Urban Form Figure-Ground Diagrams

I previously demonstrated how to create figure-ground square-mile visualizations of urban street networks with OSMnx to consistently compare city patterns, design paradigms, and connectivity. OSMnx downloads, analyzes, and visualizes street networks from OpenStreetMap but it can also get building footprints. If we mash-up these building footprints with the street networks, we get a fascinating comparative window into urban form:

Figure-ground map of building footprints and street network in New York, San Francisco, Monrovia, and Port au Prince from OpenStreetMap data, created in Python with OSMnx

Continue reading Urban Form Figure-Ground Diagrams

Square-Mile Street Network Visualization

The heart of Allan Jacobs’ classic book on street-level urban form and design, Great Streets, features dozens of hand-drawn figure-ground diagrams in the style of Nolli maps. Each depicts one square mile of a city’s street network. Drawing these cities at the same scale provides a revealing spatial objectivity in visually comparing their street networks and urban forms.

We can recreate these visualizations automatically with Python and the OSMnx package, which I developed as part of my dissertation. With OSMnx we can download a street network from OpenStreetMap for anywhere in the world in just one line of code. Here are the square-mile diagrams of Portland, San Francisco, Irvine, and Rome created and plotted automatically by OSMnx:

OSMnx: Figure-ground diagrams of one square mile of Portland, San Francisco, Irvine, and Rome shows the street network, urban form, and urban design in these cities

Continue reading Square-Mile Street Network Visualization

Animating the Lorenz Attractor with Python

Edward Lorenz, the father of chaos theory, once described chaos as “when the present determines the future, but the approximate present does not approximately determine the future.”

Lorenz first discovered chaos by accident while developing a simple mathematical model of atmospheric convection, using three ordinary differential equations. He found that nearly indistinguishable initial conditions could produce completely divergent outcomes, rendering weather prediction impossible beyond a time horizon of about a fortnight.

Lorenz system attractor animated GIF created with Python matplotlib scipy numpy PIL

Continue reading Animating the Lorenz Attractor with Python

OSMnx: Python for Street Networks

OSMnx: New York City urban street network visualized and analyzed with Python and OpenStreetMap dataOSMnx is a Python package for downloading administrative boundary shapes and street networks from OpenStreetMap. It allows you to easily construct, project, visualize, and analyze complex street networks in Python with NetworkX. You can get a city’s or neighborhood’s walking, driving, or biking network with a single line of Python code. Then you can simply visualize cul-de-sacs or one-way streets, plot shortest-path routes, or calculate stats like intersection density, average node connectivity, or betweenness centrality. You can download/cite the paper here.

In a single line of code, OSMnx lets you download, construct, and visualize the street network for, say, Modena Italy:

import osmnx as ox
ox.plot_graph(ox.graph_from_place('Modena, Italy'))

OSMnx: Modena Italy networkx street network in Python from OpenStreetMap Continue reading OSMnx: Python for Street Networks

Urban Design and Complexity

Corbusier Paris planI am presenting at the 2015 Conference on Complex Systems tomorrow in Tempe, Arizona. My paper is on methods for assessing the complexity of urban design. If you’re attending the conference, come on by!

Here’s the abstract:

Continue reading Urban Design and Complexity

Animated 3-D Plots in Python

Download/cite the paper here!

In a previous post, I discussed chaos, fractals, and strange attractors. I also showed how to visualize them with static 3-D plots. Here, I’ll demonstrate how to create these animated visualizations using Python and matplotlib. All of my source code is available in this GitHub repo. By the end, we’ll produce animated data visualizations like this, in pure Python:

Animated 3-D Poincare plot of the logistic map's chaotic regime - this is time series data embedded in three dimensional state space Continue reading Animated 3-D Plots in Python

Visualizing Chaos and Randomness

3-D Poincare plot of the logistic map's chaotic regime - this is time series data embedded in three dimensional state space

Download/cite the paper here!

In a previous post, I discussed chaos theory, fractals, and strange attractors – and their implications for knowledge and prediction of systems. I also briefly touched on how phase diagrams (or Poincaré plots) can help us visualize system attractors and differentiate chaotic behavior from true randomness.

In this post (adapted from this paper), I provide more detail on constructing and interpreting phase diagrams. These methods are particularly useful for discovering deterministic chaos in otherwise random-appearing time series data, as they visualize strange attractors. I’m using Python for all of these visualizations and the source code is available in this GitHub repo.

Continue reading Visualizing Chaos and Randomness

Chaos Theory and the Logistic Map

Logistic map bifurcation diagram showing the period-doubling path to chaosUsing Python to visualize chaos, fractals, and self-similarity to better understand the limits of knowledge and prediction. Download/cite the article here and try pynamical yourself.

Chaos theory is a branch of mathematics that deals with nonlinear dynamical systems. A system is just a set of interacting components that form a larger whole. Nonlinear means that due to feedback or multiplicative effects between the components, the whole becomes something greater than just adding up the individual parts. Lastly, dynamical means the system changes over time based on its current state. In the following piece (adapted from this article), I break down some of this jargon, visualize interesting characteristics of chaos, and discuss its implications for knowledge and prediction.

Chaotic systems are a simple sub-type of nonlinear dynamical systems. They may contain very few interacting parts and these may follow very simple rules, but these systems all have a very sensitive dependence on their initial conditions. Despite their deterministic simplicity, over time these systems can produce totally unpredictable and wildly divergent (aka, chaotic) behavior. Edward Lorenz, the father of chaos theory, described chaos as “when the present determines the future, but the approximate present does not approximately determine the future.”

Continue reading Chaos Theory and the Logistic Map

LEED-ND and Neighborhood Livability

I recently co-authored a journal article titled LEED-ND and Livability Revisitedwhich won the Kaye Bock award. LEED-ND is a system for evaluating neighborhood design that was developed by CNU, USGBC, and NRDC. Many of its criteria, particularly site location and neighborhood pattern, accordingly reflect New Urbanist and Smart Growth principles and are inspired by traditional neighborhood design.

Continue reading LEED-ND and Neighborhood Livability

The Inside Field Exam and Urban Complexity

I recently completed my inside field exam, one of the many steps involved in advancing to candidacy. The three professors on your inside field committee send you six questions – a pair per professor – and you are given 72 hours total to answer one question from each pair. The answers are to be in the form of a scholarly article with thorough citations. Long story short, you’ve got to write 30 pages of academic scholarship in three days.

The exam questions themselves are very interesting. The professors construct them based on their reading of your inside field statement, trying to probe areas that might be particularly rich or a bit weak in the statement. Here are the questions I answered:

Continue reading The Inside Field Exam and Urban Complexity