Fractal street lengths as a starting point for an urban district infill | Nels Nelson
Left to right: Veins of a leaf displaying scale hierarchies; Map of Paris displaying street scaling; H-fractal with ten scale levels.
I’ve been highly motivated by a presentation I saw by Serge Salat (Urban Morphology Lab) regarding the #resilience of urban fabric as tested by two parameters, the relative frequency of street hierarchies (length of big roads, medium roads, small roads, alleys) and the frequency of connections in streets. It has been shown that the most successful urban fabrics follow a logarithmic progression of distribution of street hierarchies equivalent to the distribution of vein sizes found in conifer leaves. Mathematically, this distribution found in nature is modeled by fractal scale hierarchies.The so-called H-fractal is one graphic representation of fractal dimension 2, the same dimension as the famous Mandelbrot tree, a space-filling fractal. In each iteration, the quantity of lines is squared, and the length of each line has the ratio of 1:√2 to the previous scale (also known as the golden ratio).
For each of the first 10 scale hierarchies in the H-fractal; the scale’s size, total length, quantity, and percentage of length over total length.While this analysis has been applied to the evaluation of urban morphology, I have been curious about how it would be applied in the (re)development of an urban area, for example the planning of an urban district. How could one make use of these principles as the starting point for a design?One starting point is the distribution of road scales in an urban area – calculation of the “best” distribution of streets – % of hierarchy 1 streets, % of hierarchy 2 streets, &c. – which would then be used as a parameter in the organization of the district in relation to the surrounding environment.To illustrate the concept, I have chosen my favorite urban tabula rasa infill, Rotterdam’s Stadshaven, with a total area of 140 hectares of post-industrial warehouse space that will be wiped clean (for the most part) and redeveloped into urban center in the coming decade. An assumption must be made about the total length of streets that will be in the final urban area in order to deduce the relational length per scale hierarchy. According to Urban Transport and Land Use Patterns Challenges and Opportunities of High Density Cities (Paul A. Barter and Jeffrey R. Kenworthy, 1997), the average street length per hectare in urban Europe is 115 meters. Thus, for a 140 hectare redevelopment, we can expect 16,100 meters of roadway (16.1 km). A quick scan of the area in Rotterdam shows that there are five road scales, ranging from 40 meter-wide split lane to 4 meter-wide pedestrian-only path.
Map of Rotterdam Stadshaven area
By performing another calculation of the H-fractal with 5 hierarchies, one for each of the road scales, a relationship between the lengths of road scales is created. I have also erased the area to be developed. The resulting road lengths can then be distributed over the site in relation to the existing environment in such a way as to also achieve a high connectivity rank, as exhibited by the leaf and the map of Paris. What is striking is the difference between the existing urban fabric around the site to be redeveloped and the Stadshaven, where the existing area is overly dependent upon scale 3 roads and an under-representation of scale 4 and 5 roads. Thus, in the development of the Stadshaven, the planners could work to achieve a more ideal mix of road scales in order to optimize the diversity of street types and uses.
Map of Rotterdam Stadshaven with the area for redevelopment cleared and optimal road length per scale represented.
Source: Fractal street lengths as a starting point for an urban district infill | Nels Nelson