The importance of cities´edges (rugosity)

Picture credit: Silvia Calvino

Mrs Silvia Calvino is a great photographer, and she was really kind to give me permission to work on this beautiful picture of hers; please do not reproduce any image here without the written permission from the authors. 

You could think, what for? Looking for Arts?. No, just to reflect on fractal urban morphology and the importance of edges.

A fractal can be conformed by a line, covering a surface. The fractal dimension will be a number between 1 and 2. Two is the result for a full covered surface.

Supposing the flower is an urban center, some points in a selected leaf will be closer, just because of the irregularity of such edge. This is what we call rugosity. 

To understand how important it is, I made an exercise. I calculated the fractal dimension of the figure shown, with two options: leaving edges in white (the area consider is what is left) and leaving the background white (the area considered is the rugosity).

First step, I make the picture approximately square and remove Silvia´s name as it doesn´t belong to the shape. Then, I sharpen the edges.

This is the first binary image I need to calculate the fractal dimension with Box counting method. Result: D=1.9598. The plant is so dense that is almost full covering the picture. For us, it is similar to urban sprawl growing free, with no regulations (except fractal patterns).

This is the second binary image I need to compare with the first one. In this case, with Box counting method, the fractal dimension D=1.7315

The edges are almost covering the area, this D value is really high!. Just a thought for fractal urban morphology........
Below, a video showing an exercise of Fractal Dimension on urban forms. Though the video is in Spanish, you´ll easily understand the methodology.