{"id":227531,"date":"2025-12-20T09:19:22","date_gmt":"2025-12-20T15:19:22","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/12\/functions-in-hyperspace"},"modified":"2025-12-20T09:19:22","modified_gmt":"2025-12-20T15:19:22","slug":"functions-in-hyperspace","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/12\/functions-in-hyperspace","title":{"rendered":"Functions in Hyperspace"},"content":{"rendered":"<p><\/p>\n<p><iframe style=\"display: block; margin: 0 auto; width: 100%; aspect-ratio: 4\/3; object-fit: contain;\" src=\"https:\/\/www.youtube.com\/embed\/349r0xJFGNw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope;\n   picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>Functions describe the world. Join me on a tour of hyperspace, and see the many strange creatures that live there. They are just functions with lots of inputs and outputs. They are parametric surfaces that take inputs u and v, and output spatial x, y, z coordinates, and r, g, b, a color outputs. This produces a colored 3D surface. Then you can add additional inputs and visualize a single slice of each input parameter, and slide through different parameter values to see different slices of the function over time. This causes the colored surface to evolve over time.<br \/> I take my time to build up the mathematical intuitions behind visualizing functions, starting with 1-in-1-out functions, and pushing it up to 7-in-7-out functions, and beyond.<\/p>\n<p>Enter Hyperspace: <a href=\"https:\/\/evolvecode.io\/hyperspace\/inde\">https:\/\/evolvecode.io\/hyperspace\/inde<\/a>\u2026 Code: <a href=\"https:\/\/github.com\/MaxRobinsonTheGrea\">https:\/\/github.com\/MaxRobinsonTheGrea<\/a>\u2026 Discord: <img alt=\"\" class=\"\"> \/ discord ~SUPPORT ME~ Scrimba: <a href=\"https:\/\/scrimba.com\/?via=EmergentGarden\">https:\/\/scrimba.com\/?via=EmergentGarden<\/a> Patreon: <img alt=\"\" class=\"\"> \/ emergentgarden Ko-fi: <a href=\"https:\/\/ko-fi.com\/emergentgarden\">https:\/\/ko-fi.com\/emergentgarden<\/a> Twitter: <img alt=\"\" class=\"\"> \/ max_romana Bluesky: <a href=\"https:\/\/bsky.app\/profile\/emergentgard\">https:\/\/bsky.app\/profile\/emergentgard<\/a>\u2026 ~SOURCES~ Functions Describe the World: <img alt=\"\" class=\"\"> \u2022 On Mathematical Maturity Thomas Garrity Hyperspace animation: <img alt=\"\" class=\"\"> \u2022 Blender Hyperspace Jump Shell Surfaces: <a href=\"https:\/\/www.geogebra.org\/m\/twfwsxb9\">https:\/\/www.geogebra.org\/m\/twfwsxb9<\/a> Music: <img alt=\"\" class=\"\"> \/ <a href=\"https:\/\/twitter.com\/acolyte\">@acolyte<\/a>-compositions Most come from this new album: <img alt=\"\" class=\"\"> \u2022 Stellar Nurseries (Full Album) AI Disclaimer: I used AI code tools for the website and animations. No AI video, images, script, voice, or music were used. ~TIMESTAMPS~ (0:00) Functions in Hyperspace (2:47) Visualizing Functions (5:37) Parametric Surfaces (10:01) Slices of Slices (14:55) More Parameters (18:28) Exploring the Zoo.<br \/> Source Code: <a href=\"https:\/\/github.com\/MaxRobinsonTheGrea\">https:\/\/github.com\/MaxRobinsonTheGrea<\/a>\u2026<br \/> Discord: \/ discord.<\/p>\n<p>~SUPPORT ME~<br \/> Scrimba: <a href=\"https:\/\/scrimba.com\/?via=EmergentGarden\">https:\/\/scrimba.com\/?via=EmergentGarden<\/a>.<br \/> Patreon: \/ emergentgarden.<br \/> Ko-fi: <a href=\"https:\/\/ko-fi.com\/emergentgarden\">https:\/\/ko-fi.com\/emergentgarden<\/a>.<br \/> Twitter: \/ max_romana.<br \/> Bluesky: <a href=\"https:\/\/bsky.app\/profile\/emergentgard\">https:\/\/bsky.app\/profile\/emergentgard<\/a>\u2026<\/p>\n<p>~SOURCES~<br \/> Functions Describe the World: \u2022 On Mathematical Maturity Thomas Garrity.<br \/> Hyperspace animation: \u2022 Blender Hyperspace Jump.<br \/> Shell Surfaces: <a href=\"https:\/\/www.geogebra.org\/m\/twfwsxb9\">https:\/\/www.geogebra.org\/m\/twfwsxb9<\/a><\/p>\n<p>Music: \/ <a href=\"https:\/\/twitter.com\/acolyte\">@acolyte<\/a>-compositions.<br \/> Most come from this new album: \u2022 Stellar Nurseries (Full Album) <\/p>\n<p>AI Disclaimer:<\/p>\n<div class=\"more-link-wrapper\"> <a class=\"more-link\" href=\"https:\/\/lifeboat.com\/blog\/2025\/12\/functions-in-hyperspace\">Continue reading \u201cFunctions in Hyperspace\u201d | &gt;<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Functions describe the world. Join me on a tour of hyperspace, and see the many strange creatures that live there. They are just functions with lots of inputs and outputs. They are parametric surfaces that take inputs u and v, and output spatial x, y, z coordinates, and r, g, b, a color outputs. This [\u2026]<\/p>\n","protected":false},"author":599,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229,42,6],"tags":[],"class_list":["post-227531","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-media-arts","category-robotics-ai"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/227531","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/599"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=227531"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/227531\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=227531"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=227531"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=227531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}