This post is the very beginning of my paper
Nagasaki along the years: An urban fractal analysis
Journal of Mathematical Modelling and Application
2011, Vol 1, No 5
You can read it also in the blog where I’m compiling my publications
(still working on this blog)
Catastrophe theory, was originated with the work of the French mathematician René Thom in the 1960s, as a branch of bifurcation theory in the study of dynamical systems. Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analysing how the qualitative nature of equation solutions depends on the parameters that appear in the equation. (Wikipedia.org). Resuming, it means the loss of a stability in a dynamic system. As I’ve stated before, cities are dynamic systems and the loss of stability is reflected in the geometry of their urban patterns.
I have made these simulations in order to prove that it is possible to regenerate the old urban fabric from total destruction. The pattern will not be exactly as the original one, and of course this is not the intention. My objective is to find a pattern that shows the same basic fractal (?)pattern before the destruction, to maintain the inhabitants’ cultural manifestations. My goal is to find a methodology of reconstruction that could be applied after different catastrophes as volcanoes eruptions, landslides, floods, earthquakes, wars. Maybe it is implicit that I do not support the reconstruction by catalogue, as done with Berlin. Though, it was an ideal solution for long years ago. Now, the technology allows us new ways of understanding the city as an organism, and as such entity, it can reconstruct itself.
This is a binary file of Nagasaki, before the atomic bomb destruction. There is no urban quadrille, its urban morphology looks like a fractal pattern. The background jpg image had to be converted into a binary file to work with different tools.
This is a binary file of what was left after the bomb. Notice that no urban pattern is seen. Just a few ruins surrounded by emptiness. These ruins will be the seed for urban regeneration.
My first simulation indicates a new urban growth beginning in the areas of more -former- densification. The pattern is dispersed as the original one. The white empty areas will be growing more slowly.
I have generated this one from a process of erotion-dilation, alternating the tools. I did not want more agglomerations, the original urban fabric was not so compact, but, it was many years ago, and now I need to consider a certain urban sprawl to be closer to reality.
I have more density now, and the process continues. I’ve emptied some small areas to include new plazas-open spaces. It is important to clarify that no center was considered, it is only a natural regeneration of the old urban fabric. The impact of a a new commercial center, for example, would change this morphogenesis. Please disregard the circle, it is part of the aerial picture I’ve been working with and does not belong to the simulation.