Four Dimensional Mandelbrot Fractal Animation

This movie is based on the principle that if you take all the Julia Sets that are perpendicular to the mandelbrot set you can combine them into a 4D object. This movie contains nearly 1000 frames and shows scenes parallel to the mandelbrot plane along the line (0, 0, 0.32, 0.545) to (0, 0.985, 0.32, 0.545). Please visit www.eddaardvark.co.uk for more information about this and other animations. Includes python source code you can use to create your own animations.

Category:

Entertainment

Tags:

• 4d
• four-dimensional
• mandelbrot
• animation

[Kuvastus]

It looks lovely at 0:24...

[drifterdaydreamer]

It looks like a marijuana leaf at 0:24...I'm going to send this animation to Willie Nelson.

[fractalsoul28]

@iAmThePhatMan I guess so, he explains it fairly well on his website. I think what we are seeing is a 2d slice moving through 4 dimensions, in the way you see mri scans of a 3d human body animated. So time kind of is an extra dimension, but you can change the direction the plane moves in.

[fractalsoul28]

@iAmThePhatMan I guess, what would the 3rd dimension be? To me it just looks 2d plus a dimension of time. I'm gonna download the source, see what he means by "perpendicular julia sets". It looks kind of like animations in which Z is initialized as a different value for each frame.

[iAmThePhatMan]

@fractalsoul28 yes but everyone is wondering why this is 4 dimensional, which is because the function looks like it "morphs" in a timeframe, ergo time is the 4th dimension I guess.

[fractalsoul28]

@iAmThePhatMan No actually the colors represent how fast that point is trending off to infinity. points within the black area never escape. Technically a point is only in the mandelbrot set if it would never escape, but in a simple program any point that never goes over 2 within a certain number of iterations is colored black. Other points are colored according to how fast they escaped.

[JaPeKePaJaKe]

Let's put mathematicians into jail like the rest of the nature!

[chuckrubenz]

Brilliant! This is the right way to go forth with fractal art!

[A9SecondSleeper]

Are all the parameters at 0:24 of the value 420?

[iAmThePhatMan]

@luckeycat34 pretty sure the fourth dimension is time. If you don't already understand, the color coding of fractals is a measure of time. The colors depict how the set evolves.... I think....

anyway the true mandelbrot set is solid/finite black and white. The colored pictures can be thought of as a snapshot or still frame of the evolving fractal.

[bobbyFisherfisher]

Looks 2D to me :P