# About

Hi, I'm Gijs Bellaard. I was born and raised in Geertruidenberg, a little city in The Netherlands. I'm 24 years old and currently doing a PhD at the Eindhoven University of Technology under the supervision of Remco Duits. My interests lie in numerical analysis, differential geometry, combinatorics, simulations, and computer graphics.

# Articles

Some articles I've written that try to (and/or) illuminate, summarize, formalize, simplify, subjects I've come across. Some of them are purely for the fun of it.

- Algebraically Manipulating the Differential
- Curvature
- Determinant
- Distance Fields
- Finite difference approximations
- Geometric Series and Positional Notation
- Kaleidoscopic IFS fractals
- Knotting
- Living on the n-sphere
- Rubik's Cube in 1 move
- Simple Atmosphere

# Snippets

Here I share pieces of code/maths that can be of use. Currently it consists of mostly distance functions for some fractals and some finite differences. I have put them on my site because I find these to be hard to find in their most basic form.

- Apollonian fractal
- Donuts fractal
- Fathauer crystal
- Four-point stencil for 3D gradient
- Kalibox
- Mandelbox
- Menger sponge
- Nine-point stencil for 2D laplacian
- Sierpinski dodecahedron
- Sierpinski icosahedron
- Sierpinski octahedron
- Sierpinski tetrahedron
- Tree fractal

# Shaders

Check out all my shaders on Shadertoy

# Apps

- Barnes-Hut Simulation
- Buoyancy Simulation
- Cake Wavelets
- Finite Difference Calculator
- Fluid Simulation
- Function Plotter
- Mandelbrot Viewer
- Node Editor
- Projective Geometry
- Raymarcher IDE
- Spherical Lens
- Union-Closed Family Visualizer

# Bachelor Final Project

My bachelor final project is about neighbour-swap graphs. Tom Verhoeff was my supervisor during this project. A Dutch introduction to this topic can be read in the so-called "A4-populair", which is meant for high schoolers in the Netherlands.

My friend Sander Spoelstra's bachelor final project is about the Union-Closed conjecture which I am also interested in. I followed the writing of his paper closely and he allowed me to share it here.

# Master Thesis

My master thesis is about the simulation of viscoplastic materials using smoothed particle hydrodynamics. This thesis was done under the supervision of Bas van der Linden at Sioux Mathware.

# Gallery

I create renders of fractals using my Raymarcher IDE. You can check them out in the gallery. In the meantime, enjoy this random picture from the gallery: