Open AccessLinear and Nonlinear Random Walks in 1d, 2d and 3d Space.
Publication year - 2019
Language(s) - English
DOI - 10.46940/gjaap.01.1001
Subject(s) - random walk , equilateral triangle , octahedron , cube (algebra) , mathematics , combinatorics , space (punctuation) , nonlinear system , geometry , computer science , crystallography , physics , statistics , chemistry , quantum mechanics , crystal structure , operating system
The regular octahedron [1] refers to the number of five Platonic figures. It can be composed of eight equal equilateral triangles or twelve identical segments. "The octahedron is dual to the cube" [2]. The regular octahedron can also be composed of many identical small cubes just as in Ancient Egypt were pyramids of stone blocks. The construction of an octahedron using small cubes can be obtained by considering a random walk in three-dimensional (3D) space. In [3] we considered a visual model of a 3D random linear and nonlinear walk in an octahedron. In [3,4] we reviewed and systematized the visual models of 1D, 2D and 3D random linear and nonlinear walks too.