Gaussian Integer

Ultra Fractal gaussianinteger Gaussian IntegerThe Gaussian Integer coloring algorithm colors fractals according to how the calculated orbits are related to Gaussian integers.

Gaussian Integer is available as a coloring algorithm in Standard.ucl, or as a trap shape plug-in in Standard.ulb that can be used together with the Orbit Traps or Direct Orbit Traps coloring plug-ins. See Example 2 – Orbit trap plug-ins .

Gaussian integers are complex numbers normalized to integer values. This coloring algorithm examines the values of z calculated by the fractal formula, and tests them against nearby Gaussian integers.

The resulting images are richly textured, containing many circles, dots, and stars. By tweaking the provided parameters, many variations are possible.

The following parameters are available:

Integer Type

Specifies the rounding method to use to find the nearest Gaussian integer. The round(z) option usually gives smoother images than the other options.

Color By

Selects how the color of each pixel is determined. For example, it can be colored by the minimum distance from a value of z to the nearest Gaussian integer.


Chooses between several ways of normalizing the distance to the nearest Gaussian integer. If you select factor or f(z), an additional parameter will appear that specifies the normalization factor or function to use.


If checked, a small randomization factor is added to each value of z before examining its behavior. Additional parameters will appear to specify the amount of randomization and a seed value. Each seed value will give different randomization patterns.

In the trap shape plug-in version, this option is not available. However, you can achieve the same effect by selecting the Randomize transformation plug-in from Standard.ulb for the Trap Position parameter in the Orbit Traps plug-in.

See Also
Example 2 – Orbit trap plug-ins
Orbit Traps
Standard coloring algorithms

Gaussian Integer