There are several coloring algorithms in the public formulas titled a variation of “Basic”. They color based on either the number of iterations or some simple calculation of the final z value. This list isn’t comprehensive; some of the “Basic” colorings are quite sophisticated and not included in this basic list. (Just one example, jam-Basic in jam2.ucl colors by iteration controlled by several parameters, and also includes smoothing, fBm, and masking. Only the simpler ones are described here.)

One of the big issues for using the final z value is how to handle negative values, since they will always use the leftmost gradient color. These colorings approach this in various ways.

In general, coloring by iterations only works for outside colorings (the number of iterations for inside points is always the same, the value of Maximum Iterations). Depending on the formula, large bailout settings often give smoother results.

In contrast, coloring using the final z value works for both inside and outside colorings and smaller bailout settings generally give better results.

Coloring using the polar angle of the final z value is also called “decomposition”, and there are a number of colorings (not included here) that specialize in that. The angle is normalized to a value between 0 and 1 for coloring (for example, 90° would be 0.25 and -30° would be 0.91667).

Coloring | Iterations | Final z | Negative Value Adjustment | Other |
---|---|---|---|---|

Basic (Standard.ucl) |
Divide by 100 | Real, Imaginary, or Sum; 4 is added and the result divided by 20 | Adding 4 fixes negative values if the bailout isn’t too large | None |

Basic (lkm.ucl) |
Divide by 100 | Real, Imaginary, Magnitude, or Polar Angle | None | None |

Basic Plus (lkm.ucl) |
Divide by 100 | Real, Imaginary, Magnitude, or Polar Angle | None | Besides z, it can also use the pixel, z-pixel, or z/pixel |

Basic 3 (lkm3.ucl) |
Divide by 100 | Real, Imaginary, Magnitude, or Polar Angle, or f(these) where f is a selectable function (like sin or abs) | Nothing built-in, but it can be done by adding a constant or using a function like abs | Besides z, it can also use the pixel, z+pixel, z-pixel, z*pixel, z/pixel, z+constant, z-constant, z*constant, or z/constant |

Basic-Z (aho.ucl) |
None | Real, Imaginary, Sum, Magnitude (called Abs), or Angle | If the value would be negative, it is shifted to be between 0 and 1 | None |

Inside (sp.ucl) |
None | Weighted sum of Real, Imaginary, and Magnitude (called cabs) | None | Inside only |

Using “z-pixel” (if supported) is especially useful for formulas like gnarls where the orbit points stay relatively close to the initial point. It can help reduce the stripes often visible when using just the final z value.