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VII. Gaussian Integers Algorithm


A Gaussian integer is a complex number whose real and imaginary components are both integers. The algorithm works by computing the distance from each zn to the nearest Gaussian integer, and then coloring based on the smallest such distance for all orbit values.

Conceptually, this is like using an orbit trap where the trap shape T (a point) is repeated over the complex plane in a regular grid, coinciding with the Gaussian integers. Once perceived in this manner, it is clear the technique can be extended to any other trap shape, with different grid spacings, and even non-rectangular grids. Radial grids and triangular grids are just two possibilities.

 


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