Free Yin Yang Grid Generator

The construction is symmetric under a half-turn about the centre, so the two regions have exactly equal area — each precisely half the circle. That is the property the symbol is about, and it is only true if the arcs are R/2. Make the S bulge a little more and the halves stop being halves; the figure still reads, but it no longer means what it claims.

Because the eye is very good at detecting broken symmetry and very bad at producing it. A freehand S is nearly always steeper at one end, which makes one region visibly fatter at the waist even when the two ends look right. The error is small in absolute terms and obvious once seen, and it is the reason hand-drawn taijitu look homemade in a way that a hand-drawn circle does not.

The eyes compound it. Placed by eye they usually drift toward the centre — the illustrator's instinct is to balance them against the whole figure rather than to place them at the arc centres — and the result reads as slightly crowded. Half a radius out is further than it feels.

The name is taijitu, the diagram of the supreme ultimate, and the graphic is a great deal younger than the idea it stands for. Robin Wang draws the distinction carefully in Yinyang: The Way of Heaven and Earth in Chinese Thought and Culture (Cambridge University Press, 2012): the concept runs through Warring States and Han cosmology, the diagram's ancestors are the layered Song-dynasty Taijitu associated with the 11th-century thinker Zhou Dunyi, and the interlocking form this overlay draws became standard only later, in the Ming. Divided-circle motifs of the same kind appear centuries earlier in Roman ornament, with no line of transmission to the Chinese use.

Which is worth knowing for the same reason it is worth knowing about the hexagram: when a figure turns up in traditions that were never in contact, the explanation is constructional before it is historical. Peter S. Stevens makes the general argument in Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions (MIT Press, 1981) — the set of figures a compass and a straightedge produce easily is small, so the same ones surface again and again. This one needs nothing but a compass and one radius halved, which is why the hexagram generator tells the same story about a different shape.

For cut, inlay and carved work, export SVG. The whole figure is arcs, and a raster version of a curve becomes a staircase at any real cutting size — the outline and the S-curve are the two paths a cutter needs, and both come out as true curves.

For inlay in particular, note that the two regions are congruent: each is the other rotated a half turn. One template cuts both pieces, which is a practical consequence of the construction being exact and one you lose the moment the S is drawn freehand.

And use the construction step while you learn it. Circle, two marks at half a radius, two arcs, two eyes — five moves, and after building it twice you will not need the overlay again except to check a drawn one.

Three failures account for nearly every hand-drawn taijitu. The first is a comma-shaped division, where the curve is drawn as two tapering teardrops rather than as two arcs; it reads as a logo rather than a diagram, and the halves stop being equal. The second is an S drawn as a single sweep, which is almost never symmetric about the centre. The third is arcs of the wrong radius — usually too small, which pinches the waist and leaves the two regions visibly different at their widest points.

To check a drawn one, lay the exact overlay over it at the same outer radius and look at three places rather than at the whole figure: where the curve crosses the vertical axis, and the two points where it meets the outer circle. If all three coincide, the arcs are right. A discrepancy at the crossing but not at the ends means the radius is wrong; a discrepancy at one end only means the S is asymmetric.

The eyes are worth checking separately, because they fail independently. Drop the overlay opacity until only its two eye positions read, and compare. A drawn taijitu almost always has them too close to the centre, and moving them out to the arc centres is usually the single change that makes a wonky one look composed.

Finally, a note on line weight. The figure is usually shown as two filled regions rather than as outlines, and this overlay draws outlines — the circle, the S-curve and the two eyes. That is the right form for a construction you are drawing over or cutting to, and the wrong form for a finished mark. If you want the filled version, export the outlines as SVG and fill the two closed paths in whatever program you are finishing in; the geometry is already correct, and filling is a five-second operation that no overlay needs to do for you.