近期兴趣起，将《易经》64卦变化通过大数据进行了分析，结果发现，虽然样本不足够大，但仍然能有一些新的发现。尤其是抛硬币和采用蓍草法得到一些不一样的结果。两个小文均已经在preprints.org网站通过预印本在线发布。这里做笔记以记录。

1. Big data reveals the change characteristics of 64 hexagrams and lines，https://www.preprints.org/manuscript/202308.0208/v1 

摘要：Chinese divination of I Ching has a history of thousands of years. The six lines changes in 64 hexagrams have exceeded one billion scenarios, and the inherent laws among them have not been well revealed to this day. By using big data's technology and coin toss method, this paper simulates the change of 64 hexagrams, and explores the probability and proportion of each hexagram during the change from the perspective of quantification, as well as the maximum and minimum conversion rate of hexagram change. This paper summarizes the basic characteristics and the basic law of hexagram change, and accordingly constructs the spatial form of hexagram change, and reveals the hidden secrets of the ancient Book of changes (I Ching). To achieve this goal, we randomly toss three coins 600 million times to generate 100 million hexagrams. According to the basic rules of hexagram divination, we calculate the hexagram changes. The results showed that: (1) Changes of things are mostly simple changes. The probability of 1 billion randomly generated hexagrams from one to three dynamic lines is close to 80%. (2) About 17% of the 64 hexagrams have no dynamic lines, which means that a significant proportion of the 64 hexagrams are invariant. (3) Small probability changing hexagram certainty and large probability changing hexagram uncertainty. (4) After generating one billion hexagrams at random, the topographic map with the probability of changing hexagrams has axial symmetry and fractal geometric characteristics, and the fractal characteristics are mainly manifested in that the changes on both sides of the symmetry are presented based on the triangle background. These results reflect the obvious characteristics and internal regularity of the changes in the 64 hexagrams of the I Ching. This article provides new ideas for scientific exploration of the internal laws of the 64 hexagrams in the I Ching.

2. Big Data Analyzing the Asymmetry of 64 Hexagrams Based on the Yarrow-stalk Method，https://www.preprints.org/manuscript/202308.1347/v1 

摘要：The divination function of China's Yijing has led to its circulation for thousands of years. In our exploration of Yijing's characteristics using big data, we have discovered variations in results between the coin toss method and the ancient yarrow-stalk method of divination, known as "the number for the great expansion method of divination(大衍之数)". The yarrow-stalk method serves as the fundamental method of divination in Yijing and continues to hold significance in studying the essential characteristics of Yijing. Despite the complexity of yarrow calculations, advancements in computer technology and big data have simplified its application. By employing the yarrow-stalk method, we simulated changes in the 64 hexagrams, calculated probabilities and proportions of hexagram alterations, and derived fundamental characteristics and patterns of hexagrams. Additionally, we constructed the spatial representation of lines and hexagrams. Through a binary system rearrangement, we created a 64x64 matrix illustrating hexagram transformations. Subsequently, we generated 100 million random hexagrams and analyzed line and hexagram changes accordingly. Our findings indicate the following:(1) Big data analysis reveals evident asymmetry in the hexagrams obtained through the yarrow-stalk method, with a triangular fractal characteristic forming the background.(2) Each of the 64 hexagrams exhibits a distinct probability distribution when transforming into other hexagrams, which can be categorized into five types.(3)The occurrence probabilities of Laoyang, Laoyin, Shaoyang, and Shaoyin are 18.61%, 6.387%, 31.38%, and 43.62% respectively. The probabilities of Yin and Yang occurrences are nearly equal, each close to 50%. However, the probability of Laoyang is approximately three times higher than that of Laoyin.(4) Visualized and analyzed the characteristics of hexagram changes greater than 100000 times using 3D statistical maps and Sankey diagram.These results demonstrate that the yarrow-stalk method effectively unveils the characteristics and underlying patterns of the 64 hexagrams. This study provides a novel approach for scientifically exploring the internal laws governing the 64 hexagrams in Yijing.