Switch feature

The switch feature allows you to switch easily between related fractal types. One fractal type can be used as a map for another. This is very useful, since Mandelbrot sets, for example, are in fact maps of the corresponding Julia sets.

To use the switch feature with your own formulas, you must include the switch section as the last section in your fractal formula. Here is an example of a typical Mandelbrot formula using the switch section:

Mandelbrot {
init:
  z = 0
loop:
  z = sqr(z) + #pixel
bailout:
  |z| < @bailout
switch:
  type = "Julia"
  seed = #pixel
  bailout = bailout
}

The type setting specifies the identifier of the formula (in the same file) to switch to. The other settings can copy parameters and the pixel value from the source formula to the destination formula (the formula Ultra Fractal is switching to). The #pixel symbol returns the coordinates of the point in the fractal window where the user clicked to initiate the switch.

When switching, Ultra Fractal now loads the Julia formula, and tries to find the parameters seed and bailout in the Julia formula. If these parameters can be found, they are set to the pixel value and the bailout of the Mandelbrot formula. Otherwise, the settings are ignored.

So, you need to take the following steps to use the switch feature:

Append the switch section to the end of your formula.
Insert the type setting and use the entry identifier of the formula you want to switch to as the setting value, enclosed in double quotes (like all string values).
Insert the setting "destination-parameter = #pixel" to let the switch feature be dependent on the point where the user clicked inside the fractal window. If you want, you can use this setting more than once, or just leave it out. The parameter in the destination formula must be complex, otherwise this setting is ignored.
Optionally, insert additional settings "destination-parameter = source-parameter" to copy other parameters from the source formula to the destination formula. Be sure that the types of the source and destination parameters are the same; otherwise, the setting is ignored. Parameters not explicitly copied here are set to the default values.

Here is an example of a Julia formula that could be used with the Mandelbrot formula shown above. Note that the Julia formula allows you to switch back to the Mandelbrot formula (of course without using the pixel value).

Julia {
init:
  z = #pixel
loop:
  z = sqr(z) + @seed
bailout:
  |z| < @bailout
switch:
  type = "Mandelbrot"
  bailout = bailout
}

Next: Perturbation equations