The taffy-like quaternion Julia sets are similar to complex Julia sets, except that they exist in four dimensions rather than just two. They aren’t really useful or significant; but, like other fractals, they tend to look pretty.
A Quick Review
Before getting into quaternion Julia sets, here is a short review of how complex Julia sets [...]

Complex Julia Sets
A Julia set, named after French mathematician Gaston Julia, is a type of fractal defined by an iterative function over the complex numbers. The study of fractals has applications in complex dynamics, partial differential equations, statistics, etc, but most people like them because they produce pretty images. The following is an [...]

I began to show the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by 3; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which [...]