The Pressure of the Linear Path
Fractals in sales route planning
Every day we experiment the reality of the world, a network of networks, a system of systems: transportation, energy, water, waste, logistics, telecommunications, economy, services, government, institutions, businesses, and social communities. There is a chaotic equation to describe any apparent randomness in real world. Fractals are just something more to add to our descriptive shapes. Networks can be seen or studied as fractals. Sales route planning, power networks, social networks, communication networks, traffic networks, river networks, tourism route planning, etc. can be modeled as fractals.
While Euclidean geometry is a description of lines, planes, circles, triangles, and so on, fractal geometry is described by algorithms, by a set of rules. Fractals are a language, a way to describe the chaotic systems that we find in nature.
Fractals in sales route planning
The physical sales process (I am not considering e-commerce) can generate complex behaviors such as chaos. In sales systems theory through the behavioral models of choice can be generated complex behaviors such chaos. In the case of sales route planning, the spatial analysis shows that sometimes they bear a fractal structure.
Shop owners would like customers to visit every corner of their shop, to maximize the chance that they will pick up something they had not planned on buying. If the path through the shop has open spaces, or branches, people can take shortcuts and avoid seeing things they do not specifically want to look at. But in most of the cases, you must have a big spatial vision to escape from the labyrinth!
Fractal dimensions can be non-integer, for instance, the Sierpinski Triangle has fractal dimension of ~1.58496, meaning that is more than a line and less than a plane. Is amazing!
For example, when I go to Ikea and I look at the shop’s map, a Peano curve comes to my mind. In 1890 Giuseppe Peano introduced a type of curve able to fill an enclosed area, known as space-filling curves and oddly enough to have an integer fractal dimension of 2. A space-filling curve is, as its name suggests, a single path which goes through every point in the space. Therefore, the ideal is to force customers to follow a space-filling curve to the checkouts, because it ensures they pass everything in the shop.
Space-filing curves, such as the Peano curves, are geometrically interesting curves and have important applications, particularly in parallel computing.
