What is Zi Wei Dou Shu?
A chart of twelve rooms — and an honest account of why Bokki does not draw one.
The idea
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』.
How it differs from Saju
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.
How the tradition builds the chart
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.
What Bokki calculates: nothing — and the three reasons
First, the lunar birthday itself. The calendar library our engine already carries does convert lunar dates, leap months included, but it follows China's almanac, which is set on Beijing time. Korea's lunar calendar is set one hour later, and the two disagree on the first day of a month 61 times between 1900 and 2050, and twice on which month is the leap one (2012 and 2017), by the count of Korea's astronomy institute. Our rokuyo already runs on the later clock, but a birth chart reaches back decades, including the 1950s, when Korea's clocks ran on 127.5°E, and we have not checked that calendar against Korea's official lunar tables for those years. A lunar birthday read one day off moves 紫微 itself. 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.
What you can do here instead
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.
Closing note — the formula is not the obstacle
To sum up: the skeleton of a Zi Wei chart is arithmetic we could run today — 命宮 = (lunar month + 1 − hour) mod 12, an 오행국 from the 命宮 stem-branch's 납음 element, and fourteen stars placed at fixed offsets once 紫微 itself is seated. What stops us is not that formula; it is three specific gaps behind it — no lunar calendar checked against Korea's official tables (the one we carry is China's, an hour earlier), no cross-checked 安紫微訣 placement table, and a four-transformation table that genuinely disagrees between schools at the stems 庚 and 壬. Any one of those, silently picked, would make a chart that looks authoritative and is a guess.