European Journal Of Advances In Engineering And Technology
Published February 28, 2019 | Version v1
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Visual Models and Classification of 1D, 2D, and 3D Random Walk

Authors/Creators

  • 1. City of Puschino, Russia

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ABSTRACT

A new visual model has been proposed for describing 1D, 2D and 2D random walk based on consideration of linear and nonlinear arithmetic triangles (1D), linear and nonlinear arithmetic squarer (2D), and linear and nonlinear arithmetic octahedrons (3D Our studies and visual constructions presented in this work show that the nonlinear case of an arithmetic triangle coincides with the optical scheme of the laser. Geometric constructions and recursive formulas are given. The studies presented in this paper show various geometric properties and nonlinear effects of 1D, 2D, and 3D spaces. For nonlinear 1D and 3D cases we can speak of filling the numbers of the arithmetic triangle (1D) and the arithmetic octahedron (3D) in the form of “islands of numbers” or separate structures of numbers. 

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