2b:null 2c:["$","title",null,{"children":"Lissajous curves | Jacob Rus | Observable"}] 31:[] 2f:{"id":"a10a4cea99f12d7e","slug":"lissajous-curves","title":"Lissajous curves","thumbnail":"9e58200f3b7c799ff87468a48f4202991f1e76b1010e8e9b222210be992f1627","access_level":"public","create_time":"$D2018-06-05T07:47:32.519Z","update_time":"$D2019-11-24T21:31:48.805Z","view_time":null,"first_public_time":"$D2018-06-05T08:11:32.250Z","fork":{"id":"cd5cfc01e695c0b1","slug":"roses","title":"Roses","owner":{"id":"9b8a8e177a49059a","login":"jrus","name":"Jacob Rus"}},"stars":10,"starred":false,"owner":{"type":"team","id":"9b8a8e177a49059a","login":"jrus","name":"Jacob Rus","avatar_url":"https://avatars-next.observableusercontent.com/c33dbeed76527c50e64208b0e005e0b6e54a3bef2a14ea6a823f1c7de4867662","tier":"starter_2024"},"version":518,"publish_version":518,"role":null,"authored":false,"authors":[{"type":"individual","id":"ddd7235babc79ce0","login":"jrus","name":"Jacob Rus","avatar_url":"https://avatars-next.observableusercontent.com/c33dbeed76527c50e64208b0e005e0b6e54a3bef2a14ea6a823f1c7de4867662","tier":null}],"members":[{"type":"individual","id":"ddd7235babc79ce0","login":"jrus","name":"Jacob Rus","avatar_url":"https://avatars-next.observableusercontent.com/c33dbeed76527c50e64208b0e005e0b6e54a3bef2a14ea6a823f1c7de4867662","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":6,"collection":null,"type":"notebook","body":{"title":"Lissajous curves","cells":[{"id":0,"value":"Title = md`# Lissajous curves`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":229,"value":"md`A [Lissajous curve](https://en.wikipedia.org/wiki/Lissajous_curve) is a parametric sinusoid: ${tex`\n\\begin{pmatrix}x(t) \\\\ y(t)\\end{pmatrix} = \\begin{pmatrix}\\cos(at + \\phi) \\\\ \\cos(bt + \\psi)\\end{pmatrix}\n`}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":16,"value":"viewof ncols = html`\n `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":14,"value":"viewof nrows = html`\n `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":447,"value":"viewof phase_x = html`\n `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":452,"value":"viewof phase_y = html`\n `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":8,"value":"multi_plot = html`\n`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":307,"value":"viewof a = html`\n `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":309,"value":"viewof b = html`\n `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":304,"value":"single_plot = html`\n`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":409,"value":"lissajous = (a, b) =>\n t => [Math.cos(a*t + phase_x), Math.cos(b*t + phase_y)]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":77,"value":"bezlissajous = (a, b) =>\n bezpts_to_svgpath(bezeval(lissajous(a, b), period(a, b), [-2, 2, -2, 2], tolerance)).replace(/\\n/g,'')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":71,"value":"transform = (i, j) =>\n `translate(-${scale/2} -${scale/2}) scale(${scale}) translate(${i} ${j}) scale(0.45 -0.45)`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":271,"value":"period = (a, b) => [0, 2 / gcd(a, b) * Math.PI]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":372,"value":"gcd = (a, b) => {\n while (b != 0) [a, b] = [b, a % b];\n return a; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":278,"value":"tolerance = 0.0001","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":85,"value":"rows = [...Array(nrows+1).keys()].slice(1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":87,"value":"cols = [...Array(ncols+1).keys()].slice(1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":35,"value":"scale = width / ncols","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":41,"value":"height = scale * nrows","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2,"value":"import {bezeval, bezpts_to_svgpath} from \"@jrus/bezplot\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"