Release 4.0

Escapetime - Transformation Formulas

A transformation formula transforms the simple rectangular shape (the default shape coming from the direct mapping of the window to a part of the complex number plane) into another shape. This formula is rather simple to write and understand, because all it does - or better - has to do, is to modify the value of the predefined variable pixel.

A transformation formula can have upto three member function:

1. void init_once(void): Called only once, i.e. when the fractal calculation starts: In this routine you can initialize variables and allocate arrays.
2. void transform(void): This is the main member function: Its purpose is to modify the value of pixel.
3. void description(void): This member function lets you define labels for your parameters, enumeration lists, default values and hints. Each formula can have a description function.

So a transformation mainly consists of a member function void transform(void) which gets called for each pixel before the main fractal loop gets called.

Thus a transformation could look as follows:

rotOrder
{
real dAngle;
real dist;

   void init_once(void)
   {
   	  // nothing to do...
   }
   void transform(void)
   {
      dAngle= arg(pixel);
      if  (dAngle< 0) {
         dAngle=dAngle+2*pi;
      }
      dist= |pixel|;
      dAngle= dAngle-floor(dAngle*4/pi)*pi/4;
      if  (dAngle> pi/8) {
         dAngle=pi/4-dAngle;
      }
      pixel= (cos(dAngle)*dist+(0,1)*(sin(dAngle)*dist));
   }
   void description(void)
   {
      this.title = "Rotation Symmetry";
   }
}

Standard fractal

With transformation from above.

So all you need to do is to modify the predefined variable pixel!