{"id":285739,"date":"2026-10-08T17:14:07","date_gmt":"2026-10-08T17:14:07","guid":{"rendered":"https:\/\/ushopwell.com\/ublog\/tuppers-self-referential-formula-it-draws-itself-then-plays-amazing-grace-manic\/"},"modified":"2026-10-08T17:14:07","modified_gmt":"2026-10-08T17:14:07","slug":"tuppers-self-referential-formula-it-draws-itself-then-plays-amazing-grace-manic","status":"publish","type":"post","link":"https:\/\/ushopwell.com\/ublog\/tuppers-self-referential-formula-it-draws-itself-then-plays-amazing-grace-manic\/","title":{"rendered":"Tupper&#8217;s Self-Referential Formula \u2014 It Draws Itself, Then Plays Amazing Grace \u2014 manic"},"content":{"rendered":"<div class=\"youtubomatic-video-container\"><iframe loading=\"lazy\" width=\"580\" height=\"380\" src=\"https:\/\/www.youtube.com\/embed\/Sqv51GYFTKI?autoplay=1&#038;controls=1&#038;hl=en\" frameborder=\"0\" allowfullscreen><\/iframe><\/div>\n<p>Tupper&#8217;s Self-Referential Formula \u2014 It Draws Itself, Then Plays Amazing Grace.<\/p>\n<p>Jeff Tupper&#8217;s formula (from his SIGGRAPH 2001 paper on reliable graphing, the method behind his GrafEq program):<\/p>\n<p>    1\/2 \uff1c floor( mod( floor(y\/17) \u00b7 2^(\u221217\u00b7floor(x) \u2212 mod(floor(y), 17)), 2 ) )<\/p>\n<p>Plot it for 0 \u2264 x \uff1c 106 and k \u2264 y \uff1c k + 17, where k is a particular 543-digit number, and it draws its own picture. (As usual for this plot, x runs right to left and y downward.)<\/p>\n<p>How: divide k by 17 to get N, write N in binary, cut it into 106 columns of 17 bits and stand them side by side \u2014 that IS the picture. The formula only reads bits back: floor(y\/17) finds N, the power of two slides to bit 17x + (y mod 17), and mod 2 reads it. So it is not really self-referential: one strip down, y + 17, the number is N + 1, and every 106 \u00d7 17 picture appears somewhere in the plane, at y = 17N for its own N.<\/p>\n<p>The whole scene is one short script \u2014 examples\/maths-with-music-103-tuppers-formula.manic in the manic repo.<\/p>\n<p>Made with manic \u2014 the animation LANGUAGE that turns plain text into precise,<br \/>\ncorrect animations. No coding, no timeline scrubbing: you describe what you<br \/>\nwant and manic animates it \u2014 math, physics, optics, algorithms, geometry \u2014<br \/>\nwith the diagram actually TRUE, not hand-drawn. One tiny script \u2192 this video.<\/p>\n<p>\u25b6 Try it free in your browser: <a href=\"https:\/\/maniclang.com\" target=\"_blank\">https:\/\/maniclang.com<\/a><br \/>\n\u25b6 Docs + guides: <a href=\"https:\/\/docs.maniclang.com\/\" target=\"_blank\">https:\/\/docs.maniclang.com\/<\/a><br \/>\n\u25b6 Full example gallery: <a href=\"https:\/\/app.maniclang.com\/gallery\" target=\"_blank\">https:\/\/app.maniclang.com\/gallery<\/a><\/p>\n<p>Copy the exact script for this scene in the gallery, change a number, run it \u2014<br \/>\nthat&#8217;s the power of manic: real animation, in a few lines.<\/p>\n<p>#tupper #maths #binary #amazinggrace #music<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tupper&#8217;s Self-Referential Formula \u2014 It Draws Itself, Then Plays Amazing Grace. Jeff Tupper&#8217;s formula (from his SIGGRAPH 2001 paper on reliable graphing, the method behind his GrafEq program): 1\/2 \uff1c floor( mod( floor(y\/17) \u00b7 2^(\u221217\u00b7floor(x) \u2212 mod(floor(y), 17)), 2 ) ) Plot it for 0 \u2264 x \uff1c 106 and k \u2264 y \uff1c k + 17, where k is a particular 543-digit number, and it draws its own picture&#8230;.<\/p>\n","protected":false},"author":1,"featured_media":285740,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","tve_updated_post":"","tve_custom_css":"","tve_user_custom_css":"","tve_globals":{},"tcb2_ready":0,"tcb_editor_enabled":0,"tve_landing_page":"","_tve_header":"","_tve_footer":""},"categories":[1],"tags":[],"class_list":["post-285739","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Tupper&#039;s Self-Referential Formula \u2014 It Draws Itself, Then Plays Amazing Grace \u2014 manic - UshopWell.com<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ushopwell.com\/ublog\/tuppers-self-referential-formula-it-draws-itself-then-plays-amazing-grace-manic\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tupper&#039;s Self-Referential Formula \u2014 It Draws Itself, Then Plays Amazing Grace \u2014 manic - UshopWell.com\" \/>\n<meta property=\"og:description\" content=\"Tupper&#8217;s Self-Referential Formula \u2014 It Draws Itself, Then Plays Amazing Grace. 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