The engineering applications of fractals

Abstract

Fractal geometry principles and mathematical models based upon the theory of Mandelbrot [1] are commonly used today in search of a more realistic simulation of natural phenomena. This paper presents the simulation of various engineering applications by using fractals. In agriculture and civil engineering, underground seepage simulation is used to determine the critical distance between the different subsurface seepage pipes in order to avoid pondage due to overlay of the seepage cones. This is done by simulating the phreatic line — the boundary of the saturated region of the soil — using fractal interpolation. A second application is the simulation of settling tanks based on fractal geometry. Settling tanks are used in civil engineering to remove impurities from water. The main objective is to find the efficiency of the tank based on the shape of the sludge zone. Using fractal interpolation techniques, the shape of this zone can be determined. The package simulates discrete particles entering the settling tank. These particles accelerate until an equilibrium is reached between the drag force induced due to the particle's mass and the driving force of water flow. The fractal interpolation algorithm uses the corrdinates of the settled particles to determine the shape of the sludge zone. A third application that this paper presents is a computer graphics simulation of the formation and growth of coral reef based on the Diffused-Limited Aggregation (DLA) algorithm, which produces a certain class of fractals based on a stochastic model.