Category Archives: Math

XNA Shader Programming source now on GitHub

As with the Commodore 64 programming tutorial series, I have now moved all the source from my XNA Shader Programming tutorial series to GitHub. The XNA Shader Programming series goes through the theory and the HLSL implementation of various effects … Continue reading

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Fundamentals of Fractals 5: The Mandelbrot Set

I give you the same question Neo got; do you take the red pill or do you take the blue pill? After studying the Mandelbrot set, the complexity, rich and beauty of a simple definition, the endless iteration of a … Continue reading

Posted in DirectX11, Fractal, Graphics, Math, Tutorial | 10 Comments

Fundamentals of Fractals 4: The Sierpinski carpet

In the last tutorial, we plotted a Sierpinski gasket using dots. I figured that I wanted to introduce the Sierpinski Carpet as well, before moving into more heavy fractals. The Sierpinski Carpet is very simple as well, but we are … Continue reading

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Fundamentals of Fractals 3: The Sierpinski gasket

The Sierpinski gasket is a fractal and a very basic fractal of self-similar sets, a mathematically generated pattern with similar patterns. The Sierpisnki gasket is typically generated using triangles, but you can render any shape you want in the space, … Continue reading

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Fundamentals of Fractals 2: What is a fractal?

There are many answers to this question, but let’s take a look at the common definitions:”A set of points whose fractal dimension exceeds its topological dimension” -Paul Bourke”A fractal is a rough or fragmented geometric shape that can be split … Continue reading

Posted in DirectX, DirectX11, Graphics, Math, Tutorial | 1 Comment

Fundamentals of Fractals 1: Introduction to Complex Numbers

This series aims to teach you the basics of programming fractals. Let’s start with introducing Complex Numbers, which is a topic within algebra and the fundamental for everything that is related to fractals. In the next tutorial, we will move … Continue reading

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