Fractals are patterns that repeat themselves at every scale. Fractals are mathematical structures, but can also be found in nature. There are many nice websites about fractals (for instance fractalfoundation, where you can find beautiful pictures as well as software to explore fractals yourself).
For my breast cancer research I used fractals to detect tumours in mammograms.
For the birth of the twins a had the following birth card with the so-called twin dragon fractal .