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This article presents a study on procedural terrain generation using Perlin noise in the Unity game engine, building upon prior research and established techniques [1,2]. The objective of the this study is to create realistic and visually appealing landscapes by leveraging algorithmic generation [3]. By utilizing a two dimensional monochrome Perlin noise map, the algorithm generates terrains with organic features such as hills, valleys, and mountains [4]. The research employs the Unity game engine, which offers a wide range of tools and technologies for implementing procedural generation algorithms [5]. The performance analysis conducted during this study yielded important insights. The execution time test revealed that the algorithm's execution time increased significantly with larger grid sizes, emphasizing the need to consider the scale and resolution of the terrains [6]. This finding highlights the trade-off between generating detailed terrains and the time required for the algorithm to complete its computations. Additionally, the memory usage test demonstrated a quadratic relationship between memory usage and grid size, indicating the necessity of efficient memory management [7] for generating higher-resolution terrains. Optimizing memory usage is crucial to avoid excessive consumption and ensure efficient resource utilization. These findings from the performance analysis provide valuable guidance for optimizing and refining the algorithm discussed in this article. Techniques such as algorithmic refinements, parallelization [8,6], and memory optimization strategies can be employed to reduce execution times and minimize memory overhead. By understanding the algorithm's performance characteristics and leveraging the insights gained from the analysis, developers can make informed decisions to generate visually compelling and diverse landscapes within the Unity game engine.

Mercury injection capillary pressure analysis is a methodology for determining different petrophysical properties, including bulk density, porosity, and pore throat distribution. In this work, distinct parameters derived from mercury injection capillary pressure tests was considered for the prediction of permeability by coupling machine learning and theoretical approaches in a dataset composed of 246 tight sandstone samples. After quality checking the dataset, the feature selection was carried out by correlation analysis of different theoretical permeability models and statistical parameters with the measured permeability. Finally, porosity, median capillary pressure, Winland model, and mean porethroat radius (corresponding to the saturation range 0.4-0.8) were chosen as the input features of the machine learning model. As the machine learning approach, a support vector machine (SVM) model with a radial basis function kernel was proposed. Furthermore, the model and its metaparameters were trained with a particle swarm optimization (PSO) algorithm to avoid over-fitting or under-fitting. In contradiction to the theoretical models, the implemented SVM-PSO model could acceptably predict the experimentally measured permeability values with an R 2 rate of over 0.88 for training and testing datasets. The introduced approach could reduce the mean relative errors from about 10 to values less than 0.45. The improvements were more significant for low permeability samples. This successful implementation shows the potential of coupled usage of theoretical and machine learning methodologies for improved prediction of permeability of tight sandstone rocks.