About

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Hi, I'm Gijs Bellaard. I was born and raised in Geertruidenberg, a little city in The Netherlands. I'm 25 years old and currently doing a PhD at the Eindhoven University of Technology under the supervision of Remco Duits in the Geometric Learning and Differential Geometry group of the Centre for Analysis, Scientific Computing and Applications cluster. My interests lie in simulations, differential geometry, combinatorics, machine learning, and computer graphics.

News

• 20 September 2023: As an instructor, I've started working on my own notes for Remco Duits' Master Course.
• 30 August 2023: I gave a presentation about Neurogeometry and PDE-Based Neural Networks at GSI2023.
• 05 August 2023: The conference paper Functional Properties of PDE-G-CNNs is published in GSI2023.
• 30 June 2023: I made a Kerr-Newman Metric Black Hole simulation.
• 12 May 2023: My conference paper Geometric Adaptations of PDE-G-CNNs is published in SSVM2023.
• 16 April 2023: My article Analysis of (sub-)Riemannian PDE-G-CNNs is published in JMIV.

Academia

Other

• My bachelor final project is about neighbor-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.
  Paper · Presentation · A4-Populair

• 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.
  Thesis · Presentation

• 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.
  Paper

Apps

• Barnes-Hut Simulation

• Buoyancy Simulation

• Cake Wavelets

• Erosion

• Finite Difference Calculator

• Fluid Simulation

• Function Plotter

• Mandelbrot Viewer

• Node Editor

• Projective Geometry

• Raymarcher IDE

• Rigid Grid Simulation

• Spherical Lens

• Union-Closed Family Visualizer

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

• Equivariant Neural Networks

• Finite Difference Approximations

• Kaleidoscopic IFS fractals

• Knotting

• Living on the n-sphere

• Rubiks 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

• Raytracer in C

• Schwarzschild Geodesics

• Sierpinski Dodecahedron

• Sierpinski Icosahedron

• Sierpinski Octahedron

• Sierpinski Tetrahedron

• Tree Fractal

Shaders

Check out all my shaders on Shadertoy

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: