Find Moving Lines of the I Ching

Find Moving Line in I Ching Hexagram is a tool developed by Kabala to help determine moving lines in an I Ching hexagram. The Kabala I Ching Hexagram tool is a special application based on the Six-Line Divination, suitable for beginners in I Ching. Kabala accurately simulates the six-line casting algorithm (with the algorithm provided below) and provides basic interpretations and integrates 384 Moving Lines. This system ensures comprehensive information for each hexagram, helping users easily understand the philosophy of I Ching.

Algorithm for Determining Moving Lines in the Hexagram

This algorithm uses probability to determine whether each line in a hexagram is a moving line, and if so, whether it is a Yin Moving Line or Yang Moving Line based on traditional probability. Designed to maintain the hexagram's initial structure, this algorithm calculates the moving probability of each line using a logical probability ratio based on the traditional three-coin method in I Ching.

Theoretical Basis

According to the traditional three-coin casting method, each cast has 4 possible outcomes with specific probabilities:

• Yin Moving Line: 12.5% (all three coins are tails)
• Yang Moving Line: 12.5% (all three coins are heads)
• Yang Static Line: 37.5% (two heads, one tail)
• Yin Static Line: 37.5% (two tails, one head)

Thus, the probability of each line being a moving line is the sum of two probabilities of 12.5%, equaling 25%.

Algorithm

1. Input Hexagram Code: The user enters the hexagram code to determine the initial state of each line (Yang or Yin).
2. Determine Moving Lines with 25% Probability:
   • For each line in the hexagram:
     • Assign a moving probability of 25% to the line.
     • Use a random value to determine if the line is moving:
       • If the line is not moving, retain its initial state (Yang or Yin).
       • If the line is moving, randomly choose to make it Yin Moving or Yang Moving, each with a 50% probability.
3. Create the Changing Hexagram: For each moving line, change its initial state in the changing hexagram:
   • Yin Moving becomes Yang in the changing hexagram.
   • Yang Moving becomes Yin in the changing hexagram.
4. Display Results: The primary hexagram and changing hexagram are displayed with illustrations for each line and its moving state.

Probability Table for the Number of Moving Lines in a Hexagram

The probability of having exactly k moving lines out of n lines with each line having a moving probability of p is given by the binomial distribution formula:

\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k} \]

Where:

• \( \binom{n}{k} \) is the combination coefficient, calculated by \( \frac{n!}{k!(n - k)!} \).
• \( p \) is the probability that a line becomes a moving line (here it is 0.25 or 25%).
• \( 1 - p \) is the probability that a line remains static (here it is 0.75 or 75%).

Example with Specific Values

If \( n = 6 \) (6 lines in a hexagram) and \( p = 0.25 \) (25% probability of each line being moving), the formula becomes:

\[ P(X = k) = \binom{6}{k} \cdot (0.25)^k \cdot (0.75)^{6 - k} \]

The table below shows the probability of having k moving lines in a hexagram with 6 lines:

Meaning of the Probability Table

• The probability of having 1 or 2 moving lines is the highest, accounting for nearly 65% of the outcomes. This aligns with the reality that most I Ching hexagrams typically have 1 to 2 moving lines.
• The probability of having 4 or more moving lines is very low, reflecting that hexagrams with many moving lines are rare.

Key Features of the Algorithm

• Ensures Natural Randomness: The 25% moving probability for each line results in a reasonable probability distribution for the number of moving lines in a hexagram.
• Simple to Implement: By iterating over each line and applying the moving probability, the algorithm can easily determine the changing hexagram without altering the hexagram input structure.
• Aligned with Tradition: The algorithm is based on the realistic probabilities of the three-coin method, aligning with traditional hexagram casting in I Ching.

Conclusion

This algorithm is simple and effective in determining moving lines, while providing natural randomness that matches the traditional probabilities of the three-coin method. This ensures that each hexagram result reflects a natural probability and produces moving lines with realistic frequency.