It may come as a surprise to you, but I like chess. I am a member of my local chess club where I play occasionally. I am not very good at chess. I would call myself a beginner that knows all the rules. This will be the first in a series of posts (jinx) […]

# Author archives: Bernard Bot

## my way or the Conway

Another day, another implementation. Today I have implemented Conway’s game of life. It is a very simple model that can show very complicated results. It is also a lot of fun. What are the rule to this game? Well, I will tell you. First, let us start with the components of the system, we […]

## it’s complicated

I have been busy with complex numbers in JavaScript. I wanted to implement the Durand Kerner root finding algorithm. This algorithm requires complex arithmetic in order to work. So, in order to implement something, you need to implement something else. You just have to hope that you have arrived at the lowest level. What […]

## brainfark

I wrote my own little brainfuck interpreter. You can read all about brainfuck on the esoteric programming website. They have a whole list of weird programming languages. So what is brainfuck? They tell you all about it on the Esolang website. But I’m gonna tell you anyway. Brainfuck is a programming language designed to […]

## Double trouble

Following up on the post about Lorenz systems I have made a visualization of the double pendulum. Both of these systems are prime examples of systems studied in chaos theory. That is: systems that are highly sensitive to initial conditions. Many of these systems can also be seen in nature. For example the weather. […]

## Lorenz system

I have been doing some stuff with differential equations. They provide some unexpected results and show random behavior. I made a little visualization with the html canvas of a Lorenz (not Lorentz) systemhttps://en.wikipedia.org/wiki/Lorenz_system You can see it live here:https://05dd8515-5617-4479-92db-df9de14327bc.htmlpasta.com/

## My mandelbrot

I have tried implementing a zoomable mandelbrot set for a while. Today I created a satisfactory implementation. There is no native support for complex numbers in JavaScript, so we keep both real and imaginary parts of the complex number separate. The mandelbrot recurrence relation is: z_{n+1} = z_{n} + c The value of z_ 0 […]

## Random number cycles

Random number generation is often done by applying a function recursively to a seed number. The function needs to be bounded to a certain domain. Obtaining a function that is bounded is easily done by applying the modulo operation on the base function. The function must be deterministic. For example the following function

## Fibonacci for beginners

The Fibonacci sequence is one of the most famous sequences. It appears everywhere in nature and mathematics. It is defined as: \[ F(1) = 1 \] \[ F(2) = 1 \] \[ F(n) = F(n – 1) + F(n – 2) \] We don’t want to calculate all these numbers by hand. For n […]