# Urban Design Excellence

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<summary>Definition</summary>

Urban Design Excellence (also called Fractality) measures how well a city’s morphological layout is organized into a balanced, self-similar structure. High scores indicate neighborhoods, buildings, parks, transit hubs, and other features arranged in a tiered, interconnected pattern. Cities with high scores tend to have better accessibility, infrastructure efficiency, and economic performance, creating more livable and sustainable environments.

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<summary>Navigation</summary>

The Urban Design Excellence KPI is visualized as a color-coded heatmap, where users can filter between neighborhood and block levels.

* Red indicates low scores (fragmented or inefficient structure).
* Blue indicates high scores (strong fractality and spatial order).
* Clicking on a specific neighborhood or block displays its Urban Design Excellence Score, ranging from 0 to 1.
* Sidebar visualizations offer comparative insights, showing how the selected location ranks relative to others in the cit

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<summary>Methodology</summary>

This KPI is based on fractal geometry and urban network science, using box-counting techniques to quantify how urban form exhibits self-similarity at different scales.

1. Grid Decomposition – The city is divided into progressively smaller grid sections.
2. Feature Detection – Identifies buildings, streets, green spaces, and other urban elements.
3. Scaling Analysis – Measures how these features repeat at different levels of the grid.
4. Fractal Dimension Calculation – Computes the extent of self-similarity in the urban layout.
5. Comparative Analysis – Scores locations based on their fractal structure relative to citywide trends.

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<summary>Calculation</summary>

Urban Design Excellence or City Form Fractality is defined as:

$$D\_f = \lim\_{\epsilon \to 0} \frac{\log N(\epsilon)}{\log \left( \frac{1}{\epsilon} \right)}$$$$D\_f=\lim\_{\epsilon \to 0}\frac{logN{\epsilon}/log(1/\epsilon)}}$$

Where:

* $$D\_f$$ = Morphological (fractal) dimension
* $$N(\epsilon)$$ = Number of boxes needed to cover the urban form
* $$\epsilon$$ = side length of the box

The generalized fractal dimension (Urban Design Excellence Index) of a given urban form is defined as:

$$D\_q = -\frac{M\_q(\epsilon)}{\ln(\epsilon)} = -\lim\_{\epsilon \to 0} \frac{1}{q - 1} \cdot \frac{\ln \sum\_{i}^{N(\epsilon)} P\_i(\epsilon)^q}{\log\left(\frac{1}{\epsilon}\right)} = \lim\_{\epsilon \to 0} \frac{\ln \left( \sum\_{i}^{N(\epsilon)} P\_i(\epsilon)^q \right)^{1 - q}}{\log\left(\frac{1}{\epsilon}\right)} = \frac{\ln C\_q(\epsilon)}{\ln\left(\frac{1}{\epsilon}\right)}$$$$\[ D\_q = -\frac{M\_q(\epsilon)}{\ln(\epsilon)}  = -\lim\_{\epsilon \to 0} \frac{1}{q - 1} \cdot \frac{\ln \sum\limits\_{i}^{N(\epsilon)} P\_i(\epsilon)^q}{\log(1/\epsilon)}  = \lim\_{\epsilon \to 0} \frac{\ln \left( \sum\limits\_{i}^{N(\epsilon)} P\_i(\epsilon)^q \right)^{1 - q}}{\log(1/\epsilon)}  = \frac{\ln C\_q(\epsilon)}{\ln(1/\epsilon)} ]$$

Where:

* $$M\_q(\epsilon)$$ = Renyi’s urban form entropy
* $$q$$ = order of moment (e.g., −2, −1, 0, 1, 2, …)
* $$N$$ = number of nonempty boxes
* $$P\_i$$ = probability associated with box i, where $$\sum{P\_i}=1$$
* $$C\_q$$ = generalized correlation function
* $$ln$$ = natural logarithm

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<summary>Interpretation</summary>

* High Scores (Close to 1): Well-balanced, structured urban form with strong connectivity and accessibility.
* Moderate Scores (0.5 - 0.8): Some level of fractality, but potential inefficiencies in land use or accessibility.
* Low Scores (Below 0.5): Fragmented, disorganized urban structure that may lead to inefficiencies in mobility and infrastructure.

Cities with a high Urban Design Excellence score tend to have:

* More efficient movement networks (better pedestrian and transit systems).
* Stronger spatial balance (harmonized distribution of streets, parks, and buildings).
* Higher economic resilience (optimized urban layouts encourage commercial activity)

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