Bacterial Colonies

Look at the picture of a bacterial colony. It shows a branching structure, which has the property that if one zooms into any region, that part looks similar to the whole. The bacterial colony is an example of a random fractal. Exact fractals appear the same at different magnification scales while random fractals appear only statistically similar at different magnification scales. Fractals are ubiquitous in Nature. Another example is the branching network of air-passages in the human lung. The advantages of such a structure are an increase in surface to volume ratio which maximises functional efficiency while minimising material and space costs. The word "fractal" itself means more than just self-similarity at different scales. It also implies a fractal dimension which we will discuss later.