Alternative Julia Set Sequence

This is a more unusual cross-section of the four-dimensional "Julia Set" fractal.
And yes, it really =IS= the Julia set! :)

Category:

Science & Technology

Tags:

• julia
• set
• fractal
• animation
• evolution
• mandelbrot
• math
• mathematics
• computer
• graphics
• cross
• section
• eric
• baird

[aljelje]

Cool! How is that generated?

[ErkDemon]

@aljelje:

It's a basic piece of Julia/Mandelbrot code, with a few simple changes.

Both sets use the same basic iterated relationship "z -->( z^2 + c)".

z and c both have two parts, a real compoennets and an imaginary component. if we label the two parts of the start value of z as "A" and "B", and the two parts of the contant added at each stage "C" and "D", we can see that the Julia Set is actually four-dimensional.

(contd)...

[ErkDemon]

...(contd)

Normally we get Julia images by slicing parallel to the plane AB, and using C and D to change the position of the cross-section. The Mandelbrot set is a special slice through the centre of the Julia Set, on the CD plane. So for this sequence I sliced the Julia set parallel to CD instead, and that's why the Mandelbrot appears halfway through it.

Codewise, it's just a question of taking standard "Julia image" code and swapping some of the axis stuff to see a different cross-section.

[ErkDemon]

The cross-section looks awfully familiar at about 28 seconds ...

[weckar]

@ErkDemon ... that's because the mandelbrot set by pure definition IS a cross section of the julia set....

[ErkDemon]

@weckar: Yes Indeedy! :) 

[CompOfHall]

That is awesome. What is the C when it appears to form a Mandelbrot?