2b:null 2c:["$","title",null,{"children":"The Kolakoski Sequence | Jean Constant | Observable"}] 31:T6ea,viewof segments = { const M = N-1 const mywidths = widths.slice(1).map(line => line.slice(1)); const segments = mywidths.map((line, j) => { const r = 200 * (1 - (j+.1)/mywidths.length); const r2 = 200 * (1 - (j+.3)/mywidths.length); // next var W = 0; const segs = line.map((w,i) => { const startAngle = map(W/M * tau); W += w; const endAngle = map(W/M * tau); if (seq[i+1] == 1) return `M ${r * Math.cos(endAngle)} ${r * Math.sin(endAngle)}`; const largeAngleFlag = (endAngle - startAngle <= tau/2) ? 0 : 1; return `M ${r * Math.cos(startAngle)} ${r * Math.sin(startAngle)} A ${r} ${r} 0 ${largeAngleFlag} 1 ${r * Math.cos(endAngle)} ${r * Math.sin(endAngle)} L ${r2 * Math.cos(endAngle)} ${r2 * Math.sin(endAngle)} A ${r2} ${r2} 0 ${largeAngleFlag} 0 ${r2 * Math.cos(startAngle)} ${r2 * Math.sin(startAngle)} L ${r * Math.cos(startAngle)} ${r * Math.sin(startAngle)}`; }); segs.unshift(`M ${r * Math.cos(map(0))} ${r * Math.sin(map(0))}`); return { r, segs }; }); const root = svg``; root.value = segments; return root; }32:T466,viewof widths = { const nextline = ws => { var W = 0; const nws = []; for (var i = 0; i < N && W < N; i++) { var w = 0; for (var j = 0; j < seq[i]; j++) { w += ws.shift() || (nws.overflow = true, 0); } W += w; nws.push(w); } return nws; }; const widths = [ (new Array(N)).fill(1), ]; while (widths[0].length > 2) { widths.unshift(nextline(widths[0].slice())); } widths.reverse(); const root = html` ${widths.map(line => ` ${line.map((w,i) => ``).join('')} `).join('')}

${seq[i]} ${(i == line.length-1 && line.overflow) ? '

…

' : ''}

`; root.value = widths; return root; }33:[] 2f:{"id":"f7f77a435329bc0e","slug":"the-kolakoski-sequence","title":"The Kolakoski Sequence","thumbnail":"654bf140fdedfd5f3067e58cd9632b06261be15ce566cdc75cb40a69b4a00ebe","access_level":"public","create_time":"$D2018-07-15T06:59:19.469Z","update_time":"$D2018-07-15T08:43:21.327Z","view_time":null,"first_public_time":"$D2018-07-15T07:17:46.613Z","fork":{"id":"3f7d0ad04a8dca01","slug":"the-kolakoski-sequence","title":"The Kolakoski Sequence","owner":{"id":"cdda271b76654961","login":"kelleyvanevert","name":"Kelley van Evert"}},"stars":2,"starred":false,"owner":{"type":"team","id":"779801569d020938","login":"bysance","name":"Jean Constant","avatar_url":"https://avatars-next.observableusercontent.com/d9f8e121946490c519c81e74442053389852cc121f55569dbcd93451890d616e","tier":"starter_2024"},"version":613,"publish_version":613,"role":null,"authored":false,"authors":[{"type":"individual","id":"8551b105ce4f03cb","login":"bysance","name":"Jean Constant","avatar_url":"https://avatars-next.observableusercontent.com/d9f8e121946490c519c81e74442053389852cc121f55569dbcd93451890d616e","tier":null}],"members":[{"type":"individual","id":"8551b105ce4f03cb","login":"bysance","name":"Jean Constant","avatar_url":"https://avatars-next.observableusercontent.com/d9f8e121946490c519c81e74442053389852cc121f55569dbcd93451890d616e","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":2,"collection":null,"type":"notebook","body":{"title":"The Kolakoski Sequence","cells":[{"id":0,"value":"md`# The Kolakoski Sequence\n\nSee the [Numberphile video](https://www.youtube.com/watch?v=co5sOgZ3XcM).\n\nBTW, the best way to read this page is, confusingly, from bottom to top :)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":245,"value":"md``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":242,"value":"md`### #3 But, it's prettier in a circle:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":545,"value":"make_N_slider()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":56,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":333,"value":"map = theta => theta * -1 + tau * -3/8","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":54,"value":"tau = 2*Math.PI","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":240,"value":"md``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":224,"value":"md`### #2 And here it is, describing itself repeatedly:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":250,"value":"make_N_slider()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":122,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":235,"value":"md``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":220,"value":"md`### #1 Here is the Kolakowski sequence:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":547,"value":"make_N_slider()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":233,"value":"viewof seq = {\n const seq = kol(N);\n const root = md`${seq.join(', ')}…`;\n root.value = seq;\n return root;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":4,"value":"function kol (m) {\n const n = m//+1;\n const seq = [];\n \n for (var i = -1; seq.length < n; i++) {\n var x = seq[i-1] || i;\n if (i % 2 == 1) {\n for (var j = 0; j < x && seq.length < n; j++) seq.push(1);\n } else {\n for (var j = 0; j < x && seq.length < n; j++) seq.push(2);\n }\n }\n \n return seq//.slice(1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":168,"value":"import { slider } from '@jashkenas/inputs'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":540,"value":"function make_N_slider () {\n const slider = html``;\n const num = html``;\n \n slider.oninput = () => (viewof N).value = slider.valueAsNumber;\n const update = () => {\n num.innerText = slider.value = (viewof N).value;\n };\n \n (viewof N).addEventListener(\"input\", update);\n update();\n \n return Generators.disposable(html`

${slider} N = ${num}

`, () => {\n (viewof N).removeEventListener(\"input\", update);\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":538,"value":"viewof N = new View(86)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":535,"value":"import { View } from '@mbostock/synchronized-views'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 30:"$2f:body"