The Box Counting method calculates the Fractal Dimension of an image. It is a way to quantify the complexity and self-similarity of irregular shapes. The algorithm reads a 1024x1024 PNG image and returns its Fractal Dimension.
The algorithm was tested on fractal images of known dimension. The results are displayed in the table below.
| Fractal Name | Theoretical Fractal Dimension |
Calculated Fractal Dimension |
|---|---|---|
| Sierpinski Triangle | 1.585 | 1.582 |
| Koch Curve | 1.262 | 1.263 |
| Koch Snowflake | 1.262 | 1.572 |
| Gosper Island | 1.129 | 1.275 |
| Douady Rabbit | 1.393 | 1.477 |
| Vicsek fractal | 1.465 | 1.466 |
| Sierpinski hexagon | 1.631 | 1.708 |
| Apollonian gasket | 1.306 | 1.248 |