About the I Ching Divination Tool1. System Overview
Quizzman's I Ching Divination tool is the first multi-school divination system that simultaneously integrates three interpretation methods: Classical (十翼 Ten Wings), Liu Yao (六爻 Six Lines), and Plum Blossom (梅花易数).
Unlike ordinary online tools that simply look up hexagram meanings from a table, our system actually "casts" using a coin/yarrow-stalk simulation algorithm, then synthesises results through a natural language processing (NLP) pipeline to provide advice tailored to your specific question and domain.
- Accurate probability simulation using classical methods (three coins, yarrow stalks)
- Complete 64-hexagram × 6-line dataset with Chinese characters + romanization + translations
- Ganzhi calendar integration using the Vietnam timezone (GMT+7)
- NLP-based question analysis to deliver domain-specific advice
- Result sharing via snapshot link — no data loss
2. Five Casting Methods
The system supports 5 hexagram-generation methods, each with distinct probability characteristics and use cases. All methods produce 6 lines with values 6–9, where a value of 6 or 9 is a moving (changing) line that transforms to produce the changed hexagram.
Three Coins (三銅錢)
Simulates tossing 3 coins 6 times. Each toss totals the face values (heads=3, tails=2) to give 6, 7, 8, or 9. The algorithm uses CSPRNG to ensure cryptographic-grade randomness.
Yarrow Stalks (蓍草)
Simulates dividing 50 yarrow stalks through 18 rounds (3 rounds × 6 lines). Moving-line probabilities are closer to the ancient text than coins — Old Yang is 18.75%, Old Yin only 6.25%.
Plum Blossom — By Time
Uses the Earthly Branch index (地支) of the current year·month·day·hour — hour calculated via true solar time from the user's longitude. Upper trigram = (Y+M+D) mod 8; lower trigram adds Hour; moving line = sum mod 6.
Plum Blossom — By Number
Enter 1–2 arbitrary numbers. First number mod 8 → upper trigram; second mod 8 → lower trigram; sum mod 6 → moving line position. Suitable for phone numbers, plate numbers, birthdates, etc.
Manual Input (6 Lines)
Enter directly 6 values (6–9) from line 1 to line 6. Used when you have already cast a hexagram manually with coins or yarrow stalks and want the system to interpret it.
crypto.getRandomValues() (Web Crypto API) on the client or the secrets module on the server — both are cryptographic-grade entropy sources, not ordinary Math.random().
| Value | Line type | Three coins | Yarrow stalks |
|---|---|---|---|
| 6 — Old Yin × | ⚋ moving → yang | 12.5% | 6.25% |
| 7 — Young Yang | ⚊ static | 37.5% | 31.25% |
| 8 — Young Yin | ⚋ static | 37.5% | 43.75% |
| 9 — Old Yang ○ | ⚊ moving → yin | 12.5% | 18.75% |
3. Historical Origins & Algorithm Analysis
Each I Ching casting method has its own historical origins and mathematically distinctive algorithm. Below is a detailed analysis from a Computer Science perspective.
🌿 Yarrow Stalks (蓍草 Shī Cǎo)
The oldest method, described in the Great Commentary (繫辭傳 Xì Cí Zhuàn)
- Era: ~3000 years old, Western Zhou (1046–771 BCE)
- Traditional author: Fuxi 伏羲 (legendary) — mythological king who created the Eight Trigrams
- Completed by: King Wen of Zhou 周文王 (arranged 64 hexagrams) + Duke of Zhou 周公旦 (wrote the line texts)
- Source text: Great Commentary (繫辭傳), section Grand Expansion Number (大衍之數五十)
- Significance: Yarrow (Achillea millefolium) was considered a sacred herb, living for a thousand years, symbolising connection to the Way of Heaven
- Hold 49 stalks (1 set aside for Taiji), divide into 2 groups (Two Modes)
- Take 1 stalk from the right group and hold between fingers (Three Powers)
- Count the left group in sets of 4 (Four Symbols — four seasons), keep the remainder
- Count the right group in sets of 4, keep the remainder
- Total remainder = 4 or 8 → called a "change" (一變)
- Repeat 3 changes (三變) → produce 1 line
- Repeat for 6 lines → complete hexagram (18 changes total)
- Algorithm type: Direct 18-step Great Expansion simulation — a multi-stage stochastic process, not a separate state-transition model
- Probability distribution: Non-uniform — yin-biased. P(Old Yin)=6.25%, P(Old Yang)=18.75%
- Entropy: ~1.87 bits/line (lower than ideal 2 bits due to skewed distribution)
- Complexity: O(18) operations/line × 6 lines = 108 minimum steps
- Random mechanism: Traditional practice uses manual division; Quizzman simulates the split with CSPRNG while preserving the canonical distribution
🪙 Three Coins (三銅錢 Sān Tóng Qián)
The most popular method — a simplified version of the yarrow-stalk method
- Era: Han dynasty (~200 BCE – 200 CE)
- Systematised by: Jing Fang 京房 (77–37 BCE) — Western Han I Ching scholar, founder of the Liu Yao school
- Context: Busier daily life demanded a faster method than yarrow stalks (which take 15–30 minutes)
- Implements: 3 ancient coins (Han/Qing dynasty bronze); inscribed side = yin (2 pts), plain side = yang (3 pts)
- Also called: "Gold Coin Hexagram" (金錢卦) or "Coin Tossing Method" (擲錢法)
- Toss 3 coins into the air
- Count: inscribed side = 2, plain side = 3
- Total determines the line:
- 6 pts (2+2+2) = Old Yin (moving)
- 7 pts (2+2+3) = Young Yang (static)
- 8 pts (2+3+3) = Young Yin (static)
- 9 pts (3+3+3) = Old Yang (moving)
- Repeat 6 times → 6 lines = 1 hexagram
- Algorithm type: Binomial Distribution with n=3, p=0.5
- Sample space: 2³ = 8 outcomes → mapped to 4 line values
- Probability: P(6)=1/8, P(7)=3/8, P(8)=3/8, P(9)=1/8 → yin-yang symmetric
- Entropy: ~1.81 bits/line (closer to ideal than yarrow stalks)
- Complexity: O(6) coin tosses = 6 simple operations
- Encoding: Binary sum aggregation — each coin is 1 bit, 3-bit sum → 1 line value
🌸 Plum Blossom Numerology (梅花易數 Méi Huā Yì Shù)
The "no-tools" method — uses numbers, time, or phenomena
- Founded by: Shao Kangjie 邵康節 (real name: Shao Yong 邵雍, 1011–1077 CE)
- Dynasty: Northern Song (北宋) — pinnacle of Song Neo-Confucian philosophy
- Background: Philosopher, astronomer, and mathematician; author of Huangjí Jīngshì (皇極經世) — a monumental work on cosmology
- Legend: One morning in 1050, Shao Yong sat under a plum tree that blossomed unusually early and watched two sparrows fight and fall to the ground. He used the time (Chen hour, day 17, month 12) to cast a hexagram and predicted that the next day a girl would break a branch picking flowers and be bitten on the thigh by a dog — which came true exactly.
- Work: "Plum Blossom Numerology" (梅花易數) — the textbook of this method, transmitted through disciples
- Take Earthly Branch indices (地支 1–12) for Year, Month, Day, Hour — hour via true solar time (longitude-corrected)
- Y + M + D = Supper
- Supper mod 8 → upper trigram (1=Qian, 2=Dui, … 8=Kun, Xiantian order)
- Supper + H = Slower
- Slower mod 8 → lower trigram
- Slower mod 6 → moving line position (1–6)
- Upper + Lower → primary hexagram (64 hexagrams)
- Algorithm type: Deterministic Hash Function — same input always produces same output
- Entropy: 0 bits (no intrinsic randomness)
- Input space: Time or arbitrary numbers → hashed to a hexagram
- Modular arithmetic: mod 8 (8 trigrams) + mod 6 (6 lines) = cyclic mapping
- Collision: Very high — many different inputs map to the same hexagram
- Philosophy: "Resonance of like kinds" — the moment of asking and the answer share a causal connection (synchronicity)
🎲 Electronic Random Number (CSPRNG)
The modern method used on digital platforms
- Era: From ~1990s, widespread since 2000s with the internet
- Principle: Simulate the probability of traditional methods using a computer
- Entropy source: Hardware RNG (Intel RDRAND chip), OS entropy pool, or CSPRNG
- Quizzman uses: Web Crypto API (
crypto.getRandomValues()) — standard, cryptographically secure CSPRNG
- Request entropy from OS/Hardware
- Generate random number in range [0, 7]
- Map 8 outcomes → 4 line values:
- 0 → Old Yin (6)
- 1,2,3 → Young Yang (7)
- 4,5,6 → Young Yin (8)
- 7 → Old Yang (9)
- Repeat 6 times → 6 lines
- Algorithm type: CSPRNG (Cryptographically Secure Pseudo-Random Number Generator)
- Entropy: ~1.81 bits/line (equivalent to real coins)
- Properties: Unpredictable, uniform distribution, passes all statistical tests (NIST SP 800-22)
- Advantages: Fast (microseconds), no physical bias, algorithm can be audited
- Debate: Some argue it lacks the "spiritual element" of manual action
📊 Comprehensive Method Comparison Table
| Criterion | Yarrow Stalks 蓍草 | Three Coins 三銅錢 | Plum Blossom 梅花 | CSPRNG |
|---|---|---|---|---|
| Founder | Fuxi 伏羲 (legend) King Wen, Duke of Zhou (completion) | Jing Fang 京房 (77–37 BCE) | Shao Kangjie 邵康節 (1011–1077) | — |
| Era | ~1000 BCE | ~200 BCE | ~1050 CE | ~1990 CE |
| Casting time | 15–30 min | 2–5 min | 30 sec | <1 sec |
| Entropy/line | ~1.87 bits | ~1.81 bits | 0 bits | ~1.81 bits |
| Algorithm type | Direct 18-step simulation (stochastic process) | Binomial Distribution (coin simulation) | Hash Function (Deterministic) | CSPRNG (Cryptographic) |
| Tools | 50 dried stalks | 3 ancient coins | None needed | Computer |
| Learning complexity | High | Low | Medium | Low |
| Yin/yang distribution | Yin-biased (6.25% Old Yin) | Symmetric (12.5%/12.5%) | N/A (deterministic) | Symmetric |
| Core philosophy | Reverence, ritual Communion with Heaven | Simplified while preserving probability | Resonance of like kinds (Synchronicity) | Simulating traditional probability |
📅 I Ching Development Timeline
4. Three Interpretation Schools
Once a hexagram is obtained, the system runs three interpretation modules in parallel and then synthesises them into a unified result. "Balanced" mode draws equally from all three; specialised modes prioritise a specific school.
📜 Classical (十翼)
Based on the original I Ching text and the Ten Wings
- Hexagram statement (卦辭) — general oracle
- Line text (爻辭) — oracle for each moving line
- Great Image (大象傳) — image of the hexagram
- Judgment Commentary (彖傳) — explanation of meaning
- Zhu Xi's rules — which line or hexagram to consult
☯ Liu Yao (六爻)
Jing Fang school, popular in practical divination
- Six Spirits — Azure Dragon, Vermilion Bird, Hook Chen, Spiral Snake, White Tiger, Black Warrior
- Five-Element generation/conquest between lines
- Host/Guest (世/應) — key positions in the hexagram
- Day/Month generation or clash influence
🌸 Plum Blossom (梅花)
Shao Kangjie school, fast and flexible
- Body/Use (體/用) — which trigram represents self, which represents the matter
- Five-Element trigrams — Qian Metal, Kan Water…
- Nuclear hexagram (互卦) — supplements hidden information
- Changed hexagram — future trend
- 0 moving lines → consult hexagram statement of primary hexagram
- 1 moving line → consult that line's text
- 2 moving lines → consult the upper line text, use lower as supplement
- 3 moving lines → consult hexagram statements of both primary and changed hexagrams
- 4 moving lines → consult the 2 static line texts; lower is primary
- 5 moving lines → consult the single static line's text
- 6 moving lines → Qian/Kun use the "Use" text; others consult changed hexagram
5. 64-Hexagram Data Structure
Each hexagram is stored with complete classical text (Chinese characters + romanization + translation) and pre-computed attributes to reduce processing time.
The changed hexagram is computed via XOR: flipping bits at moving-line positions. The nuclear hexagram (互卦) takes lines 2-3-4 as the new lower trigram and lines 3-4-5 as the new upper trigram — the tool automatically computes and displays both alongside the result.
| Field | Type | Meaning |
|---|---|---|
| number | 1–64 | Sequence number according to King Wen's order (序卦傳) |
| name_vi / name_han | text | Hexagram name in Vietnamese and Chinese characters |
| lines | int[6] | Values 6–9 from line 1 (bottom) to line 6 (top) |
| moving_lines | int[] | Positions of moving lines (1–6) |
| upper / lower | Trigram | Upper and lower trigrams (Qian, Kan, Gen…) |
| nuclear | Hexagram | Nuclear hexagram — lines 2-3-4 combined with lines 3-4-5 |
| changed | Hexagram? | Changed hexagram if moving lines exist |
| gua_ci | text | Hexagram statement (卦辭) — King Wen of Zhou |
| yao_ci[6] | text[] | 6 line texts (爻辭) — Duke of Zhou |
| da_xiang | text | Great Image Commentary (大象傳) |
| tuan_zhuan | text | Judgment Commentary (彖傳) |
6. Ganzhi Calendar Integration by Coordinates
The moment of casting is recorded precisely based on the user's actual geographic coordinates. This is an important differentiator of Quizzman from other tools:
Most I Ching tools use a fixed timezone (GMT+7 or GMT+8). However, Local Apparent Solar Time at each location differs depending on longitude.
- Hanoi (105.85°E) and Ho Chi Minh City (106.63°E) differ by ~3 minutes in solar time
- Da Nang (108.21°E) is ~9.5 minutes ahead of Hanoi
- This difference can cause incorrect Ganzhi hours when near a boundary
When casting, the system requests location access (Geolocation API) to obtain your longitude. If you deny it, the system defaults to GMT+7.
The calendar engine (Calendar Engine) provides:
- Four Pillars — year·month·day·hour in Ganzhi according to solar term definition + longitude correction
- Solar terms — 24 terms based on exact solar longitude (Sun's ecliptic degrees)
- Monthly hexagram (消息卦) — the hexagram representing the month (Fu, Lin, Tai…)
- Day officer — Jian, Chu, Man, Ping, Ding, Zhi, Po, Wei, Cheng, Shou, Kai, Bi
- Auspicious/inauspicious stars — Yellow Road and Black Road by day branch
- Local Apparent Solar Time — computed from the user's longitude
Calendar data is used to compute the day spirit in Liu Yao, determine the Plum Blossom palace by actual hour, and ensure accurate Ganzhi based on geographic location.
7. NLP Analysis & Domain Recognition
Your question is analysed through a lightweight NLP pipeline to extract:
- Domain — career, finance, romance, health, education, legal
- Sentiment — positive/negative/neutral mood
- Keywords — primary nouns/verbs to cross-reference with hexagram imagery
The analysis results appear in the "NLP Analysis" section (collapsed by default). The Domain-Specific Advice section is customised based on these results — for example, if the question is about "changing jobs", the advice will focus on career strategy rather than romance.
8. Void Lines (空亡) — False Void vs True Void
In the Liu Yao system, Void Lines (空亡 kōng wáng) is an important concept representing a state of "emptiness" or "temporal misalignment".
Each 10-day week (旬) begins from the Jia (甲) day, with the 10 Heavenly Stems sequentially paired with the 12 Earthly Branches. Since 12 > 10, the last 2 branches have no pairing → called Void.
甲戌旬: 甲戌 乙亥 丙子 丁丑 戊寅 己卯 庚辰 辛巳 壬午 癸未 → 申酉 Void
⚖️ Void state classification
Quizzman does not treat Void Lines as simply "cancelled" — instead it classifies them into 3 logical states:
A line that falls into Void and is also in a state of resting/imprisoned (休囚), and receives no generation support from day or month. The matter will definitely not succeed or a major incident will occur.
A line that falls into Void but is in a prosperous/powerful state or receives generation support from day or month. Like a martial arts master under house arrest — the power is there but cannot be expressed yet. When it meets a clashing day (冲) or direct day (值), it exits the void and the matter succeeds.
A line in Void that meets the day branch in a clash (6 positions apart in the branch cycle). This is considered activated and the line can exert its effect. However, other factors should also be checked.
🎯 Application in the Engine
- Auto-classification: Each line is assigned a
void_state(not_void, true_void, false_void, clash_void) - NLP influence: If the use-line (dụng thần) falls into True Void → advice will emphasise "the timing has not yet come" or "patience is needed"
- False Void: The system will suggest possible dates for void-exit (clashing or direct days)
"A vessel's usefulness lies in its emptiness" (埏埴以為器，當其無，有器之用 — Tao Te Ching). Void is not "nothing" — it is a latent state, a thing with form but not yet substance, holding promise but not yet ready to manifest.
9. Sharing Results via Snapshot Link
After casting, the "Copy link" button creates a URL containing the complete result snapshot:
- Primary and changed hexagram numbers (if any)
- List of moving lines
- Original question (up to 200 characters)
- Chosen method, mode, and domain
- Casting timestamp
- Short conclusion and result badge
The snapshot is stored server-side in the database. The URL contains only a short hash (~22 chars) as a retrieval key:
/tool/iching-divination?hash=<~22-char hash>
When the recipient opens the link, the server returns the full JSON snapshot for rendering — no client-side decoding needed. Legacy base64url links remain backward compatible. AI agents can read the full snapshot directly via GET /api/tool-module/iching/snapshot/:hash.
10. Frequently Asked Questions
Is online I Ching divination reliable?
Reliability depends on the data, algorithm, and interpretation. Quizzman's tool is transparent about its methods (three coins, yarrow stalks, Plum Blossom) and displays the evidence chain for users to verify.
What is the difference between Liu Yao and Plum Blossom?
Liu Yao focuses on individual lines, six spirits, host/guest positions, and Five-Element generation/conquest. Plum Blossom focuses on body–use, image-number, and the overall hexagram trend based on time or numbers.
What are Void Lines (空亡)? Why can a void line's matter still succeed?
Void Lines are the 2 earthly branches left unpaired with heavenly stems in each 10-day week. However, Quizzman distinguishes True Void (genuinely hopeless) from False Void (temporarily suppressed). A line in a prosperous/powerful state or supported by day/month is only False Void — when it meets a clashing day it exits the void and the matter can still succeed.
Which method should I use as a beginner?
Beginners should use Three Coins or Balanced mode. Both are easy to understand, produce stable results, and still provide enough information for deeper learning.
Can I share hexagram results with others?
Yes. Use the "Copy link" button to generate a quick-lookup link so the recipient can open the exact hexagram without re-casting.
What are yarrow stalks? Why is this method difficult?
Yarrow stalks (蓍草) are a plant used for I Ching divination since the Western Zhou period (~1000 BCE). The method requires 50 dried stalks and 18 complex steps per line — approximately 108 minimum steps for one hexagram. In Quizzman, the engine directly simulates the 18-step Great Expansion method using CSPRNG to preserve the traditional yin-biased probability distribution.
Is Plum Blossom Numerology a random method?
No. Plum Blossom Numerology is a deterministic method — the same moment or number always produces the same hexagram. From a CS perspective it is a hash function mapping input (time/number) to a hexagram through modular arithmetic. The Plum Blossom school's philosophy is based on "resonance of like kinds" (synchronicity) — the belief that the moment of asking and the answer share a causal connection.
10. Explore More
You can go directly to related pages to continue your research: