{"id":137,"date":"2026-08-02T23:36:00","date_gmt":"2026-08-02T23:36:00","guid":{"rendered":"https:\/\/vexel.codes\/?p=137"},"modified":"2026-08-02T23:37:49","modified_gmt":"2026-08-02T23:37:49","slug":"a-bit-more-math-singing-that-sycl-song","status":"publish","type":"post","link":"https:\/\/vexel.codes\/?p=137","title":{"rendered":"A bit more math, singing that Sycl song."},"content":{"rendered":"\n<section class=\"vexafracta-vocabulary\"> <p> <strong>VEXEL:<\/strong> One point-unit in the geometry, containing the mathematical state and data fields for that coordinate. <\/p>\n\n<p> <strong>NGine:<\/strong> The active transformation associated with each VEXEL. It reads the VEXEL, consults neighboring state, rules, and lookup tables, and produces the next state. <\/p>\n\n<p> <strong>VEXAFRACTA:<\/strong> The complete <em>N &times; N &times; N<\/em> volume formed from stacked VEXEL planes. <\/p>\n\n<p><strong>Conceptual relationship:<\/strong><\/p>\n\n<p style=\"margin-left: 2em; font-family: monospace;\"> NGine(V<sub>i<\/sub>, N<sub>i<\/sub>, R, L) &rarr; V<sub>i<\/sub>&prime; <\/p>\n\n<p>Where:<\/p>\n\n<ul> <li> V<sub>i<\/sub> is the current VEXEL. <\/li> <li> N<sub>i<\/sub> is its neighborhood. <\/li> <li> R is the rule set. <\/li> <li> L is the collection of lookup tables. <\/li> <li> V<sub>i<\/sub>&prime; is the resulting next state. <\/li> <\/ul>\n\n<p> Conceptually, every VEXEL has an NGine. <\/p>\n\n<p> Physically, the GPU does not store millions of separate copies of the code. One compiled NGine kernel is executed across many VEXELs, with each invocation operating on a different coordinate and state record. <\/p>\n\n<p> <strong>The VEXEL holds.<\/strong><br> <strong>The NGine acts.<\/strong><br> <strong>The VEXAFRACTA emerges.<\/strong> <\/p> <\/section>\n","protected":false},"excerpt":{"rendered":"<p>VEXEL: One point-unit in the geometry, containing the mathematical state and data fields for that coordinate. NGine: The active transformation associated with each VEXEL. It reads the VEXEL, consults neighboring state, rules, and lookup tables, and produces the next state. VEXAFRACTA: The complete N &times; N &times; N volume formed from stacked VEXEL planes. Conceptual [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-137","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/vexel.codes\/index.php?rest_route=\/wp\/v2\/posts\/137","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vexel.codes\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vexel.codes\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vexel.codes\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vexel.codes\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=137"}],"version-history":[{"count":1,"href":"https:\/\/vexel.codes\/index.php?rest_route=\/wp\/v2\/posts\/137\/revisions"}],"predecessor-version":[{"id":138,"href":"https:\/\/vexel.codes\/index.php?rest_route=\/wp\/v2\/posts\/137\/revisions\/138"}],"wp:attachment":[{"href":"https:\/\/vexel.codes\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=137"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vexel.codes\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=137"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vexel.codes\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}