The Fibered Fractal Tiler allows you to define the first stage of a discrete self-similar fractal and then to simulate its 'growth', stage by stage.
Initially (or any time immediately after the 'Reset' button is pushed), the simulation is in stage 1. (For more about fractal 'stages', see the definitions here.) When the 'Forward' button is pushed, all points currently selected in the grid are multiplied and translated according to the definition of discrete self-similar fractals. As long as no new points are manually selected during stages > 1, the shape formed will be exactly that of the ith stage of the discrete self-similar fractal whose first stage was defined in stage 1. [This growth can be forced to deviate at any point beyond stage 1 by selecting or deselecting points in the grid.] The dimensions of the grid will be automatically resized if necessary to accomodate the growth of a particular stage.
The simulation can be reset to stage 1 at any point, and in fact must be reset to stage 1 if you wish to generate a fibered tileset for the defined 'nice' fractal.
Note that the growth of any discrete self-similar fractal can be simulated, while only the subset defined as 'nice' can be used to generate fibered tilesets.