Learn · Essay · 14 min read · Updated September 2026

Understanding the Bagua

Eight figures of three lines each, arranged in a ring and in a square. Where the trigrams come from and what the Book of Changes hangs on them, the two arrangements and who drew them, what Leibniz saw in the older one, the grid the tradition lays over a floor plan, and the two ways of laying it that give different answers.

Oriented N 000°

Water

Fig. 01 Light, shadow and a right angle. The bagua reduces the world to broken and unbroken lines, and then to eight ways of stacking three of them.

Take a line. Break it or leave it whole. Stack three such lines and you have eight possible figures, and the tradition gave each a name, an image, a direction and a family of meanings. That is the bagua: eight trigrams, and the arrangement of them around a centre. This essay gives the eight, the two ways of arranging them and who arranged them, the square the ring becomes on a floor plan, and the one decision, where to put north, on which the schools disagree.

The eight figures

A whole line is yang: active, bright, firm. A broken line is yin: receptive, dark, yielding. Three whole lines, Qian, is heaven, pure yang. Three broken, Kun, is earth. Between them lie the six mixed figures: thunder and wind, water and fire, mountain and lake. Each is read from the bottom up, and each is a small picture. Kan, water, is a whole line between two broken ones, a current between its banks. Li, fire, is the reverse, a flame clinging to what it burns. Gen, mountain, is a whole line resting on two broken ones, weight held still. Zhen, thunder, is a whole line under two broken, movement starting from below; Xun, wind, is two whole over one broken, something that gets in underneath; Dui, lake, is two whole under one broken, an open surface over depth.

The trigrams are older than feng shui. They are the elements of the Yijing, the Book of Changes, whose core of sixty-four hexagrams, each a pair of trigrams, dates from the early Zhou, around the ninth century BCE, and whose commentaries were added over the following six hundred years. One of those commentaries, the Shuogua, the Discussion of the Trigrams, is where most of what feng shui says about the eight comes from. It makes them a family: Qian the father and Kun the mother, Zhen, Kan and Gen the eldest, middle and youngest sons, Xun, Li and Dui the eldest, middle and youngest daughters. It gives each an animal, a horse for Qian and an ox for Kun, a dragon for Zhen, a cock for Xun, a pig for Kan, a pheasant for Li, a dog for Gen, a sheep for Dui, and a part of the body, the head, the belly, the foot, the thigh, the ear, the eye, the hand, the mouth. And it gives each a direction, in a passage that is the textual source of the arrangement feng shui uses. Smith’s history of the book follows these lists through two thousand years of readers, and finds the geomancers among the most literal of them.

Fig. 01 The eight trigrams in the Earlier Heaven sequence, Qian to Kun, as Shao Yong set them out in the eleventh century and as Leibniz read them in 1703. Take a whole line as one and a broken line as nought, read each figure from the bottom, and the sequence counts down from seven to nought in binary. Leibniz, who had just worked out binary arithmetic, was sent the diagram from Beijing by the Jesuit Joachim Bouvet and recognised his own system in it. The sequence is a counting order, which is why the Earlier Heaven ring, the same sequence bent into a circle, pairs opposites across its centre and describes a world in balance rather than in motion. The Later Heaven ring, the one feng shui uses, is on the sheet below. The lines are read from the bottom up in every tradition; which end is the more significant digit is a choice, and reading the other way gives the same sequence counted in the other direction. The images are the Shuogua’s, the commentary on the trigrams appended to the Yijing.

Evidence · What Leibniz saw

In 1701 the Jesuit Joachim Bouvet, in Beijing, sent Leibniz a diagram of the sixty-four hexagrams in the order attributed to Fu Xi. Leibniz had just worked out binary arithmetic, and he saw at once that the sequence was his own: read a whole line as one and a broken line as nought and the figures count. He published the observation in 1703 as part of his paper on the binary system, and it is the first Western reading of the trigrams as anything but a curiosity. The drawing above does the same for the eight: the Earlier Heaven sequence, Qian to Kun, is the numbers seven to nought. It is a counting order, which is the reason the Earlier Heaven ring pairs opposites across its centre so neatly, and the reason it is a poor map of a house, which is not a counting order.

Fig. 02 The eight trigrams on one sheet, drawn from their lines. A whole line is yang and a broken one yin; each figure is read from the bottom up, and the bottom line is the one that sits toward the centre of a luopan. Heaven and earth are the pure figures; the six between are the mixed ones, in the pairs the tradition gives them: thunder and wind, water and fire, mountain and lake. Under each, its direction in the Later Heaven arrangement, its element, and its place in the family of eight. The directions are the ones the site uses everywhere: Kan north, Li south, Zhen east, Dui west. The family is the Yijing’s and is what Eight Mansions turns into the two groups. The pictures are mnemonics the tradition itself uses: Kan is a current between two banks, Li a flame with a dark heart, Gen a ridge over hollow ground.

The sheet is the eight figures with what the tradition hangs on them. Read the lines first: heaven is three whole, earth three broken, and each of the six between is a picture of its name. Then read the row under each, because that is what feng shui borrowed. Every trigram has a direction in the Later Heaven arrangement, and so a sector of the compass and of a plan; an element, which is how the colours and materials pages get from a direction to a paint; and a member of the family of eight, which is what the Eight Mansions method turns into the East and West groups. A reader who can name the eight from the sheet can read a luopan’s inner ring and the bagua map without another table.

Two arrangements

There are two canonical ways of placing the eight around a circle. The Earlier Heaven arrangement, attributed to the legendary Fu Xi, puts heaven at the top and earth at the bottom and pairs opposites across the centre: Qian against Kun, Li against Kan, Zhen against Xun, Gen against Dui. It describes the world in its ideal, symmetrical state, before anything has happened. The Later Heaven arrangement, attributed to King Wen, puts fire in the south and water in the north, and describes the world in motion, through the seasons and the day. It is the Later Heaven arrangement that feng shui uses for rooms, and it is the one you will find on every bagua map and on this site.

Tradition · Who drew them

The attributions are old and the diagrams are not. The Later Heaven order is in the Shuogua, which has the ruler come forth in Zhen, the east, set things in order in Xun, see them in Li, labour in Kun, rejoice in Dui, struggle in Qian, rest in Kan and complete the year in Gen: the eight directions clockwise from east, and the year from spring to the end of winter. The Earlier Heaven order is later as a diagram, and belongs to the Song. Shao Yong, the philosopher of the eleventh century who read the Changes as number, set out the sequence and the ring; Zhu Xi printed both arrangements at the head of his commentary of 1177, which became the standard text of the book for six centuries; and every luopan and bagua mirror since carries the diagrams that the Song made. The tradition’s two rings are a Zhou text and a Song drawing.

Fig. 03 The two rings, drawn with north at the top as every plan on this site is, which turns the classical diagrams upside down: the old woodcuts put south at the top, since the emperor faced south and the map was drawn from his chair. The Earlier Heaven ring, attributed to Fu Xi and drawn in the Song, pairs each trigram with its opposite across the centre, heaven against earth, fire against water, thunder against wind, mountain against lake, and every pair adds up to six lines of which three are whole and three broken: the world in balance, before anything has happened. The Later Heaven ring, attributed to King Wen and given in the Shuogua, puts fire in the south and water in the north, thunder in the east where the year begins and the mountain in the north-east where it ends, and it is the one on every bagua map, every luopan and every page of this site. A bagua mirror over a door carries the Earlier Heaven ring, since the mirror is meant to hold the world still; a plan carries the Later Heaven ring, since a house is lived in through the year. The Shuogua for the Later Heaven order; Smith 2008 for the Song diagrams and Shao Yong; Skinner 2008 for which ring sits on which instrument. Each trigram is read from the bottom up, and the bottom line is the one toward the centre.

The drawing sets the two rings side by side with north at the top, which is the site’s convention and the opposite of the woodcuts’, where south is at the top because the emperor faced it. Read the Earlier Heaven ring across its centre and every pair adds up to three whole lines and three broken, heaven against earth, fire against water, thunder against wind, mountain against lake: a world in balance and not yet in motion, which is why the bagua mirror over a shop door carries this ring and not the other, since a mirror is meant to hold things still. Read the Later Heaven ring clockwise from the east and it is the year, thunder in spring, fire in summer, lake in autumn, water in winter, with the four corner trigrams between them, which is why a plan carries this ring and not the other, since a house is lived in through the year. Both are printed on every luopan, in rings that the luopan page takes apart, and a reader who can tell them by eye, heaven at the south in one and fire at the south in the other, can tell a mirror from a map.

In the Later Heaven ring, going clockwise from north: Kan (water, north), Gen (mountain, north-east), Zhen (thunder, east), Xun (wind, south-east), Li (fire, south), Kun (earth, south-west), Dui (lake, west), Qian (heaven, north-west). The directions pages take each in turn, and the luopan page shows the ring divided again into the twenty-four mountains, three to each trigram, on which the compass methods work.

The ring and the square

The eight trigrams occupy eight directions, and the ninth position, the centre, belongs to nobody, or to Earth. Draw the arrangement as a three-by-three grid and you have the bagua map, the form in which it is laid over a floor plan. Number the cells with the Lo Shu magic square, in which every row, column and diagonal adds to fifteen, and you have the numbers used by the Flying Star method and by every practitioner who refers to “the one” or “the nine.” The square is the ring flattened: the corners of the grid are the intercardinal trigrams, the sides the cardinal ones, and nothing is lost except the sense that the eight are a circle, which the compass restores.

Fig.The bagua as a nine-sector plan, north up, with Lo Shu numbers. Each cell carries its trigram, its element and the life area assigned to it in the Western bagua.

The map on the plan

How the grid is placed over a house is where the schools part company, and it matters, because the two methods give different answers.

The life areas are the part of the bagua most people encounter first and, historically, the newest: they are a late-twentieth-century reading of the trigrams’ older associations, taught by Lin Yun in the United States from the 1970s and spread by Rossbach’s book of 1983. Kan’s depth and persistence became career; Qian’s authority and patronage became helpful people; Kun’s receptivity became relationships; Xun, the eldest daughter and the wind that gets in everywhere, became wealth. The older associations are in the Shuogua and the newer ones are not; Bruun’s history follows the translation. We show them throughout the site because you will meet them everywhere, and label them so you know where they come from.

What it can and cannot tell you

Read as a map of orientation the bagua is genuinely useful. It insists that you find north, that you notice which rooms take morning light and which take evening, that you treat the centre of the plan as something to keep clear, and that a house has a front and a back. Read as a promise, that the south-east corner of a flat governs its occupant’s income, it is a claim about the world that nothing supports, and one that the Zhou text and the Song diagram never made.

The Explorer puts the ring and the square in one instrument, and on a phone it will follow the compass so that you can turn toward a wall and read its sector. Use it that way: as a way of seeing where you are.