Colouring schemes

General colouring

Colour schemes can be selected and customised via the Colour map menu. Colouring is applied to both interior and exterior points. The former lie inside the fractal, i.e., they are attracted to a cycle or a single fixed point, whereas the latter typically escape to infinity. For both types of points there are various options for colouring, depending on the escape times, the distances, the angles, and so forth, as well as various predefined colouring methods. Note that it is possible to define tiger stripes for exterior points. Depending on whether or not a point's escape time is even or odd, the colour map switches between the main one and the tiger striping one.

Colour maps can be inverted (e.g., going from white to black instead of black to white) or wrapped around (e.g., going from black over gray to white, returning over gray to black).

There is a range of default colour maps available, and it is possible to modify these or create a custom colour map.

Traditionally, colours are linearly interpolated across the specified colour map, based on the minimum and maximum value occurring within the calculated fractal. This can lead to an inbalance typically seen when there are vast regions of constant values with rapidly increasing values near the border between interior and exterior points. In order to compensate for this effect, you can scale the colour map. Possible methods are logarithmic, exponential, and square root scaling. Each time, you can specify the parameters for these scaling properties. A more powerful method that superseeds modern histogram colouring is based on rank order scaling, in which the probabilities of using the colours are all equal. Because this technique can smear out the more extreme high values, you can select the Restrict high iteration count colours option. This will effectively apply a logarithmic scaling after the rank order scaling.

Note that when the Cycle colours menu option is selected, Fraxion will cycle through all the colours in the chosen colour map in real-time. This is a rather time consuming process, as the 24-bit colours are calculated instead of just being taken from a lookup table.

Choosing from available colour maps

A selection of predefined colour maps is available, as shown in the following submenu (all colours are linearly interpolated).

Creating custom colour maps

Aside from using one of the predefined colour maps, you can also create your own custom colour map. To that end, select the Set custom colour map components option from the Specify interior/exterior colour map submenu. This will give the following dialog, allowing you to modify 10 control points (locations and colours). By selecting the Convert current colour map to custom option from the submenu, you can modify one of the predefined colour maps.

Options for colouring

There is a wide variety of colouring methods available, with the simplest one based on discrete level sets (i.e., the escape times), resulting in typical visible banding. In case of Newton / Raphson fractals, the colour options will also enable colouring of roots (if they are tracked), both discrete and smooth.

Predefined colouring methods

For quick reference, Fraxion also allows you to select a predefined colouring method, as shown in the following examples. You can always go back to the default by selecting the Reset to default colour map settings option from the menu. In that case, the colour map reverts to the Jet colour map, and using normalised level sets, no tiger striping, linear scaling, no inversion, wrapping, repetition, offset, or limited range.

Binary decomposition
Contours
Dark softening filter
Binary decomposition followed by contours

Enabling post-processing filters

Once an colouring scheme is selected, you can apply a chain of post- processing filters to the final image. There are five filters available, i.e., blurring, sharpening, edge/contour detection, colour inversion, and colour posterising. For blurring and edge/contour detection you can specify the kernel size and strength, respectively. If the Auto proof checkbox is ticked (by default), then the filter chain is automatically previewed on the visible fractal.


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