Lab: the visual version
Every widget from the article Lab: numbers that match what you see, in one place, for when you would rather play than read. Under each heading is a short note on what that widget illustrates. The last one is a bigger version of the article's chart, with more to play with.
The lightness curve
Lab's lightness (L*) is roughly a cube root of the amount of light. The straight line is for comparison. An 18% gray, the "middle gray" of photography, lands halfway.
HSL lightness vs real lightness
Twelve colors with the same HSL saturation and lightness, and the L* each one really has. Yellow is far lighter than blue, so HSL's "50%" is not one lightness. Flip the switch to see each color as the gray with the same L*.
The a*/b* plane
A slice of Lab at one lightness: a* across, b* up, gray in the middle. Pick a point to see its color, chroma and hue, and whether sRGB can show it. Close to black or white there is almost no room for color.
For the formulas and the reasoning, read the full article.