Year: 2015

Categories
Travel

Hong Kong at Night

Hong Kong is a remarkable place. It is the 4th-densest sovereign state or self-governing territory in the world (in 1st place is its neighbor across the delta: Macau). Yet this density is fantastically constrained by the mountains and the sea into narrow, snaking corridors of high-rises wherever the terrain permits. At no time is this unique urban development better seen than at night, when Hong Kong lights up like a carnival.

I took these photos from the top of Victoria Peak on Hong Kong island and from the Tsim Sha Tsui promenade on the Kowloon peninsula, using long exposures of between 3 and 12 seconds.

hong-kong-skyline-night-2

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Categories
Data

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

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Categories
Data

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.

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Categories
Data

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.”

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Categories
Planning

LEED-ND and Neighborhood Livability

I recently co-authored a journal article titled LEED-ND and Livability Revisited, which 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.

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Categories
Academia

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:

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