1024%2C555&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/fift-iteration-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=300%2C163&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/fift-iteration-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=768%2C416&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/fift-iteration-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=1200%2C650&amp;ssl=1 1200w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/fift-iteration-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?w=1440&amp;ssl=1 1440w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption>Aqu\u00ed tiene la 5\u00aa iteraci\u00f3n abierta en Inkscape.<\/figcaption><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n<\/div>\n\n<p class=\"wp-block-paragraph\">A continuaci\u00f3n abr\u00ed la 4\u00aa iteraci\u00f3n en otra instancia de Inkscape y la \u00abcopi\u00e9 y pegu\u00e9\u00bb en el dibujo de la 5\u00aa iteraci\u00f3n. Tras redimensionarlo un poco, lo coloqu\u00e9 dentro del contorno de la 5\u00aa iteraci\u00f3n. A continuaci\u00f3n apliqu\u00e9 el mismo proceso a la 3\u00aa, 2\u00aa y 1\u00aa iteraci\u00f3n.  <\/p>\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-image size-full coblocks-animate\" data-coblocks-animation=\"slideInLeft\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"488\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/innermost-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=900%2C488&#038;ssl=1\" alt=\"Copos de nieve Koch superpuestos\" class=\"wp-image-2296\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/innermost-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?w=1440&amp;ssl=1 1440w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/innermost-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=300%2C163&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/innermost-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=1024%2C555&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/innermost-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=768%2C416&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/innermost-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=1200%2C650&amp;ssl=1 1200w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption>Copos de nieve Koch superpuestos en Inkscape.<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-paragraph\">En esta imagen puede ver que el copo de nieve m\u00e1s interior es simplemente un tri\u00e1ngulo equil\u00e1tero con tri\u00e1ngulos equil\u00e1teros m\u00e1s peque\u00f1os de longitud de arista \u2153 del original situados en el centro de esas aristas.<br\/>El mismo proceso que Koch realiz\u00f3 minuciosamente a pluma y tinta.<\/p>\n<\/div>\n<\/div>\n\n<div style=\"height:75px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<h2 class=\"wp-block-heading\">Copos de nieve y l\u00e1seres<\/h2>\n\n<h3 class=\"wp-block-heading\">\u00a1Pew-Pew! \u00a1ZAP! <\/h3>\n\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-paragraph\">Bien, \u00a1hora del l\u00e1ser! El corte por l\u00e1ser. Utilizo <a href=\"https:\/\/www.ponoko.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Ponoko<\/a> porque he comprobado que navego bien en sus procesos y sus precios son razonables. <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-image size-large coblocks-animate\" data-coblocks-animation=\"slideInRight\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"482\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image2.jpg?resize=900%2C482&#038;ssl=1\" alt=\"\" class=\"wp-image-2302\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image2.jpg?resize=1024%2C548&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image2.jpg?resize=300%2C161&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image2.jpg?resize=768%2C411&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image2.jpg?resize=1200%2C642&amp;ssl=1 1200w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image2.jpg?w=1368&amp;ssl=1 1368w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption>Aqu\u00ed est\u00e1 <a href=\"https:\/\/www.ponoko.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">la p\u00e1gina de Ponoko<\/a>.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-themeisle-blocks-font-awesome-icons\" id=\"wp-block-themeisle-blocks-font-awesome-icons-0dbf1668\"><span class=\"wp-block-themeisle-blocks-font-awesome-icons-container\"><i class=\"fas fa-file-import\"><\/i><\/span><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">Vamos a subir un dise\u00f1o. Ponoko requiere que el dise\u00f1o sea un archivo vectorial escalar. Un nombre mejor para esto podr\u00eda ser \u00abArchivo Vectorial Escalable\u00bb, porque eso es lo que hace tan bien, conserva la forma del dise\u00f1o a lo largo de ampliaciones y encogimientos.  <\/p>\n<\/div>\n<\/div>\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-image size-large coblocks-animate\" data-coblocks-animation=\"slideInLeft\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"482\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/design-process-ponoko-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=900%2C482&#038;ssl=1\" alt=\"Acabado del dise&#xF1;o con Ponoko\" class=\"wp-image-2311\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/design-process-ponoko-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?w=1000&amp;ssl=1 1000w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/design-process-ponoko-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=300%2C161&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/design-process-ponoko-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=768%2C411&amp;ssl=1 768w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption>Acabado del dise\u00f1o con Ponoko.<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-paragraph\">Aqu\u00ed est\u00e1 nuestro post de copo de nieve subiendo. Ponoko sigue unos pasos como analizar y terminar, as\u00ed que la primera vez que lo hice tard\u00f3 unos dos minutos. Me preocupaba haber sobrecargado su servicio inform\u00e1tico o haber roto las redes internas&#8230; no, s\u00f3lo lleva algo de tiempo.    <\/p>\n<\/div>\n<\/div>\n\n<p class=\"wp-block-paragraph\">Los pasos importantes ahora son definir qu\u00e9 l\u00ednea de color hace qu\u00e9. Yo cre\u00e9 el contorno en azul y el interior en negro, de modo que, como puede ver a continuaci\u00f3n, el azul es para el corte y el negro para el grabado. <\/p>\n\n<p class=\"wp-block-paragraph\">Tras confirmar el dise\u00f1o, es hora de elegir el material. Nos decidimos por plexigl\u00e1s transparente de 3 mm o ~\u215b\u00bb. Unos clics m\u00e1s y este dise\u00f1o estar\u00e1 listo para cortar. Confirma el material. Ponoko es prolijo en cuanto al n\u00famero de pasos. Tambi\u00e9n puede retroceder en el proceso. Su servicio de atenci\u00f3n al cliente tambi\u00e9n es bastante bueno.       <\/p>\n\n<div class=\"wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular\"><div class=\"tiled-gallery__gallery\"><div class=\"tiled-gallery__row\"><div class=\"tiled-gallery__col\" style=\"flex-basis:50%\"><figure class=\"tiled-gallery__item\"><img decoding=\"async\" role=\"button\" tabindex=\"0\" aria-label=\"Abrir la imagen 1 de 2 en pantalla completa\"srcset=\"https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image13.jpg?strip=info&#038;w=600&#038;ssl=1 600w,https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image13.jpg?strip=info&#038;w=900&#038;ssl=1 900w,https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image13.jpg?strip=info&#038;w=1200&#038;ssl=1 1200w,https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image13.jpg?strip=info&#038;w=1368&#038;ssl=1 1368w\" alt=\"Elegir el material del copo de nieve\" data-height=\"732\" data-id=\"2316\" data-link=\"https:\/\/mathemalchemy.org\/?attachment_id=2316\" data-url=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image13.jpg\" data-width=\"1368\" src=\"https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image13.jpg?ssl=1\" layout=\"responsive\"><\/figure><\/div><div class=\"tiled-gallery__col\" style=\"flex-basis:50%\"><figure class=\"tiled-gallery__item\"><img decoding=\"async\" role=\"button\" tabindex=\"0\" aria-label=\"Abrir la imagen 2 de 2 en pantalla completa\"srcset=\"https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image14.jpg?strip=info&#038;w=600&#038;ssl=1 600w,https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image14.jpg?strip=info&#038;w=900&#038;ssl=1 900w,https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image14.jpg?strip=info&#038;w=1200&#038;ssl=1 1200w,https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image14.jpg?strip=info&#038;w=1368&#038;ssl=1 1368w\" alt=\"Los copos de nieve ser\u00e1n de acr\u00edlico transparente\" data-height=\"732\" data-id=\"2317\" data-link=\"https:\/\/mathemalchemy.org\/?attachment_id=2317\" data-url=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image14.jpg\" data-width=\"1368\" src=\"https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image14.jpg?ssl=1\" layout=\"responsive\"><\/figure><\/div><\/div><\/div><\/div>\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-paragraph\">Ahora es pr\u00e1cticamente igual que cualquier otro sitio de compras en l\u00ednea. Pero hay un problema. Las l\u00edneas grabadas no se ven muy bien en las fases finales de su proceso, como puede ver en la foto de abajo. Su servicio de atenci\u00f3n al cliente me asegur\u00f3 que segu\u00edan ah\u00ed.    <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-image size-large coblocks-animate\" data-coblocks-animation=\"slideInRight\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"482\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image16.jpg?resize=900%2C482&#038;ssl=1\" alt=\"Captura de pantalla de la fase final del proceso.\" class=\"wp-image-2320\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image16.jpg?resize=1024%2C548&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image16.jpg?resize=300%2C161&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image16.jpg?resize=768%2C411&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image16.jpg?resize=1200%2C642&amp;ssl=1 1200w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/image16.jpg?w=1368&amp;ssl=1 1368w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption>Etapas finales del proceso de nuestro Ponoko.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n<p class=\"wp-block-paragraph\">OK, el pedido est\u00e1 hecho, las bater\u00edas de condensadores se est\u00e1n cargando en previsi\u00f3n de la gran acci\u00f3n l\u00e1ser. As\u00ed que ahora toca esperar. Podr\u00eda haber optado por el d\u00eda siguiente, pero el recargo es considerable. Eleg\u00ed cinco d\u00edas. Ponoko env\u00eda informaci\u00f3n de seguimiento tanto si env\u00edan por UPS como por USPS. Saber el d\u00f3nde y el cu\u00e1ndo de la entrega del paquete siempre es agradable.     <\/p>\n\n<div style=\"height:75px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<h2 class=\"wp-block-heading\">Las cosas buenas vienen en paquetes grandes<\/h2>\n\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u00a1Pues aqu\u00ed est\u00e1!  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El acr\u00edlico est\u00e1 recubierto de papel por ambas caras con un adhesivo muy tenaz para protegerlo de ara\u00f1azos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Saca los copos de nieve y luego llega la hora del ba\u00f1o.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"758\" height=\"1000\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/delivered-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=758%2C1000&#038;ssl=1\" alt=\"Entrega de copos de nieve\" class=\"wp-image-2332\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/delivered-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?w=758&amp;ssl=1 758w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/delivered-koch-snowflake-edward-vogel-mathemalchemy-art-project.jpg?resize=227%2C300&amp;ssl=1 227w\" sizes=\"auto, (max-width: 758px) 100vw, 758px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular\"><div class=\"tiled-gallery__gallery\"><div class=\"tiled-gallery__row\"><div class=\"tiled-gallery__col\" style=\"flex-basis:46.75223789163804%\"><figure class=\"tiled-gallery__item\"><img decoding=\"async\" role=\"button\" tabindex=\"0\" aria-label=\"Abrir la imagen 1 de 2 en pantalla completa\"srcset=\"https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/protected-snowflakes-edward-vogel-mathemalchemy-art-project-1.jpg?strip=info&#038;w=600&#038;ssl=1 600w,https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/protected-snowflakes-edward-vogel-mathemalchemy-art-project-1.jpg?strip=info&#038;w=717&#038;ssl=1 717w\" alt=\"Copos de nieve protegidos\" data-height=\"900\" data-id=\"2367\" data-link=\"https:\/\/mathemalchemy.org\/2021\/03\/24\/snowflakes-and-lasers\/protected-snowflakes-edward-vogel-mathemalchemy-art-project-1\/\" data-url=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/protected-snowflakes-edward-vogel-mathemalchemy-art-project-1.jpg\" data-width=\"717\" src=\"https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/protected-snowflakes-edward-vogel-mathemalchemy-art-project-1.jpg?ssl=1\" layout=\"responsive\"><\/figure><\/div><div class=\"tiled-gallery__col\" style=\"flex-basis:53.247762108361975%\"><figure class=\"tiled-gallery__item\"><img decoding=\"async\" role=\"button\" tabindex=\"0\" aria-label=\"Abrir la imagen 2 de 2 en pantalla completa\"srcset=\"https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/pop-snowflakes-edward-vogel-mathemalchemy-art-project.jpg?strip=info&#038;w=600&#038;ssl=1 600w,https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/pop-snowflakes-edward-vogel-mathemalchemy-art-project.jpg?strip=info&#038;w=700&#038;ssl=1 700w\" alt=\"Sacando los copos de nieve\" data-height=\"771\" data-id=\"2369\" data-link=\"https:\/\/mathemalchemy.org\/2021\/03\/24\/snowflakes-and-lasers\/pop-snowflakes-edward-vogel-mathemalchemy-art-project\/\" data-url=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/pop-snowflakes-edward-vogel-mathemalchemy-art-project.jpg\" data-width=\"700\" src=\"https:\/\/i2.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/pop-snowflakes-edward-vogel-mathemalchemy-art-project.jpg?ssl=1\" layout=\"responsive\"><\/figure><\/div><\/div><\/div><\/div>\n<\/div>\n<\/div>\n\n<div style=\"height:75px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<h2 class=\"wp-block-heading\">La hora del ba\u00f1o de los copos de nieve<\/h2>\n\n<p class=\"wp-block-paragraph\">Los dej\u00e9 en remojo unas tres horas y el papel se desliz\u00f3 enseguida. En otros pedidos han utilizado un papel marr\u00f3n que al parecer tiene m\u00e1s pegamento. Eso tarda toda la noche en agua jabonosa.  <\/p>\n\n<div class=\"wp-block-image coblocks-animate\" data-coblocks-animation=\"slideInBottom\"><figure class=\"aligncenter size-large is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/bathing-snowflakes-edward-vogel-mathemalchemy-art-project.jpg?resize=500%2C405&#038;ssl=1\" alt=\"Copos de nieve en un ba&#xF1;o peque&#xF1;o\" class=\"wp-image-2336\" width=\"500\" height=\"405\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/bathing-snowflakes-edward-vogel-mathemalchemy-art-project.jpg?w=1000&amp;ssl=1 1000w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/bathing-snowflakes-edward-vogel-mathemalchemy-art-project.jpg?resize=300%2C243&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/bathing-snowflakes-edward-vogel-mathemalchemy-art-project.jpg?resize=768%2C621&amp;ssl=1 768w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><figcaption>Copos de nieve ba\u00f1\u00e1ndose durante la noche.<\/figcaption><\/figure><\/div>\n\n<div style=\"height:75px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n<h2 class=\"wp-block-heading\">\u00a1Voil\u00e0! 2\u00aa parte <\/h2>\n\n<p class=\"wp-block-paragraph\">Y aqu\u00ed estamos, un precioso copo de nieve en la orilla del mar. \u00a1Precioso!   <\/p>\n\n<div class=\"wp-block-image is-style-rounded coblocks-animate\" data-coblocks-animation=\"zoomIn\"><figure class=\"aligncenter size-large is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/snowflakes-laser-edward-vogel-mathemalchemy-art-project.jpg?resize=768%2C695&#038;ssl=1\" alt=\"Copo de nieve resultante, cortado finamente con l&#xE1;ser\" class=\"wp-image-2344\" width=\"768\" height=\"695\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/snowflakes-laser-edward-vogel-mathemalchemy-art-project.jpg?resize=1024%2C926&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/snowflakes-laser-edward-vogel-mathemalchemy-art-project.jpg?resize=300%2C271&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/snowflakes-laser-edward-vogel-mathemalchemy-art-project.jpg?resize=768%2C694&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/snowflakes-laser-edward-vogel-mathemalchemy-art-project.jpg?resize=1200%2C1085&amp;ssl=1 1200w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/03\/snowflakes-laser-edward-vogel-mathemalchemy-art-project.jpg?w=1300&amp;ssl=1 1300w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/figure><\/div>\n\n<p class=\"wp-block-paragraph\">Sin embargo, en una \u00e9poca las funciones matem\u00e1ticas como \u00e9sta se consideraban \u00ab\u00a1Monstruos!\u00bb.<\/p>\n\n<p class=\"wp-block-paragraph\">Puede encontrar una muy buena lectura sobre este tema en el Archivo MacTutor de Historia de las Matem\u00e1ticas de la Universidad de St Andrews, Escocia &#8211; <a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/fractals\/\" target=\"_blank\" rel=\"noreferrer noopener\">A History of Fractal Geometry (Historia de la geometr\u00eda fracta<\/a>l)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Siempre nieva sobre la colina de Riemann-Lebesgue. Es probable que esta nieve sea un poco distinta de la que ve caer en su regi\u00f3n. Los copos de nieve de la exposici\u00f3n Matemlquimia se forman utilizando las matem\u00e1ticas y el l\u00e1ser.   <\/p>\n","protected":false},"author":44503787,"featured_media":13866,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[6325],"tags":[7414],"class_list":["post-13865","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-non-classe","tag-copos-de-nieve-de-koch","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - 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