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The United Nations projects a global population of over 12 billion by 2100, and the year 2015 marks an astounding transition in the age demographic of the population. Where will people live, and how will urban cities grow? According to the Sante Fe Institute, future cities should grow just like other distributed natural systems like the branches of rivers and the vasculature of leaves or humans. They should branch like fractals into smaller and smaller roads to connect greater populations over larger and larger areas.

Leanardo daVinci proposed many fractal designs in building and city architecture. He had a fascination with consistency in geometry across scales in nature. Image: Phys.org

The Sante Fe Institute published a study in 2013 titled City Population Dynamics and Fractal Networks.  The paper evaluates urban road networks in terms of fractal geometry to better understand transportation efficiency for the scale up of cities as populations continue to grow. Instead of focusing on road length and other statistics, the branching hierarchies and fractal dimensions of transportation infrastructure were evaluated. Key Information:

  • In 2011, the United Nations reported that 3.6 billion people are living in urban areas
  • This is expected to grow to 6.3 billion people by 2050
  • 51% of the world population is living in urban areas
  • This comprises only 3% of the world’s surface
  • Urban areas aggregate human biomass at density ~ 2X > than any other living organisms
  • The growth of 200 urban agglomerations from 1950 to 2010 was examined
  • The population growth rate has been slowly decreasing from the 1950s to the present
  • Urban population data was utilized from GeoHive Global Statistics


  • In the past 60 years, population growth rate has declined significantly in largest 200 cities
  • People are living over a larger and less centralized area
  • Are road networks constraining population growth and facilitating urban sprawl?
  • Transport networks can be characterized by a recurrent, scale invariant geometry
  • Cities on more developed continents tend to exhibit higher road network fractal dimension
  • Fractal transportation networks might improve the transition to higher densities over larger areas

Featured Image: PaulBourke.net