### Transformations

Transformation formulas “transform” the complex plane used for calculating the fractal. So they can be used to apply any kind of mapping: For example they can map the fractal onto a sphere. Any kind of distortion can be performed using transformations.

 Original fractal Spherical mapping Lens mapping

As you can see, transformations do not introduce new “shapes” into or add more details to the fractal: They only can distort the fractal or parts of the fractal in an arbitrary manner.

In order to fully understand the use of transformation formulas you need to know some basics of fractal iteration:

A fractal gets drawn into a window, which is a rectangular area. Each “screen-”pixel in that window corresponds to a specific complex number, so that the window basically is a small rectangular area cut out from the complex number plane. In order to calculate the fractal the complex number corresponding to a pixel gets passed to the calculation routine, which finally returns a color for that pixel.

 This screen pixel corresponds to a specific complex number. The transformation then takes this complex number and modifies it. The modified complex number then gets fed into the fractal calculation routine.

Managing transformations is done in the mapping tab of the parameter window of Escapetime or Quaternion fractals. This tab looks as follows:

 The icons on the left side let you manage the list of transformations. You can add several transformations to the list: They are applied subsequently, and so they allow you to apply several distortions to a fractal at the same time. By clicking onto this button a modal window will open: It allows you to browse through the list of transformations. Select your desired transformation by double clicking onto the formula. The transformation will be added to the list and inserted after the currently selected transformation. This button removes the currently selected transformation from the list of transformations. By pressing this button the currently selected transformation is moved up. By pressing this button the currently selected transformation is moved down. If you look at the list of transformations you can see the icon to the left side of the transformation label. By clicking onto this icon you can enable or disable the transformation.

Sometimes transformations try to distort the input area but cannot determine a reasonable complex value, for example if they perform a spherical mapping. For these and other special cases the transformation can set the pixel to a solid color and a fixed opacity value. You can adjust these parameters by selecting the solid color and adjusting the opacity value of the solid color right beneath.

If you select a transformation you can see that the lower part of the window will change: It contains the parameters of the transformation as defined by the author of that formula. To read more about formula parameters and the user interface provided to them read User Interface.