# Dynamic Mechanism of Dendrite Formation in Zhoukoudian, China
## 1 Introduction  
Dendrite, a typical multi-branching formation, with a bushy, or feather-like pattern, is a kind of dendritic film, much like the impression of bryophytes or algae, which is mainly produced in the bedding plane, joint, fissure or mineral surface, cleavage plane, etc., of limestone, dolomite, marble, sandstone, etc. [1]. Because of its plant-like appearance, it is often mistaken for plant fossils (Figure 1). The name comes from the Greek word dendron (\(\delta\)\(\
u\)8\(\rho\)ov), which means \"tree,\" since the crystal's structure resembles that of a tree [2]. It has long been recorded in the literature of the [PERSON] and Yuan Dynasties of China [3]. Dendrite samples were collected in Jinzigou area, Zhoukoudian, Beijing (Figure 1), and developed in the limestone of the Majiagou Formation and marble of the Jingeryu Formation; they are iron dendrites. Morphological observation of dendrite shows that its local pattern and overall pattern have a high degree of morphological similarity, or self-similarity, which means that the dendritic pattern of dendrite has fractal geometric morphological characteristics. Here, the similar morphology is determined by the micro dynamic mechanism. To a certain extent, it can be approximately considered as a geochemical gene [4; 5; 6; 7; 8; 9], just as genes determine biological characteristics. Since the fractal term was creatively proposed by mathematician [PERSON] in 1967 [10; 11; 12], with the gradual growth, maturity, and development of fractal itself, ithas been cited by many disciplines and departments, and, at the same time, shows the vitality of fractal application in various disciplines. This is because it can reveal the essential structure of nature and describe the actual life of human beings [13; 14; 15]. It is an intuitive geometric language to describe the motion of chaos. In fact, it is a mathematical system in closer agreement with the real world, integrating many nonlinear science contents. Earth sciences are concerned with extremely diverse sets of strongly interacting and synergetic phenomena [16; 17; 18]. In order to better understand these phenomena, it is often necessary to accurately describe complex structures and their evolution far from equilibrium. The development of fractal geometry has provided a valuable new approach towards the quantitative description of the statistical properties of various structures ranging in size from large molecules to continental coastlines [11; 12]. In recent years, many simple non-equilibrium growth models have been developed [18], one of which is the diffusion-limited aggregation model (DLA), introduced by [PERSON] and [PERSON] [19]. As for the formation of dendrite, it is generally believed that it is the result of the infiltration and diffusion precipitation of iron and manganese solutions along the bedding surface or fracture surface after the formation of rock [1]. It is tree-like pattern of some crystal aggregates of oxide of iron and manganese, exhibits fractal morphological structural characteristics, and should be the growth pattern formed by fractal growth [14; 15]. In order to investigate the dynamic mechanism of the dendrite formation, the diffusion-limited aggregation model, a typical growth process in fractal growth, was selected to simulate the micro dynamic mechanism of its formation, providing a reference for revealing the formation essence of dendrite. As mentioned above, dendrite has only been mentioned in a few studies, and it is only a very simple introduction, without systematic discussion, especially regarding the dynamic mechanism of its formation. In fact, dendrite is a typical geological pattern, representing a large class of important systems and structures in geoscience, such as fault systems, sand dune ripples, rock cracks, mud cracks, river networks, mineral growth, ore vein morphology, and the deposit formation process. Although the characteristics of these systems or structures are very obvious, we do not know the micro-dynamic mechanism of their formation process.