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:
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.
Using 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.”
Our paper on collecting and analyzing U.S. housing rental markets through Craigslist rental listings has been accepted for publication by the Journal of Planning Education and Research. Check out the article here. This map of rental listings in the contiguous U.S. is divided into quintiles by rent per square foot:
This post is part of a series on visualizing data from my summer travels.
I’ve previously discussed visualizing the GPS location data from my summer travels with CartoDB, Leaflet, and Mapbox + Tilemill. I also visualized different aspects of this data set in Python, using the matplotlib plotting library. However, these spatial scatter plots used unprojected lat-long data which looked pretty distorted at European latitudes.
Today I will show how to convert this data into a projected coordinate reference system and plot it again using matplotlib. These projected maps will provide a much more accurate spatial representation of my spatial data and the geographic region. All of my code is available in this GitHub repo, particularly this notebook.
This guide was written in 2014 and updated slightly in November 2020.
I recently went through the exercise of installing geopandas on Windows. Having learned several valuable lessons, I thought I’d share them with the world in case anyone else is trying to get this toolkit working in a Windows environment. It seems that pip installing geopandas usually works fine on Linux and Mac. However, several of its dependencies have C extensions that can cause compilation failures with pip on Windows. This guide gets around that issue.
This is a series of posts about visualizing spatial data. I spent a couple of months traveling in Europe this summer and collected GPS location data throughout the trip with the OpenPaths app. I explored different web mapping technologies such as CartoDB, Leaflet, Mapbox, and Tilemill to plot my travels. I also used Python and matplotlib to run some descriptive statistics and visualize other aspects of my trip.
Here is the series of posts:
My Python code is available in this GitHub repo. I also did some more involved work under the hood to prep the data and support these visualizations. For example, in the following posts I reverse-geocoded the spatial data set and reduced its size with clustering algorithms and the Douglas-Peucker algorithm:
This post is part of a series on visualizing data from my summer travels.
I’ve previously discussed visualizing the GPS location data from my summer travels with CartoDB, Leaflet, and Mapbox + Tilemill. Today I will explore visualizing this data set in Python, using the matplotlib plotting library. All of my code is available in this GitHub repo, particularly this notebook.
This post is part of a series on visualizing data from my summer travels.
I’ve previously discussed my goals in visualizing GPS data from my summer travels and explored visualizing the data set with CartoDB and with Leaflet. The full OpenPaths location data from my summer travels is available here and I discussed how I reverse-geocoded it here.
Mapbox is a major provider of online web mapping services such as tiled web maps, the Tilemill cartography IDE, and the mapbox.js javascript library. Today I’ll run through how to create an interactive data map in Tilemill’s design studio, export the map as a set of tiles, upload the tileset to Mapbox, and then use a javascript client to display the map on a web page. Our final result will look something like this:
This post is part of a series on visualizing data from my summer travels.
I’ve previously discussed my goals in visualizing GPS data from my summer travels and explored visualizing the data set with CartoDB. The full OpenPaths location data from my summer travels is available here and I discussed how I reverse-geocoded it here.
Lastly, I reduced the size of this spatial data set so Leaflet can render it more quickly on low-power mobile devices. I discussed why this is important and how to do it with the DBSCAN clustering algorithm and also with the Douglas-Peucker algorithm. The final data set I’ll be working with is available here.