What is Zi Wei Dou Shu?
A chart of twelve rooms — and an honest account of why Bokki does not draw one.
Zi Wei Dou Shu (紫微斗數 · 자미두수, “Purple Star astrology”) lays a life out as a map rather than a balance. Twelve houses sit in a fixed ring on the twelve earthly branches, and each house is one area of living: self, siblings, spouse, children, wealth, health, travel, friends, career, property, inner fortune, parents. Onto that ring go the stars — fourteen major ones, plus a crowd of helpful and harmful lesser ones — and you read a house by whichever stars landed in it. Tradition credits the method to the Song-dynasty Daoist Chen Xiyi (陳希夷), and the source book is 『紫微斗數全書』.
Same culture, different instrument. Saju takes eight characters of stem and branch and reads the balance of five elements across them; its calendar is solar, so the year turns at 立春 and the month at the 24 solar terms. Zi Wei takes the lunar month, day and hour and places stars on a grid, which means it needs a lunar calendar with leap months — something Saju never needs. Many practitioners run both, because one reads temperament as a mixture and the other reads a life as a set of rooms.
The skeleton is reproducible, and we have written it down. Index the branches 子=0 … 亥=11 and put the birth hour on the same index; then 命宮 = (lunar month + 1 − hour) mod 12, and 身宮 = (lunar month + 1 + hour) mod 12. That is just the classical counting-round in arithmetic form: place the first month at 寅, count forward to your birth month, call that spot the 子 hour, and count backward to your birth hour. The other eleven houses fill in backwards from 命宮 in fixed order. Each house takes its stem from the birth year's stem by 五虎遁 — the very rule Saju uses for the month stem. The stem-and-branch of 命宮 gives a 납음 element, which fixes the 오행국: Water 2, Wood 3, Metal 4, Earth 5, Fire 6. That number together with the lunar day places 紫微 itself, and once 紫微 is placed the rest of its series follows at fixed offsets — 天機 one back, 太陽 three, 武曲 four, 天同 five, 廉貞 eight — while the 天府 series runs forward, 太陰 +1 through 破軍 +10. Last, the birth year's stem attaches the four transformations 化祿·化權·化科·化忌 to four of the stars.
First, the engine has no lunar-to-solar conversion with leap months. Saju never needed one, because Saju runs on solar terms — so this is a missing subsystem, not a missing line of code. Second, placing 紫微 from the 오행국 and the lunar day is done in practice with a lookup table (安紫微訣) that we have not sourced and cross-checked across editions. Third, the four-transformation table disagrees between schools exactly at the stems 庚 and 壬: depending on whose book you open, 庚 hands 化科 to 太陰 or 天府 or 天同, and 化忌 to 天同 or 天相. A chart that silently picked one would look authoritative and be a guess. Until all three are settled, a Bokki 자미 chart would be a drawing of a chart rather than a chart.
The neighbouring tradition — and the one Bokki computes all the way down — is Saju. Four pillars built from a perpetual calendar, with 立春 as the year boundary, the 24 solar terms as the month boundaries, and true solar time at your birthplace for the hour. Every one of those was checked against an independent almanac before we shipped it. If you came looking for a map of a life, that is the one we can actually draw.