Simulate complex life-like behaviour from simple rules!

Navigate the cosmos with this high-performance Barnes-Hut simulation. Accurately models thousands of stars forming a galaxy, guaranteeing an optimized celestial experience.

View any first-order differential equation of the form \(\frac{dy}{dx} = f(x, y)\) as a slope field.

A 3d function grapher that allows for rotation and scaling of various mathematical functions.

Solar Synesthesia allows users to view songs as a solar system. The movement of the planets in the system is synced with the notes and instruments in the song, creating a visually engaging and interactive way to experience music.

Displays bubble sort, selection sort, insertion sort and cocktail shaker sort with step-by-step iteration.

A particle simulation that shows elastic collisions between particles under the influence of external forces.

Simulates the solar system using Newton's laws of gravitational motion.

Explore the Mandelbrot set and uncover the beauty of hidden fractal patterns.

Simulates an elastic collision between two objects.

A general-purpose Discord bot with prebuilt games and mathematical features.

A clone of the popular game of 2048 written in PyGame.

Describing the Motion of a Line Segment Moving Along a Vertical Line

This paper derives that \(\begin{cases} x=t+ \frac{L}{\sqrt{1+\left(\frac{F}{C-t}\right)^2}}\\ y=\frac{F(x-t)}{C-t} \end{cases} t\in \mathbb{R},L \geq 0, C\neq t\) describes the motion of the line segment.

Finding the Equation of a Curved Surface

This paper derives that \(f(x) = x+\lambda -2\sqrt{x\lambda} \, x\in (0, \lambda)\) describes the shape of the curved surface.