A Quaternion Fractal Chorus

Treating my last attempt at rendering quaternion Julia sets as a study, I wanted to move on to alternate methods of visualising the deep structure of these four dimensional objects. There’s a lot of complexity there which results in some compression artifacts – watch it in HD to get the full effect.

There is a four dimensional Julia set for every four dimensional quaternion. We can label each quaternion using four numbers.

quaternion

I decided to “unfold” the first two values of the quaternion onto a plane and animate the last two values. The camera is centered at (0,0) and Julia sets are placed at intervals of 0.1 off to infinity for both axes.

grid

You can start to see the larger structure present more clearly. Perhaps a three dimensional unfolding next?

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