### Fun with FFT

For a project I work on, the designer had the idea of having real-time sound waves on the background of the application. Challenge accepted! See below the result of the first prototype. The current implementation measures the energy of sound by doing fast Fourier transformations and sum the…

### Deep Dream in HD

Around may 2015, a researcher at Google, Alexander Mordvintsev, took a deep network meant to recognize objects in an image, and instead used it to *generate new objects in an image. The internet quickly exploded after seeing one of the images it produced. Soon after, Google posted a blog entry on…

### L-Systems

L-systems are a mathematical formalism proposed by the biologist Aristid Lindenmayer in 1968 as a foundation for an axiomatic theory of biological development. More recently, L-systems have found several applications in computer graphics [Smith 1984; Prusinkiewicz and Hanan 1989; Prusinkiewicz and…

### Phyllotaxis

Tonight I was reading some interesting publications about math in nature. I was drawn to the phenomena of Phyllotaxis. The beautiful and dense arrangement of leaves in nature is stunning to see. The text below is cited from the free book "the algorithmic beauty of plants", available on the website…

### Ray marching

I started to experiment with a technique called "ray marching", also called "ray casting" or "sphere tracing". The method is quite new and different from the classic method with 3D vertex models or ray tracing. There is an excellent paper, written by Prof. John C. Hart. You can read it here:…

### Painting with deep neural network

I'm fascinated by computer generated art and I think it would be great if a computer would be able to learn how to paint. As an experiment, I've created a deep neural network that takes coordinates input X of 2 neurons, mapped to 5 hidden layers with 64, 128, 256, 128 and 64 neurons respectively.…

### 2D strange attractors

I've always been fascinated by fractals and strange attractors. One of the most famous strange attractor system is the Lorenz system. But with some trial and error, you can find some formulas that create "chaos". In this post, I used a system of equations, described in the book "Chaos In…

### Diffusion-Reaction, creating animal patterns

I while ago, I stumbled upon a famous paper of Alan Turing called The chemical basis of morphogenesis. It is fascinating to see the idea of using diffusion - reaction equations to simulate the creation of animal patterns. In his paper, he describes his idea to use two non-uniform…