FractalX – A fractal simulation project in Unity

Overview

Goals

FractalX is a fractal simulation game project where the player can explore and customize to his – her liking, various types of recursive mathematical equations that end up creating beautiful and increasingly complex geometrical patterns, commonly known as fractals! So, the goal of this problem is for students to become familiar with fractals by visualize and customize them in an easy to use game-like software.

Learning Objectives

Fractals are extremely complicated. Because of their chaotic tendency, the mathematical concept of fractals is difficult to define formally, even for mathematicians, but key features can be understood with a little mathematical background. So we thought of a fun, interactive and artistic way to explore one of the most mysterious and omnipresent field of Mathematics. Therefore, through this simulation, students can explore a real time simulation of the Mandelbrot set and all of the Julia sets and learn about the relation between the two most distinctive sets in fractal geometry.

Context

The player can explore every one of the 5 Mandelbrot Set equations and all of the Julia Sets based on his-her real-time interaction with the Julia Seeds sliders. There is an integrated UI that can be separated to two sectors: The top sector, which is responsible for the fractal that the game is rendering (5 Mandelbrot set fractals and all of the Julia sets) and the iterations that the fractal is iterating through every frame. The bottom sector, which is responsible for the more aesthetic-artistic tone of the game that the player can experiment with.(colors, style..etc) In addition, pressing F12 will activate ‘immersion mode’ where all the integrated UI is hidden so the player can experience a more immersive and distraction-free gameplay.