{"version":"1.0","provider_name":"SOUL OF MATHEMATICS","provider_url":"https:\/\/soulofmathematics.com","author_name":"Rajarshi Dey","author_url":"https:\/\/soulofmathematics.com\/index.php\/author\/rajarshidey1729gmail-com\/","title":"CHAOS THEORY - SOUL OF MATHEMATICS","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"v9AQtP1MVZ\"><a href=\"https:\/\/soulofmathematics.com\/index.php\/chaos-theory\/\">CHAOS THEORY<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/soulofmathematics.com\/index.php\/chaos-theory\/embed\/#?secret=v9AQtP1MVZ\" width=\"600\" height=\"338\" title=\"&#8220;CHAOS THEORY&#8221; &#8212; SOUL OF MATHEMATICS\" data-secret=\"v9AQtP1MVZ\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/* ]]> *\/\n<\/script>\n","thumbnail_url":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/10\/O8Bm.gif?fit=250%2C188&ssl=1","thumbnail_width":250,"thumbnail_height":188,"description":"Chaos theory\u00a0is a branch of\u00a0mathematics\u00a0focusing on the study of chaos states of\u00a0dynamical systems\u00a0whose apparently random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to\u00a0initial conditions. When employing mathematical theorems, one should remain careful about whether their\u00a0hypotheses are valid\u00a0within the frame of the questions considered. Among such hypotheses in the domain of dynamics, a central one is the\u00a0continuity of time and space\u00a0(that an infinity of points exists between two points). This hypothesis, for example, may be invalid In the cognitive neurosciences of perception, where a finite time threshold often needs to be considered. The golden age of chaos theory Felgenbaum and the logistic map Mitchell Jay Feigenbaum proposed the scenario called\u00a0period doubling\u00a0to describe the transition between a regular dynamics and chaos. His proposal was based on the\u00a0logistic map\u00a0introduced by the biologist Robert M. May in 1976.\u00a0While so far there have been no equations this text, I will make an exception to the rule of explaining physics without writing equations, and give here a rather simple example. The logistic map is a function of the segment [0,1] within itself defined by: xn+1=rxn(1-xn) where n = 0, 1, &#8230; describes the discrete time, the single dynamical variable, and 0\u2264r\u22644 is a parameter. The dynamic of this function presents very different behaviors depending on the value of the parameter r: For 0\u2264r\u22643, the system has a fixed point attractor that becomes unstable when r=3. Pour 3&lt;r&lt;3,57&#8230;, the function has a periodic orbit as attractor, of a period of 2n&nbsp;where n is an integer that tends towards infinity when r tends towards 3,57&#8230; When r=3,57&#8230;, the function then has a Feigenbaum fractal attractor. When over the value of r=4, the function goes out of the interval [0,1] COURTESY- Christian Oestreicher,\u00a0Department of Public Education, State of Geneva, Switzerland;*\u00a0E-mail:hc.eg.ude@rehciertseo.naitsirhc"}