{"id":1830,"date":"2008-06-19T09:31:07","date_gmt":"2008-06-19T07:31:07","guid":{"rendered":"http:\/\/www.randform.org\/blog\/?p=1830"},"modified":"2008-06-19T09:35:27","modified_gmt":"2008-06-19T07:35:27","slug":"la-done-butterfly","status":"publish","type":"post","link":"https:\/\/www.randform.org\/blog\/?p=1830","title":{"rendered":"La done butterfly"},"content":{"rendered":"<p><center><img src='http:\/\/www.randform.org\/blog\/wp-content\/2008\/06\/bublancmange250.jpg' alt='bublancmange250.jpg' \/><\/center><\/p>\n<p>The above image displays a visualization of the socalled <a href=\"http:\/\/mathworld.wolfram.com\/BlancmangeFunction.html\">blancmange curve<\/a> at various iteration steps and with a slightly randomized sawtooth function. The blancmange curve -not to confuse with the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Blancmange\">blancmange pudding<\/a>&#8211; is -like e.g. also the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Devil%27s_staircase\">devils staircase<\/a> a socalled <a href=\"http:\/\/mathworld.wolfram.com\/Pathological.html\">pathological function<\/a>, i.e. a function which displays a counterintuitive behaviour. In order to obtain the blancmangecurve one sums up little sawteet h which get smaller and smaller. However also if the sawteeth are getting in the end infinitely small this particular curve will never be smooth.  <\/p>\n<p>mathematical subleties after the more<\/p>\n<p><!--more--><br \/>\n<\/p>\n<p>thanks for being interested in mathematical subtleties. I was just joking. The above image is a detail of the below first butterfly image set into a high contrast mode with <a href=\"http:\/\/en.wikipedia.org\/wiki\/GIMP\">gimp<\/a> and rotated by 90 degrees.<\/p>\n<p>The butterfly looked quite dead.<br \/>\n<img src='http:\/\/www.randform.org\/blog\/wp-content\/2008\/06\/butterflyschmetterling3450.jpg' alt='butterflyschmetterling3450.jpg' \/><\/p>\n<p><img src='http:\/\/www.randform.org\/blog\/wp-content\/2008\/06\/butterflyschmetterling2450hochkant.jpg' alt='butterflyschmetterling2450hochkant.jpg' \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The above image displays a visualization of the socalled blancmange curve at various iteration steps and with a slightly randomized sawtooth function. The blancmange curve -not to confuse with the blancmange pudding&#8211; is -like e.g. also the devils staircase a socalled pathological function, i.e. a function which displays a counterintuitive behaviour. In order to obtain [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[2,8,14],"tags":[],"_links":{"self":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1830"}],"collection":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1830"}],"version-history":[{"count":0,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1830\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1830"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1830"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}