## Make a hierarchical FSM in Unity/C#

Let’s improve the basic FSM we made in a previous tutorial and add a jump state!

Read More »Make a hierarchical FSM in Unity/C#Let’s improve the basic FSM we made in a previous tutorial and add a jump state!

Read More »Make a hierarchical FSM in Unity/C#Let’s design a simple 2 states-FSM for 2D physics-based player movement!

Read More »Make a basic FSM in Unity/C#In 1952, Alan Turing published an article called *The Chemical Basis of Morphogenesis* in which he offered an idea as to how reaction-diffusion equations could help explain various biological structures: the spacing of rows of alligator teeth, the spots on cheetahs, the position of leaves on some plants… Beside the article itself that is quite fascinating, it’s interesting to see that today, nearly 70 years later, there is still no scientific consensus on whether to accept or deny his theory.

This week, let’s continue exploring some concepts that the Advent of Code (AoC) challenges bring back to my memory. During Day 12 this year, Eric Wastl offered to examine how we could simulate a very basic newtonian system of 4 moons that attract each other and move in a periodic pattern over time. Just like for Day 15, I also made a little visualization to make the explanation a bit more catchy to the eye 🙂

In this last article from the FEM series, I present some additional concepts related to the finite element method and further developments. In particular, I focus on finite element analysis, some methods for solving time-dependent problems and optimization ideas.

Read More »Solving PDEs numerically: the finite element method (3)

Today, let’s continue with the finite element method and focus on how to implement it on a computer. How do we discretize our domain? How do we actually compute the stuff that’s in our variational formulation – efficiently, that is? How do we store and visualize our solution?

Read More »Solving PDEs numerically: the finite element method (2)

The study of partial differential equations is a fascinating field of mathematics with many concrete applications, be it in physics, mechanics, meteorology, medicine, urbanism… Mathematicians model the world as equations to better understand it and, if possible, compute a theoretical solution to a physical problem. However, we can’t always get an analytical solution – for example if the geometry is too complex – and sometimes must rely on numerical methods to get an approximation.

Read More »Solving PDEs numerically: the finite element method (1)

Although I’m not much of a physicist, I am always fascinated with how simple laws, such as Newton’s, can create beautiful and complex movements. I tried to illustrate this by working out little simulations of basic physical models: particles elastic collision, free fall and pendulum evolution.