Triangle Inequality Average

The Triangle Inequality Average coloring algorithm creates smoothly colored fractals with large flame-like patterns that extend from the fractal outwards.

Because it uses the same smoothing as Smooth (Mandelbrot), it only works with most divergent fractal formulas, such as Mandelbrot and Julia.

There are two parameters available: Exponent and Bailout. These should be set to match the corresponding parameters of the fractal formula. Otherwise, the coloring will not be smooth.

Use very large bail-out values for good results. The default value 1e20 (a 1 with 20 zeroes) is a good starting point. The Mandelbrot (Built-in) formula cannot handle such large values, so use the non-built-in Mandelbrot instead.

Triangle Inequality Average is available as a coloring algorithm in Standard.ucl and as a coloring plug-in in Standard.ulb.

See Also
Orbit Traps
Standard coloring algorithms