{"id":4476,"date":"2014-08-03T09:20:52","date_gmt":"2014-08-03T08:20:52","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=4476"},"modified":"2014-08-03T09:20:52","modified_gmt":"2014-08-03T08:20:52","slug":"more-experiments-with-random-walks","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2014\/08\/03\/more-experiments-with-random-walks\/","title":{"rendered":"More experiments with random walks"},"content":{"rendered":"<p>I have again been playing with some random walks, using the same method as <a href=\"http:\/\/blogs.scienceforums.net\/ajb\/?p=4459\" title=\"Blog\" target=\"_blank\">here<\/a>. This time I used 1000000 iterations and added some colour.<\/p>\n<blockquote><p>\nBelow are random walks, on the plane (not a lattice) for which step size gets (on average) smaller and smaller with each step. I pick the step size using the Maxwell-Boltzman distribution (with a =1) and a suitable scaling which depends on the iteration parameter. I the add a opacity depending on how many times the points are visited: bright white means a lot, while grey means not many and black never.<\/p><\/blockquote>\n<p><img decoding=\"async\" src=\"https:\/\/scontent-b.xx.fbcdn.net\/hphotos-xap1\/v\/t1.0-9\/p417x417\/10574230_538461072947163_6330392381579252452_n.jpg?oh=3cc5d22e6ca885b5b45e4219ad953385&amp;oe=543409E7\" alt=\"walk\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/scontent-a.xx.fbcdn.net\/hphotos-xfa1\/l\/t1.0-9p417x417\/10574230_538461076280496_5461831089102456456_n.jpg?oh=3cc5d22e6ca885b5b45e4219ad953385&amp;oe=543409E7\" alt=\"walk\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/scontent-b.xx.fbcdn.net\/hphotos-xap1\/t1.0-9\/10574230_538461079613829_174312939122976795_n.jpg?oh=3cc5d22e6ca885b5b45e4219ad953385&amp;oe=543409E7\" alt=\"walk\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/scontent-a.xx.fbcdn.net\/hphotos-xfa1\/t1.0-9\/10574230_538461082947162_5230829344397698659_n.jpg?oh=3cc5d22e6ca885b5b45e4219ad953385&amp;oe=543409E7\" alt=\"walk\" \/><\/p>\n<p>Once again, these images are rather for artistic purposes than scientific purposes.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have again been playing with some random walks, using the same method as here. This time I used 1000000 iterations and added some colour. Below are random walks, on the plane (not a lattice) for which step size gets (on average) smaller and smaller with each step. I pick the step size using the &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/ajb\/2014\/08\/03\/more-experiments-with-random-walks\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">More experiments with random walks<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4476","post","type-post","status-publish","format-standard","hentry","category-mathematical-art"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/4476","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/comments?post=4476"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/4476\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=4476"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=4476"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=4476"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}