Buddhabrot 4-Dimensional Rotation
I’ve been playing with fractals recently. More specifically, the Buddhabrot fractal.
The Buddhabrot set is closely related to the Mandelbrot set:
The mandelbrot set is displayed on the complex plane, where one axis is the real component of (we’ll call it
) and the other is the imaginary component of
(a.k.a
).
With the Buddhabrot set, we can add a few more axes. Instead of just using and
, we also use the real and imaginary components of
as axes. Whereas in the Mandelbrot set,
is assumed to be
, in our 4D Buddhabrot set, we make these values variable as well.
So instead of the two dimensional image you’re used to seeing of the Mandelbrot set, we’ve instead got 4 axes: and
.
Which leads us to our next problem — how do you visualise a 4 dimensional object on a computer? Well, it’s difficult. You obviously can’t just draw an image of it, or even just show a 3 dimensional picture of it. Instead, we show it rotation in 4 dimensional space.
So, here’s the result:
I’ve made all of this code open source — here’s the project page.
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