{"id":138,"date":"2010-12-28T15:13:00","date_gmt":"2010-12-28T15:13:00","guid":{"rendered":"http:\/\/witpoko.com\/?p=138"},"modified":"2010-12-28T15:13:00","modified_gmt":"2010-12-28T15:13:00","slug":"a-barnsleys-fern-in-7-lines-of-mathematica","status":"publish","type":"post","link":"https:\/\/witpoko.com\/?p=138","title":{"rendered":"A Barnsley’s Fern In 7 Lines of Mathematica"},"content":{"rendered":"
I used to draw a Barnsley’s fern<\/a> with a program written in Pascal when I was 19 years old. Yesterday someone asked about it in a forum I visited, so I drew another one using Mathematica<\/i>. The code is much shorter this time. (I’m sure that many people can shorten it even more.)<\/div>\n
<\/div>\n
Here’s the code to draw the fern with 10,000 points. You can copy and paste and run it in Mathematica<\/i>:<\/div>\n

<\/p>\n

          
ifsFern[p_] := Module[{i},
  i = Random[Integer, 99];
  If[i < 1, Return[{{0., 0.}, {0., .16}}.p ]];
  If[i >= 1 && i < 86, Return[{{0.85, 0.04}, {-0.04, 0.85}}.p + {0., 1.6}]];
  If[i >= 86 && i < 93, Return[{{0.20, -0.26}, {0.23, 0.22}}.p + {0., 1.6}]];
  If[i >= 93, Return[{{-0.15, 0.28}, {0.26, 0.24}}.p + {0., 0.44}]]] <\/p>

<\/p>
<\/p>
Graphics[{RGBColor[0, 0.5, 0], Point[NestList[ifsFern, {0, 0}, 10000]]}]<\/p>   
<\/p>

<\/pre>\n
<\/p>\n
The result looks like this:<\/div>\n
\"\"<\/div>\n
<\/div>\n
<\/div>\n","protected":false},"excerpt":{"rendered":"
I used to draw a Barnsley’s fern with a program written in Pascal when I was … A Barnsley’s Fern In 7 Lines of Mathematica<\/span>Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":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":[31,108,29],"tags":[137],"class_list":["post-138","post","type-post","status-publish","format-standard","hentry","category-math","category-math-geek","category-mathematica","tag-graphics-programming"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4UNq0-2e","_links":{"self":[{"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/posts\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/witpoko.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=138"}],"version-history":[{"count":0,"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/posts\/138\/revisions"}],"wp:attachment":[{"href":"https:\/\/witpoko.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/witpoko.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/witpoko.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}