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…

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…

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…

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…

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?…

Newton’s Method: Explanation and Example Usage

Polynomials are compex to solve. Sometimes they can be solved quite easily and sometimes it seems like solving them is impossible. Fortunately there exists something called Newton’s Method which lets you approximate roots of a polynomial by using the Taylor Series. The Taylor Series is defined as follows By using the first two terms of the…

Trailing Zeros of Factorials

Since I’m bored to hell in programming class, my teacher, who is also my physics teacher, gave me the task to find out the trailing zeros of and then for . I then began searching for patterns in factorials starting from to 10!. Interestingly, has one trailing zero and has two trailing zeros. By induction you could determine the…