25:["$","title",null,{"children":"Laver Tables | Matt Diamond | Observable"}] 4b:T24e2,const N = 2 ** n; const laver = laverTable(n); // Derivation of p ⋆ q using the rules that laverTable() fills the table with function derivation(p, q) { const v = laver[p][q]; const lhs = `${p} ⋆ ${q}`; const pad = " ".repeat(lhs.length + 1); // aligns continuation "=" under the first "=" if (p === N) return [`${lhs} = ${v}`, `row ${N} = 2ⁿ is the identity: 2ⁿ ⋆ q = q`]; if (q === 1) return [`${lhs} = ${v}`, `p ⋆ 1 = p + 1 (mod 2ⁿ)`]; const a = laver[p][q - 1], b = laver[p][1]; return [ `${lhs} = ${v}`, `p${" ".repeat(p.toString().length)}⋆ q${" ".repeat(q.toString().length)}= (p ⋆ (q − 1)) ⋆ (p ⋆ 1)`, `${lhs} = (${p} ⋆ ${q - 1}) ⋆ (${p} ⋆ 1)`, `${pad}= ${a} ⋆ ${b}`, `${pad}= ${v}` ]; } const laverPlot = (() => { const size = Math.min(800, Math.max(300, N * 40)); const m = {top: 30, left: 36}; const dpr = window.devicePixelRatio || 1; const W = size + m.left, H = size + m.top; const color = (v) => d3.color(d3.interpolateTurbo((v - 1) / Math.max(1, N - 1))); const palette = Array.from({length: N + 1}, (_, v) => (v ? color(v) : null)); // View window, in 0-based cell units: top-left corner (x0, y0) and span (cells visible per side) const minSpan = Math.min(N, 4); const view = {x0: 0, y0: 0, span: N}; const clampView = () => { view.span = Math.max(minSpan, Math.min(N, view.span)); view.x0 = Math.max(0, Math.min(N - view.span, view.x0)); view.y0 = Math.max(0, Math.min(N - view.span, view.y0)); }; const canvas = html`