With the use of graphs and fractals, scientists from the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN) in Cracow looked at the structure of the massifs of our planet. The diverse ranges such as the Alps, the Pyrenees, the Scandinavian Mountains, the Baeric Mountains, the Himalayas, the Andes, the Appalachians, the Atlas Mountains and the Southern Alps, all went under the statistical magnifying glass.
The analysis of the researchers, presented in the Journal of Complex Networks, resulted in an unexpected observation. It turns out that there is a universal similarity in the structure of the Earth's massifs. It can be seen in mountain ranges on all continents, regardless of the side of the peaks, their age, or even whether they are of tectonic or volcanic origin.
Dr. Jaroslaw Kwapien (IFJ PAN), said that it would seem that the only thing that the various mountain ranges have in common is that when you look at them, you have to bend your head back. The real similarity only becomes visible when they transform a simple topographic map of the mountains into a ridge map, i.e., one that shows the axes of all the ridges. Dr. Kwapien explained further that the axis of the ridge is a line running along the top of the mountain ridge in such a way that on both its sides the terrain falls downwards. It is thus the opposite of the axis of a valley.
Not only are mountain ridges discrete creations, they merge into a large, branched structure, resembling a tree: from the main ridge ("the trunk") there are longer or shorter side ridges of the first order ("branches"), from them arise side ridges of the second order, and from these subsequent ones again and again.
The whole has a clear hierarchical structure and the number of degrees of complexity depends on the size of the area covered with mountains and can reach even several dozen. Structures of this type are presented in the form of various graphs. The instance is each ridge of a given massif can be treated as a node. Two nodes are connected by lines (edges of the graph) when the corresponding ridges are also connected. In this sort of graph, some nodes are connected to many nodes, whereas others are connected to only a few.
Where are the sources of mountain diversity if different mountain ranges are so similar in terms of size? Will it be possible to study them using graph theory and fractal geometry? Will it be possible to create a model in which an evolving graph will imitate the successive stages of the formation of a mountain sculpture? Finally, will it be possible to apply the transformation of ridge maps into graphs in practice, for example, in cartography? Future research will need to have answers to these and many more questions.
