Fun With Binary Palindromes

My recent vicissitudes have led me into the realm of palindromes. Binary palindromes. Essentially, palindromes are words or numbers that appear the same when read from left or right. The word “Anna” is a palindrome for example, as well as the number 13931. But my focus has been primarily on binary palindromic numbers, such as 11011 and 01011010. There is nothing inherently useful about them, though they possess a certain beauty which is only evident to someone who likes to fumble with ones and zeroes....

March 17, 2017 · 4 min · 834 words · Gian Sass

The Julia set

Quite like I described the Mandelbrot set, the Julia set is also a Mathematical fractal that is computed with almost the exact iteration. The iteration is a quadratic polynomial in this case. Here, and are both complex numbers, but play a rather different role than in the Mandelbrot equation. Going back to our original understanding of this iteration, was a constant mapped to a point in the set, and a value used for computation with an initial value of ....

November 20, 2016 · 3 min · 591 words · Gian Sass

Computational Complexity of Recursive Functions

A function is deemed recursive if it satisfies the following three rules: There must be at least one halting condition. The function must call itself. The parameters thereof must be altered such that the halting condition will eventually stop the recursion. The easiest example of a recursive function would be calculating the factorial of a (natural) number. int fact(int n) { if (n == 0) /* 1. Halting condition */ return 1; else return n * fact ( n - 1 ); /* 2....

November 7, 2016 · 2 min · 386 words · Gian Sass

The Mandelbrot Set, Part 2: OpenGL Program

In the last part I tried to give a general overview of how the Mandelbrot set is generated and how it can be rendered using a simple algorithm. This part will focus on programming a simple realtime renderer that can also zoom and move around, as I showed in this video. Additionally, it will serve as small introduction to modern OpenGL programming. In this tutorial we work with C++, but you may use any other language you feel comfortable with that also binds with OpenGL....

November 6, 2016 · 11 min · 2212 words · Gian Sass

The Mandelbrot Set, Part 1: Overview

Recently, I have been experimenting with the Mandelbrot set. I made a video where I showcased a simple Mandelbrot explorer, written in C++ and OpenGL. In this little series I want to explain what the Mandelbrot set really is, how to generate it, and how to program it in OpenGL! What is the Mandelbrot set? The Mandelbrot set is a set of points, which are determined by a simple iteration. For a certain amount of iterations, this equation is repeated for each points in the set and coloured appropriately....

July 6, 2016 · 3 min · 566 words · Gian Sass