2b:null 2c:["$","title",null,{"children":"Rubik's cubes and permutation groups (HACKY) (IN PROGRESS) | 💧 | Observable"}] 31:[] 2f:{"id":"731f9a92e55a91fe","slug":null,"title":"Rubik's cubes and permutation groups (HACKY) (IN PROGRESS)","thumbnail":"9e9ef9bf1861b9173e8529e19f47b7ee9252da213b678f649c4d7659c14337bf","access_level":"public","create_time":"$D2023-10-30T02:13:40.862Z","update_time":"$D2023-10-31T15:14:38.074Z","view_time":null,"first_public_time":"$D2023-10-30T02:13:40.862Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"6fae8e92fb4d3e1c","login":"modellifluous","name":"💧","avatar_url":"https://avatars-next.observableusercontent.com/e90df5560d470e589bf245189722d04c6778f4dcaa39a019b7ab07af15e2866e","tier":"starter_2024"},"version":586,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"5e97f0fec2101966","login":"modellifluous","name":"💧","avatar_url":"https://avatars-next.observableusercontent.com/e90df5560d470e589bf245189722d04c6778f4dcaa39a019b7ab07af15e2866e","tier":null}],"members":[{"type":"individual","id":"5e97f0fec2101966","login":"modellifluous","name":"💧","avatar_url":"https://avatars-next.observableusercontent.com/e90df5560d470e589bf245189722d04c6778f4dcaa39a019b7ab07af15e2866e","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Rubik's cubes and permutation groups (HACKY) (IN PROGRESS)","cells":[{"id":0,"value":"# Rubik's cubes and permutation groups (HACKY) (IN PROGRESS)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":16,"value":"Looking at Rubik's cube solutions from a permutation group point of view, using the tools developed in my previous notebook https://observablehq.com/@modellifluous/a-fun-puzzle-about-permutation-groups.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":500,"value":"Related/similar:\n- http://cube.rider.biz/visualcube.php","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":107,"value":"toc()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"## General permutation code","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":110,"value":"Import permutation class from previous workbook, using the opposite conjugation/commutator convention.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":25,"value":"// Convention used for conjugation and commutators\n// We set conventionInverseLast = false, i.e. put inverses first (q^{-1} w q; p^{-1} q^{-1} p q)\n// E.g. (a, b, c).conj(q) = (q(a), q(b), q(c)) under this convention (easier to work with than q^{-1} under conventionInverseLast = true)\nconventionInverseLast = false","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"import {Permutation, commutator, mapOrId}\nwith {conventionInverseLast}\nfrom \"@modellifluous/a-fun-puzzle-about-permutation-groups\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":503,"value":"## Experiments II - cleaning things up","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":509,"value":"Let's take a more systematic approach to constructing/rendering the cube and its rearrangements.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":505,"value":"cartesianProduct = (xss, yss) => xss.flatMap(xs => yss.map(ys => xs.concat(ys)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":529,"value":"// 3x3 square centered on the origin\nsquare3 = Array(2).fill([-1, 0, 1].map(v => [v])).reduce(cartesianProduct)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":513,"value":"// 3x3x3 cube centered on the origin, excluding the center\ncube3noCenter = Array(3).fill([-1, 0, 1].map(v => [v])).reduce(cartesianProduct).filter(p => !_.isEqual(p, [0, 0, 0]))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":531,"value":"// Positions of unit faces of a 3x3 cube centered on the origin, after moving each face outwards by 1 unit\nrubik3unitFaces = Array(3).fill([-1, 0, 1].map(v => [v])).flatMap((_, i, arr) => {\n var newArr = [...arr]\n newArr[i] = [-2, 2].map(v => [v])\n return newArr.reduce(cartesianProduct)\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":574,"value":"rubik3faceCenters = rubik3unitFaces.filter(xs => xs.map(x => x === 0 ? 1 : 0).reduce((a, b) => a+b) === 2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":580,"value":"rubik3frontFace = rubik3unitFaces.filter(xs => xs[2] === -2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":585,"value":"// TODO (next): Implement the cross product","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"## Experiments","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":28,"value":"// Check that conventionInverseLast has been successfully changed to false\nnew Permutation(\"(123)\").conj(new Permutation(\"(345)\")) // should return (124)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":114,"value":"Render (nearly) square color patches","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":40,"value":"// https://observablehq.com/@observablehq/htl\n\n// TODO: Find a web-safe square ('block' monospace) typeface to use here\n// Possible hack/workaround: https://graphicdesign.stackexchange.com/questions/113534/monospace-font-that-supports-both-english-and-japanese\n// (English fonts usually have a 2:1 aspect ratio, whereas Japanese fonts usually have a 1:1 aspect ratio)\n\n// Oh wait ... does that mean we can just put two spaces next to each other?\n// On my computer, this almost works (blue box is 17 chars high and 16 wide, likewise for the orange box)\n// I guess that's good enough for now :)\n\nhtl.html` `","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":133,"value":"// https://stackoverflow.com/questions/805107/creating-multiline-strings-in-javascript\nrubik3net = `\n |333\n |333\n |333\n555|111|222|444\n555|111|222|444\n555|111|222|444\n |666\n |666\n |666\n`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":175,"value":"// https://www.w3schools.com/cssref/css_colors.php\n// Color 3 is meant to be white, initially tried beige, but let's change it to black\nlegend = new Map([[\"1\", \"green\"], [\"2\", \"darkRed\"], [\"3\", \"black\"], [\"4\", \"blue\"], [\"5\", \"darkOrange\"], [\"6\", \"#EEEE00\"]])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":198,"value":"// https://observablehq.com/@observablehq/htl\nhtl.html`\n ${Array.from(\"123456\").map(i => htl.html.fragment` `)}\n`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":306,"value":"// Was [3, 5, 1, 2, 4, 6].flatMap(v => Array(9).fill(v)), but this doesn't output the middle rows in the right order\nrubik3array = Array.from(rubik3net).filter(c => /\\d/.exec(c)).map(Number)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":267,"value":"rubik3fill = arr => {\n var i = 0\n return Array.from(rubik3net).map(c => {if (/\\d/.exec(c)) {i = i + 1; return arr[i - 1]} else {return c}})\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":285,"value":"rubik3fill(rubik3array).map(String).join(\"\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":154,"value":"// https://en.wikipedia.org/wiki/Rubik%27s_Cube\n// Since 1988, the arrangement of colours has been standardised with white opposite yellow, blue opposite green, and orange opposite red, and the red, white, and blue arranged clockwise in that order.\n// https://ruwix.com/the-rubiks-cube/japanese-western-color-schemes\n// This color scheme is also called Minus Yellow because if you add or extract yellow from any side you get its opposite.\nrubik3render = arr => {\n const s = rubik3fill(arr).map(String).join(\"\")\n return htl.html`\n ${Array.from(s).map(i => {\n if (/\\r|\\n/.exec(i)) {\n return htl.html.fragment`
`\n } if (/[|]/.exec(i)) {\n return htl.html.fragment``\n } else {\n return htl.html.fragment` `\n }\n })}\n `\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"rubik3render(rubik3array)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":322,"value":"import {fetchp} from '@tomlarkworthy/fetchp'","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":350,"value":"// https://observablehq.com/@observablehq/working-with-apis-remote-files\n// https://stackoverflow.com/questions/59499885/how-to-get-a-text-of-a-specific-section-via-wikipedia-api\n// https://www.mediawiki.org/wiki/API:Parsing_wikitext\n// If using oldid (for a specific revision), can't use page as well\n// oldid=1181742775 is the 23:14, 24 October 2023 revision for the Rubik's_Cube page (freezing this so we can reliably excerpt text within it)\nwikiSections = await fetchp(\"https://en.wikipedia.org/w/api.php?action=parse&format=json&oldid=1181742775&prop=sections&disabletoc=1\")\n .then(d => d.json())","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":355,"value":"section = wikiSections.parse.sections.filter(o => /Singmaster/.exec(o.line)).map(o => o.index)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":331,"value":"response = await fetchp(`https://en.wikipedia.org/w/api.php?action=parse&format=json&oldid=1181742775§ion=${section}&disabletoc=1&formatversion=2`).then(d => d.json())","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":437,"value":"rubik3fill([...Array(54).keys()].map(n => String(n).padStart(2, '0'))).map(s => {if (/[ ]/.exec(s)) {return s + s} else {return s}}).join(\" \")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":435,"value":"F = new Permutation(\"(06 15 47 35)(07 27 46 23)(08 39 45 11)(12 14 38 36)(13 26 37 24)\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":477,"value":"rubik3render(rubik3array.map((v, i) => rubik3array[Number(mapOrId(F.inverse().value, String(i).padStart(2, '0')))]))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":343,"value":"html`${response.parse.text.replace(/

The 4×4×4.*(?=

.*?<\\/li>/sg, \"\")}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"# Notebook setup","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":9,"value":"import {toc} from \"@ariofrio/toc\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"import {notebookFormatting} from \"@modellifluous/notebook-formatting\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"notebookFormatting({max_width: 1050})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"