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Produced by Andy Burbanks
Quaternionic numbers may be represented by points in four-dimensional space. A separate Introduction to quaternions shows how they may be introduced as an extension of the complex numbers. Quaternionic Fractals are fractals in four-dimensional space. By taking three-dimensional slices through these objects, it is possible to visualise them.
Shown here are some example pictures, the resolution is 512 x 512 x 512. The left-hand set is a slice through a quaternionic Julia set (for q = -0.1 + 0.6i + 0.1j - 0.6k). The right-hand set is a slice through the so-called Quandelset.
In order to calculate the shape of a slice, the usual method would be to take a grid of points in 3D and test each one to see if it lies inside or outside the object. Unfortunately, this calculation would be very time-consuming since many points would need to be tested.
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