Dot-World: The Easy 2D and 3D Simulator to Enhance Education in Developing Countries

Abstract

Of the many worthy humanitarian concerns that the world still has to address, one in which technical professionals can have an immediate impact is the development of freely-available and sustainable scientific tools. These scientific tools are vital for increasing educational attainment in developing countries. Studies in these countries have shown that fun, game-like simulations are both engaging and educational. While there exists free simulation software, we believe there is a need for a free, easy to use, and easy to understand 2D and 3D partial differential equation (PDE) solver. Typically, PDE solvers are complex tools with high learning curves. Thus, in the current research, we endeavor to create a general 2D and 3D PDE solver that is fun, versatile, and approachable for those with limited math, science, and computer experience. Our result is Dot-World, a fully-functioning PDE solver written in Python. Dot-World allows users to draw custom 2D and 3D environments in CSV, which they can then import to Python to render. Dot-World has a graphical user interface for users to input their desired PDE, parameters, initial conditions, and boundary conditions. Dot-World can automatically recognize PDE terms by using a combination of pre-built algorithms and symbolic programming with the SymPy library. As validation, we used Dot-World to perform 2D and 3D simulations of PDEs such as the Allen-Cahn, Fisher-KPP, Turing diffusion reaction, wind-pollutant diffusion advection, and transient heat equations, all incorporating obstacles and arbitrary boundaries. We believe Dot-World is the ideal introductory simulation software for students in developing countries.