Breathtaking Mandelbrot Videos – Now in Brilliant 3D
By on September 6th, 2011

Yesterday, I saw the most amazing videos. These are called Mandelbulb videos, and half the fun of watching them is understanding the science and mathematics behind them. If you don’t want to learn how these are made, you can skip to the end of this article.

What is a Mandelbulb?

It’s a type of mathematical entity that’s based on ideas behind  Fractals  which were discovered in the 17th century. Fractal mathematics describe  geometric patterns that repeat at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractal patterns are often seen in nature, such as in snowflakes. Here’s an example of a Von Koch curve, which is one of the simplest forms of a fractal.

 

von koch curve

When a fractal shape is calculated, it is calculated in steps, or iterations. You can see the shape change, above, as it goes through each iteration.

Here’s another example of a complex fractal which was generated by the  GoogleLabs JuliaMap Generator.

Google Labs Juliamap web app

If you follow that link to Google Labs, your web browser will generate a fractal. One of the unique properties of fractals are that you can zoom in on the patterns and see even smaller but very similar patterns.

Over the years, many mathematicians have tried to determine the formulas for true 3D fractals. Finally, in 2007,  an amateur fractal image maker,  Daniel White, came up with some formulas that seem to generate these 3D fractal shapes. Daniel started his work by using one of the most famous fractal types, called the  Mandelbrot set. The resulting shapes are called Mandelbulbs.

A couple of months later, some software hackers and fractal enthusiasts got together to work on software to render Mandelbulbs on computers. The Mandelbulber Project has been a success, and as you’ll see below, it’s also resulted in some very fantastic images and videos.

Here’s a screenshot of what the software looks like, running on a Linux PC. The software is Open Source, completely free to download  and also runs on Windows PCs.

Mandelbulb Interface

Here are a few screen-shots of Mandelbulber’s artificial worlds.

mandelbulb 45

 

mandelbulb 14a

 

mandelbulb image

 

mandelbulb 1

 

mandelbulb 2

 

mandelbulb 3

 

mandelbulb 4

Finally, we have reached the video. As you’ll see, Mandelbulber can create entire virtual worlds that can be explored. In fact, it can create an infinity of different worlds and some of them are almost scary in their complexity.

Video:  Trip to center of hybrid fractal

Here are more Mandelbulb videos from XLACE. It’s interesting to see how his videos have evolved over the years, and how Mandelbulber has suddenly changed the world of fractals forever. Someday, I expect to see these artificial worlds appear in movies. If you need an alien place for a Sci-Fi movie, it’s pretty easy to see where you could get one.

 

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Author: Clif Sipe Google Profile for Clif Sipe
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