Almeida J S, Carriço J A, Maretzek A, Noble P A, Fletcher M
ITQB/Universidade Nova Lisboa, PO Box 127, 2780 Oeiras, Portugal.
Bioinformatics. 2001 May;17(5):429-37. doi: 10.1093/bioinformatics/17.5.429.
Chaos Game Representation (CGR) is an iterative mapping technique that processes sequences of units, such as nucleotides in a DNA sequence or amino acids in a protein, in order to find the coordinates for their position in a continuous space. This distribution of positions has two properties: it is unique, and the source sequence can be recovered from the coordinates such that distance between positions measures similarity between the corresponding sequences. The possibility of using the latter property to identify succession schemes have been entirely overlooked in previous studies which raises the possibility that CGR may be upgraded from a mere representation technique to a sequence modeling tool.
The distribution of positions in the CGR plane were shown to be a generalization of Markov chain probability tables that accommodates non-integer orders. Therefore, Markov models are particular cases of CGR models rather than the reverse, as currently accepted. In addition, the CGR generalization has both practical (computational efficiency) and fundamental (scale independence) advantages. These results are illustrated by using Escherichia coli K-12 as a test data-set, in particular, the genes thrA, thrB and thrC of the threonine operon.
混沌游戏表示法（CGR）是一种迭代映射技术，它处理单元序列，如DNA序列中的核苷酸或蛋白质中的氨基酸，以便找到它们在连续空间中位置的坐标。这种位置分布具有两个特性：它是唯一的，并且可以从坐标中恢复源序列，使得位置之间的距离衡量相应序列之间的相似性。在先前的研究中，完全忽略了利用后一个特性来识别连续方案的可能性，这就增加了CGR可能从单纯的表示技术升级为序列建模工具的可能性。
CGR平面中的位置分布被证明是马尔可夫链概率表的推广，它适用于非整数阶。因此，马尔可夫模型是CGR模型的特殊情况，而不是像目前所认为的那样相反。此外，CGR推广具有实际（计算效率）和基本（尺度独立性）优势。以大肠杆菌K-12作为测试数据集，特别是苏氨酸操纵子的thrA、thrB和thrC基因，来说明这些结果。
