## 1 Introduction  
The terrain model is a very important asset in open world virtual environments, e.g., military training systems or video games [1; 2; 3; 4]. It is responsible for getting an accurate impression of the appropriate scale and proportion of other objects placed in the scene. A more accurate synthetic terrain increases the visual acceptability of the virtual environment and leads to better immersion. Thus, models of natural landscapes should depict the impact of erosion forces on terrain structures [5; 6; 7]. The importance of the internal structure in terrain modelling was under consideration in related research [8; 9; 10] and addressed especially in the physically-inspired simulation of the hydraulic erosion [11; 12] and geology driven method [13]. Materials' distributions are also important in the modelling of table mountains. The topic was previously discussed by [PERSON] and [PERSON] [14] in a simulation-based method. In their technique, the terrain was composed from two different materials. The hard material (rock) eroded to the soft one (sand) due to exposure to an environmental condition. The soft material was transported down by gravity-driven diffusion and deposited at the model base. Data structures for terrain models can be categorised into two main types, however, both of them have weaknesses and advantages. The matrices of elevation values i.e., height fields are the simplest and most commonly used for terrain models. This is due to the ease of implementation of procedural methods for generating and rendering synthetic landforms [9; 15; 16; 17; 18]. The main disadvantage of this representation is the inability to replicate models with aspherical topology [19]. Complex models are based on volumetric representation. In this case, all techniques are much more complicated, but it is possible to achieve landforms unreachable in height-based structures (also in aspherical topology) e.g., caves, rock shelves, or arches [13; 14; 17]. Hybrid methods can be also isolated by trying to cumulate positive aspects of both main representations, while minimising their weaknesses. [PERSON] and [PERSON] introduced layered representation consisting of stacked horizontal materials, where each has its own elevation and geological attributes [8; 15; 16; 18]. Since the works of [PERSON], fractal geometry plays an important role in computer-assisted terrain modelling [18; 20; 21; 22]. Fractal based terrains range from the basic self-similar, noise-based structures to more naturally eroded landforms expanded by rivers and coastlines [9; 10; 23; 24; 25; 26; 27; 28]. Further research into landscape synthesis was inspired by natural phenomena, especially erosion and their new directions. Modern modelling techniques are inspired by hydrology [7; 29; 30; 31; 32], geology [13; 33], genetic programming [34], patch and feature identification [35], hierarchical models [36], shape grammar [37], or particle systems [38; 39]. Another interesting approach to terrain modelling is to synthesise complete landscapes by machine learning procedures. The methods are user oriented and provide tools for modelling with few simple starting rules [5]. In this article, a procedural technique is proposed for the generation of buttes and mesas terrain formations. The method is not intended to simulate dynamic, complex, and time-consuming erosive processes, but the effects they cause is directed for artist and designers, so as to quickly provide assets for further use. In the proposed solution, a terrain model is layered [8], represented by classic height-field [15; 16; 18] extended by information about distribution and hardness of the materials. The method is based on fractal geometry [22] and modified by the Poisson Faulting algorithm [40], whereby the geometry layer is obtained. On this basis, the material classification is performed and stored in the materials' layer. This layer also provides information on the materials' distribution. Next, the hardness layer is filled with desired data [41].