Percolation Properties of Triangles With Variable Aspect Ratios

Abstract

Percolation is the study of random networks and their nature of connectivity. An exponential relationship between the percolation threshold and the aspect ratio of a shape is observed within this paper. Matlab simulations and a novel experimental method are utilized to determine the percolation threshold across a conductive sheet as triangles of variable aspect ratios are cut with a Universal Laser System X2-600 100 Watt CO2 laser. Resistance is measured as a voltage of 100mV is applied across the conductive sheet of aluminum coated Mylar film. This data is then analyzed to yield the percolation threshold relating to a triangle with a specified aspect ratio. We establish an equilateral triangle to have an aspect ratio of one.