Linear, Power and Log Scales

d3.scaleLinear() maps with y = a·x + b; d3.scalePow().exponent(k) raises the value first, and d3.scaleSqrt() (k = 0.5) is the right scale for circle radii, because area should grow with the value. d3.scaleLog() suits data spanning orders of magnitude but its domain must not touch zero; d3.scaleSymlog() accepts zero and negatives. The page draws total units (sample data) with both radius scales:

Linear versus square-root radii, and what a scale reportsHTML
<script src="https://cdn.jsdelivr.net/npm/d3@7.9.0/dist/d3.min.js"></script>
<script src="booknest-sales.js"></script>
<svg width="620" height="128" font-family="Arial" font-size="14"></svg>
<pre id="log" style="margin:0; font-size:13px"></pre>
<script>
  const units = SALES.books.map(b => d3.sum(SALES.sales, s => s.book === b.id ? s.units : 0));
  [['linear r', d3.scaleLinear()], ['sqrt r', d3.scaleSqrt()]].forEach(([label, r], row) => {
    r.domain([0, d3.max(units)]).range([0, 28]);
    const g = d3.select('svg').append('g').attr('transform', `translate(0, ${32 + row * 64})`);
    g.append('text').attr('y', 5).text(label);
    g.selectAll('circle').data(units).join('circle').attr('r', r)
      .attr('cx', (d, i) => 120 + i * 85).attr('fill', (d, i) => SALES.books[i].color);
  });
  const x = d3.scaleLinear().domain([0, 1218]).range([0, 500]).nice();
  d3.select('#log').text(`x.domain() after nice(): ${x.domain()}   x.ticks(5): ${x.ticks(5)}\n`
    + `x.invert(250): ${x.invert(250)}  x(2000): ${x(2000)}  clamped: ${x.clamp(true)(2000)}`);
</script>
Browser output of Listing 6.9
Browser output of 9

Linear radii give the best seller over seven times the area of Small Steps to Big Summits for 2.7 times the sales; square-root radii get it right. nice() extended the domain to 1300, ticks(5) treated 5 as a hint, clamp(true) stops extrapolation, and invert() turns pixels back into data (Zoom, Brush and Drag).

Linear versus square-root radius scales for units sold, plus nice, ticks, invert and clampHTMLLive
<!doctype html>
<style>
  body { margin: 0; padding: 8px; background: #fafaf7; font: 13px system-ui, sans-serif; color: #263238; }
  svg { width: 100%; max-width: 600px; display: block; }
  pre { margin: 0; font-size: 12px; }
</style>
<script src="https://cdn.jsdelivr.net/npm/d3@7.9.0/dist/d3.min.js"></script>
<svg viewBox="0 0 600 200" font-size="13"></svg>
<pre id="log"></pre>
<script>
  // BookNest sample data, invented for these examples (not real sales)
  const SALES = (() => {
    const books = [
      { id: 1, key: 'harbor', title: 'The Quiet Harbor', author: 'Elena Marsh', genre: 'Fiction', color: '#1f5f8b', price: 18.99, rating: 4.6 },
      { id: 2, key: 'deepweb', title: 'Patterns of the Deep Web', author: 'Ravi Menon', genre: 'Technology', color: '#5b3f99', price: 39.5, rating: 4.3 },
      { id: 3, key: 'saffron', title: 'Salt and Saffron', author: 'Leila Haddad', genre: 'Cooking', color: '#e09a10', price: 24, rating: 4.8 },
      { id: 4, key: 'summit', title: 'Small Steps to Big Summits', author: 'Tom Okafor', genre: 'Self-Help', color: '#3f7d3a', price: 14.99, rating: 4.1 },
      { id: 5, key: 'clock', title: "The Clockmaker's Paradox", author: 'Iris Vale', genre: 'Science Fiction', color: '#b5452f', price: 16.2, rating: 4.5 },
      { id: 6, key: 'glass', title: 'Gardens in Glass', author: 'June Park', genre: 'Gardening', color: '#2a9d8f', price: 22.5, rating: 4.4 },
    ];
    const units = {        // units sold per month, January 2025 to August 2026
      1: [40, 47, 46, 47, 57, 51, 46, 54, 60, 60, 71, 111, 52, 42, 49, 56, 59, 48, 53, 51],
      2: [40, 37, 35, 41, 48, 43, 40, 42, 50, 53, 53, 84, 42, 35, 38, 41, 45, 41, 46, 46],
      3: [46, 45, 41, 46, 53, 49, 46, 45, 60, 51, 63, 100, 48, 48, 49, 48, 53, 49, 48, 52],
      4: [100, 80, 72, 70, 66, 66],                    // released March 2026
      5: [48, 47, 54, 52, 65, 55, 57, 58, 64, 66, 75, 124, 58, 49, 59, 56, 63, 57, 54, 57],
      6: [31, 30, 28, 35, 31, 32, 29, 30, 41, 36, 45, 64, 31, 30, 30, 38, 40, 38, 36, 38],
    };
    const months = d3.utcMonths(new Date('2025-01-01'), new Date('2026-09-01')).map(d3.utcFormat('%Y-%m'));
    const sales = books.flatMap(b => units[b.id].map((n, i) =>
      ({ month: months[i + months.length - units[b.id].length], book: b.id, units: n })));
    const ratings = [[4, 8, 20, 87, 293], [6, 10, 22, 95, 147], [2, 3, 8, 45, 342], [2, 3, 8, 24, 28],
      [4, 8, 20, 90, 228], [4, 7, 20, 82, 147]].map((counts, i) => ({ book: i + 1, counts }));  // 1 to 5 stars
    const regions = [{ id: '826', name: 'United Kingdom', units: 1480 }, { id: '276', name: 'Germany', units: 1120 },
      { id: '250', name: 'France', units: 760 }, { id: '372', name: 'Ireland', units: 540 },
      { id: '528', name: 'Netherlands', units: 410 }, { id: '724', name: 'Spain', units: 320 }];
    const links = [[5, 1, 38], [1, 3, 24], [2, 5, 18], [3, 6, 21], [4, 1, 12], [2, 6, 9], [4, 3, 15], [5, 6, 14]]
      .map(([source, target, value]) => ({ source, target, value }));   // customers who bought both
    return { books, sales, ratings, regions, links };
  })();

  const units = SALES.books.map(b => d3.sum(SALES.sales, s => s.book === b.id ? s.units : 0));
  const svg = d3.select('svg');
  // Area should grow with the value: sqrt radii get that right, linear radii exaggerate
  [['linear r', d3.scaleLinear()], ['sqrt r', d3.scaleSqrt()]].forEach(([label, r], row) => {
    r.domain([0, d3.max(units)]).range([0, 28]);
    const g = svg.append('g').attr('transform', `translate(0, ${32 + row * 64})`);
    g.append('text').attr('y', 5).text(label);
    g.selectAll('circle').data(units).join('circle').attr('r', r)
      .attr('cx', (d, i) => 120 + i * 80).attr('fill', (d, i) => SALES.books[i].color);
    if (row) g.selectAll('text.v').data(units).join('text').attr('class', 'v').attr('font-size', 10)
      .attr('x', (d, i) => 120 + i * 80).attr('y', 44).attr('text-anchor', 'middle').text(d => d);
  });

  // A log axis for values spanning orders of magnitude (the domain must not touch zero)
  const log = d3.scaleLog([1, 10000], [120, 580]);
  svg.append('text').attr('y', 184).text('log x');
  svg.append('g').attr('transform', 'translate(0,170)').call(d3.axisBottom(log).ticks(4, '~s'));
  svg.selectAll('circle.u').data(units).join('circle').attr('class', 'u').attr('r', 4)
    .attr('cx', d => log(d)).attr('cy', 170).attr('fill', (d, i) => SALES.books[i].color);

  const x = d3.scaleLinear().domain([0, d3.max(units)]).range([0, 500]).nice();
  d3.select('#log').text(`x.domain() after nice(): ${x.domain()}   x.ticks(5): ${x.ticks(5)}\n`
    + `x.invert(250): ${x.invert(250)}  x(2000): ${x(2000)}  clamped: ${x.clamp(true)(2000)}`);
</script>