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

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Scientific Python for Raspberry Pi

Raspberry Pi 3 Model BA guide to setting up the Python scientific stack, well-suited for geospatial analysis, on a Raspberry Pi 3. The whole process takes just a few minutes.

The Raspberry Pi 3 was announced two weeks ago and presents a substantial step up in computational power over its predecessors. It can serve as a functional Wi-Fi connected Linux desktop computer, albeit underpowered. However it’s perfectly capable of running the Python scientific computing stack including Jupyter, pandas, matplotlib, scipy, scikit-learn, and OSMnx.

Despite (or because of?) its low power, it’s ideal for low-overhead and repetitive tasks that researchers and engineers often face, including geocoding, web scraping, scheduled API calls, or recurring statistical or spatial analyses (with small-ish data sets). It’s also a great way to set up a simple server or experiment with Linux. This guide is aimed at newcomers to the world of Raspberry Pi and Linux, but who have an interest in setting up a Python environment on these $35 credit card sized computers. We’ll run through everything you need to do to get started (if your Pi is already up and running, skip steps 1 and 2). Continue reading Scientific Python for Raspberry Pi

Urban Informatics and Visualization at UC Berkeley

The fall semester begins next week at UC Berkeley. For the third year in a row, Paul Waddell and I will be teaching CP255: Urban Informatics and Visualization.

This masters-level course trains students to analyze urban data, develop indicators, conduct spatial analyses, create data visualizations, and build Paris open datainteractive web maps. To do this, we use the Python programming language, open source analysis and visualization tools, and public data.

This course is designed to provide future city planners with a toolkit of technical skills for quantitative problem solving. We don’t require any prior programming experience – we teach this from the ground up – but we do expect prior knowledge of basic statistics and GIS.

Our teaching materials, including IPython Notebooks, tutorials, and guides are available in this GitHub repo, updated as the semester progresses.

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Clustering to Reduce Spatial Data Set Size

In this tutorial, I demonstrate how to reduce the size of a spatial data set of GPS latitude-longitude coordinates using Python and its scikit-learn implementation of the DBSCAN clustering algorithm. All my code is in this IPython notebook in this GitHub repo, where you can also find the data.

Traditionally it’s been a problem that researchers did not have enough spatial data to answer useful questions or build compelling visualizations. Today, however, the problem is often that we have too much data. Too many scattered points on a map can overwhelm a viewer looking for a simple narrative. Furthermore, rendering a JavaScript web map (like Leaflet) with millions of data points on a mobile device can swamp the processor and be unresponsive.

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