About Colour Schemes

Colour schemes in Mandelbrot Explorer are defined by defining a series of layers.

First, read one of the introductions to the Mandelbrot Set to learn about what the Dwell of a point is. All that matters for now is that every point outside the Mandelbrot Set is given a numeric Dwell value; the closer it is to the Mandelbrot Set itself, the higher the value will be. Every point inside the Mandelbrot Set is given a Dwell of Infinity.

We colour the Mandelbrot Set by creating a colour scheme. Colour schemes tell Mandelbrot Explorer how to work out the colour for a pixel given its Dwell value. Traditionally, points inside the Mandelbrot Set (with infinite Dwell) are coloured black, but this can be changed.


So what do layers do? Each layer defines a rule to turn Dwell values into colours. It also defines the range of Dwell values over which that layer operates. For example:

  • Rule: Colour a pixel bright red, whatever its Dwell value
  • Dwell Range: This layer applies to Dwell values between 100 and 200 only.

When Mandelbrot Explorer colours a fractal drawing, it takes each point in turn. The sequence is:

  1. Look up the Dwell value for the point. Start at the first layer.
  2. Does this layer apply to this Dwell value?
  3. If Yes: Apply the Rule for this layer; that gives the Colour for the point, and there is nothing else to do.
  4. If No: Look at the next Layer. Go to step 2 and keep going until you run out of layers.
  5. If you have been through every Layer, and none of them apply to your Dwell value, colour the point White if it is outside the Mandelbrot Set, and Black if it is inside.

Setting the Dwell Range

The first thing to be done, in defining a Layer, is to define the Dwell range over which it operates. You need to specify the minimum and maximum value.

  • These could both be finite numbers, in which case the Layer applies to those points outside the Mandelbrot Set having a Dwell between the minimum and maximum.
  • There are also two special values you can use for the minimum or the maximum. One is defined as "Edge of Fractal" and one as "Inside Fractal". These work as follows:
    • If the maximum Dwell for a Layer is "Edge of Fractal", the Layer applies to points right up to the edge of the fractal. No matter how high the Dwell value is, as long as it is above the minimum value, the point is covered by the Layer.
    • If the maximum Dwell for a Layer is "Inside Fractal", the Layer applies to points inside the fractal as well.
    • If the minimum Dwell for a Layer is "Edge of Fractal", the maximum would have to be "Inside Fractal", as anything else would be lower than the minimum. This Layer will then apply to points that are at least as big as the minimum Dwell, that is to say, at least as big as the very edge of the Fractal. It follows that no points outside the Mandelbrot Set would be included. But the Layer applies right up to the inside of the fractal, so every point in the Set is included. Conclusion:The Layer colours points inside the Mandelbrot Set, and only those points. This is how you can change the traditional "Black for inside" colouring.
    • The only option we have not considered is when the Minimum is set to "Inside Fractal". This Layer would match nothing, so don't use it!

Setting the Colour Rule

Having set the range of Dwell values that a Layer effects, the second step is to set the precise rule that turns a Dwell value into a Colour. How this is done depends on the type of Layer. There is a separate help page for each kind of layer, so read the help page that concerns you: