EXPERIMENTAL DESIGN OF BROWNIAN MOTION USING FRACTAL GEOMETRY

Abstract

Brownian motion refers to the random movement of a particle, resulting from collisions with surrounding molecules. This movement appears irregular and asymmetric, occurring in random directions and at random rates. The behavior of Brownian motion can be studied using fractal geometry, as demonstrated by 2D graphics that plot particle movement along the x and y axes. These graphics are generated using a computer program written in the Pascal programming language. To analyze the pattern of Brownian motion, 30 graphics were selected as a statistical sample. Each graphic is measured from its starting point to its endpoint, following a thousand collisions. The average distance is then calculated, and each distance value is divided by the mean distance to obtain a ratio. The resulting ratios were used to construct a histogram, which represents the distribution of distances. This distribution is then compared to the ratio distribution predicted by physics theory, allowing for further analysis and interpretation of the Brownian Motion behavior. In this study, a novel approach is proposed for analyzing Brownian Motion behavior using fractal geometry and statistical analysis. Specifically, 2D graphics are used to plot particle movement, and a statistical sample of 30 graphics is analyzed to obtain distance ratios, which are then used to construct a distribution histogram. The resulting distribution is compared to the predicted ratio distribution, providing new insights into the underlying physics of Brownian Motion. This approach may have implications for understanding complex systems in fields such as physics, chemistry, and biology. Keywords: Motion, Fractal, Random Walk, Free Walk DOI： https://doi.org/10.35741/issn.0258-2724.58.2.8