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This article is from the Fractal FAQ, by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by others.

8b: How does quaternion arithmetic work?

Quaternions have 4 components (a+ib+jc+kd) compared to the two of
complex numbers. Operations such as addition and multiplication can be
performed on quaternions, but multiplication is not commutative..
Quaternions satisfy the rules i^2=j^2=k^2=-1, ij=-ji=k, jk=-kj=i, ki=-ik=j.

See:

http://www.dtek.chalmers.se/Datorsys/Project/qjulia/index.html
QJulia page (quaternions) (Henrik Engstrvm)

 

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science, engineering, fractals, chaos, complexity, Mandelbrot