A living structure is a mathematical concept and a physical phenomenon meaning that there are far more small things than large ones across all scales. For example, a tree consists of one big stock with many branches of various sizes. There are far more small branches than large ones. 

Living structures include main structures and substructures, where the small structures are far more than the large ones. This principle is called the scaling law. Within each hierarchy of the living structure, the structures tend to be more or less similar to each other depending on how close they are related and located. This principle is called Tobler's law. Scaling law is a universal law, which applies to all scales. Tobler's law is limited to each hierachy within the structure (Jiang & Slocum 2020).

Even though the concept of fractal geometry has been known for a long time, it has not gained much attention within the field of cartography, until recently. When moving away from euclidean geometry and Guassian statistics, towards fractal, living geometry and Pareto statistics, a new paradigm in mapping takes shape. With this organismic way of thinking we can create maps that are not only more living, but also more structurally beautiful and cognitively appealing (Jiang & Slocum 2020).

A fractal can be described as a pattern in which there are far more small things than big ones. Fractal geometry is a statistical approach to a natural structure, e.g. a coastline.

A top-down approach in the subject is the Koch curve, invented by the swedish mathematician Helge von Koch in 1904. In short, the recursive Koch curve demonstrates how a line can be divided into fractals an infinite number of times through iterations. Fractal geometry was developed further by Benoit B. Mandelbrot, who coined the term "fractal" and introduced statistical fractals in the 1980's. This approach is also top-down, although it offers a more relaxed view of the fractals (Jiang 2019).

A third definition of fractal geometry has been formulated as a set or pattern is fractal if the scaling of “far more small things than large ones” recurs multiple times. In the third definition of fractals, it's pointed out that not only natural features are fractal, but also humanmade features - given the right scale (Jiang 2019).