Pianificare la città frattale Defence plea for using fractal geometry in town planning Dr Cécile Tannier (University of Franche-Comté, National Centre for Scientific Research) Gilles Vuidel (University of Paris VI) FRACTALS AND THE CITY (La città frattale) Martedì 10 dicembre 2002, Facoltà di Ingegneria, Lecco (Italia)

Urban development policy Guiding principles Urban development policy Planning rules Laws, plans

Requirement of a best understanding of the urban development process Relations between spatial behaviour of people and location of activities (residential, industrial, retailing…) Relations between town planning policy and the urban patterns resulting Respective rules of individual behaviours and town planning policy in the urban development

Framework: using fractal geometry in order to best understand the urban development process implies Concentrate on morphological aspects of the process Deal with geometrical problems

Deal with geometrical problems Two possibilities: Euclidean geometry Fractal geometry

Morphological aspects of the urban development process Which forms (circle, square, Sierpinski carpet…) to answer which planning arrangements? Which processes generate which forms?

Morphological aspects of the urban development process Three action possibilities: Describe the morphological characteristics of urban patterns Traduce planning rules in a geometrical way Simulate urban growth

1. Describe the morphological characteristics of urban patterns Two main measures: Density measures Fractal measures

1. Describe the morphological characteristics of urban patterns Density measures A ratio: quantity per surface unit A threshold … Which refers to the ecologic capacity of socio-economic systems A geometrical reference: homogeneous spatial distribution of elements An intrinsically static indicator Fractal measures Complementary properties

2. Traduce planning rules in a geometrical way Urban development plans, land-use plans Geometrical reference Euclidean geometry Fractal geometry

Principles to generate fractal forms 3. Simulate urban growth Fractal geometry Control parameters Principles to generate fractal forms

Possible contributions of fractals in the field of town planning Why use fractal measures? Or... …Because land use patterns don’t fit with the laws of Euclidean geometry non homogeneity characteristics of the relation between perimeter and surface urban patterns are fragmented, shredded internal organisation principle of the urban patterns is often hierarchical

Possible contributions of fractals in the field of town planning Or... Why use fractal measures? …Because land use patterns don’t fit with the laws of Euclidean geometry …Because the properties of fractal objects are the same as the properties of urban patterns Spatial distribution of elements follows a hierarchical law Same distribution principle of elements at a multitude of scales Existence of clusters at each scale The homogeneity exists as limit case of the fractal geometry

Morphological aspects of the urban development process Which properties of the urban patterns could be revealed by which measures of fractal dimensions? What traduce these properties in terms of individual behaviours?

Different methods for measuring the fractality of cities The main goals of fractal measures: Verification of the existence of a hierarchy Identification of spatial thresholds Determination of the degree of heterogeneousness

Different methods for measuring the fractality of cities A software: Fractalyse

Principles to calculate fractal dimension Input data: a black and white image of a city

Besançon

Principles to calculate fractal dimension Counting the number of black pixels at each iteration step As result, two elements varying according to the iteration step: - the number of counted elements - the size of the counting window

Principles to calculate fractal dimension Make fit the obtained curve (i.e. the empirical curve) with an estimated curve A constraint: the estimated curve must correspond to a fractal law (y = xD).

Principles to calculate fractal dimension The fractal dimension corresponds to the exponent D of the fractal law. y = xD Fractal dimension

Different method for measuring fractal dimensions Fractal dimension of surfaces correlation analysis dilation analysis Fractal dimension of borders gaussian convolution

Correlation analysis

Dilation analysis