{"id":19,"date":"2007-10-01T16:08:06","date_gmt":"2007-10-01T15:08:06","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=19"},"modified":"2010-06-17T17:40:37","modified_gmt":"2010-06-17T16:40:37","slug":"secret-messages-hidden-inside-equations","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=19","title":{"rendered":"Secret messages hidden inside equations"},"content":{"rendered":"

At the moment I am writing an introductory Mathematica course and was recently looking for inspiration for potential exercises. One website I came across (I have lost the link unfortunately) suggested that you get something interesting looking if you plot the following equation over the region -3<x<3, -5<y<5. It also suggested that you should only plot the z values in the range 0<z<0.001.<\/p>\n

\"\light f(x,y)=e^{-x^2-\frac{y^2}{2}} \cos (4 x)+e^{-3<\/p>\n

Suitably intrigued, I issued the required Mathematica commands and got the plot below which spoke to me in a way that no equation ever has before.<\/p>\n

\"\"<\/p>\n

So now I have a question – What other messages could one find hidden inside equations like this? For example, is it possible to generate a three letter word with a relatively simple equation such as the one above? Of course if you were allowed to use very complex equations (and make use of Fourier transforms maybe) then I guess you could spell out whatever you choose but that’s no fun.<\/p>\n

If anyone finds other such messages in simple(ish) equations then please let me know.<\/p>\n","protected":false},"excerpt":{"rendered":"

At the moment I am writing an introductory Mathematica course and was recently looking for inspiration for potential exercises. One website I came across (I have lost the link unfortunately) suggested that you get something interesting looking if you plot the following equation over the region -3<x<3, -5<y<5. It also suggested that you should only […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[6,4,8,11],"tags":[],"class_list":["post-19","post","type-post","status-publish","format-standard","hentry","category-general-math","category-math-software","category-mathematica","category-matlab"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3swhs-j","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=19"}],"version-history":[{"count":2,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/19\/revisions"}],"predecessor-version":[{"id":2732,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/19\/revisions\/2732"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}