结合分形几何、动力系统与词上组合等方法技巧，我们拟从三个方面去研究自相似序列内在性质及表征的信息:(1)研究自相似序列的因子结构、因子复杂度和Hankel行列式性质等;(2)研究以自相似序列为b-进展式的实数(特别的，以代换序列和自动机序列为b-进展式的实数分别称为代换实数和自动机实数)的丢番图性质;(3)探讨自相似序列与分形之间的联系，以及自相似序列的复杂度熵与分形集维数之间的关系。因此本项目将涉分形几何、词上组合、理论计算机与数论的交叉，同时也是这些研究方向的热点问题。我们将在已有工作的基础上，继续深入研究自相似序列与对应的实数和分形集三者之间的关系，并找出解决问题的新方法。

Combined with Fractal Geometry, Dynamic System and Combination on Words, we will research the self-similar sequences and their characterization information from three aspects:(1)The study of the structures、complexities and Hankel determinants of the self-similar sequences;(2)The study of the irrationality exponents of the real numbers corresponding the self-similar sequences;(3)The study of fractal sets associated with self-similar sequences.Those problems are at the intersection of fractal theory, combination on words, formal language theory and number theory. Our research will base on the previous results, study self-similar sequences，the related fractal sets and Diophantine properties. And try to find new methods to solve such problems.