A simple demo of k-means clustering. The little squares are the observations and the cirles are the centroids. Press the 'Step:' button to step through the algorithm. Restart

This is just D3 and L-Systems with live controls, but now state is managed by Redux. Oh, and also arrow functions, because they're available everywhere I care about. I've been reading about Redux and wanted to try it out. It seems nice, as it forced me to consolidate everything about page state, which caused me to clean up the code quite a bit. I like that in a tool. It's also the reason I like Go and way it handles 'error', it forces me to think about the not-happy-path as opposed to the happy-path, which always makes my code better.

The rural areas of North Carolina are emptying out. North Carolina County Population vs Count Population Growth Rate (2010 - 2014). Click on the graph to toggle between population density and county population. North Carolina is not immune to Rural Flight, nor is it a special victim, as the phenomenon is happening world wide. Countrysides around the world are emptying out. It's important to keep these broader patterns in mind, first so you don't go blaming random local events that look like correlation: Mary Hobbs has been living in Woodland for 50 years and said she has watched it slowly becoming a ghost town with no job opportunities for young people.

Geometric Algebra can be applied to Physics, and many of the introductions to GA online cover this, but they immediately jump to electromagnetic fields or quantum mechanics, which is unfortunate since GA can also greatly simplify 2D kinematics. One such example is uniform circular motion. You should be familiar with all the concepts presented in An Introduction to Geometric Algebra over R^2 before proceeding. If we have a vector p that moves at a constant rate of ω rad/s and has a starting position p0, then we can describe the vector p very easily: $$\boldsymbol{p} = \boldsymbol{p_0} e^{\omega t \boldsymbol{I}}$$ Start/Stop Let's figure out what the derivative of a Rotor looks like, by first recalling its definition: $$ e^{\theta \boldsymbol{I}} := \cos(\theta) + \sin(\theta)\boldsymbol{I}$$ We take the derivative with respect to θ: $$ \begin{align*} \frac{d}{d \theta} e^{\theta \boldsymbol{I}} &= \frac{d}{d \theta} (\cos(\theta) + \sin(\theta)\boldsymbol{I}) \\ &= -\sin(\theta) + \cos(\theta)\boldsymbol{I} \\ \end{align*} $$ At this point observe that cos and sin just changed places, along with a sign change, but we know of another operation that does the same thing, which is multiplication by I, so we get: $$ \begin{align*} \frac{d}{d \theta} e^{\theta \boldsymbol{I}} &= \frac{d}{d \theta} (\cos(\theta) + \sin(\theta)\boldsymbol{I}) \\ &= -\sin(\theta) + \cos(\theta)\boldsymbol{I} \\ &= \boldsymbol{I} (\cos(\theta) + \sin(\theta)\boldsymbol{I}) \\ &= \boldsymbol{I} e^{\theta \boldsymbol{I}} \\ \end{align*} $$ Not only does the derivative have a nice neat expression, we can read off from the formula what is happening, which is that the derivative is a vector that is rotated 90 degrees from the original vector.

Linear Algebra Geometric Algebra Applications Multiplying Vectors Rotors Double Angle Formula Complex Numbers Characterizing B Ratios Conjugates Geometric Algebra is fascinating, and I believe solves a large number of problems that arise from a more traditional approach to vectors, but I've been very disappointed with the quality of books and explanations I've found, most of them zooming off into abstract realms too quickly, or spending an inordinate amount of time building up a generalized theory before finally getting to something useful.

To get an idea of voter suppression in action let's overlap the The Racial Dot Map with Wake County's early voting locations.

Restart ESF Pauli % Low Entropy High Entropy Initial Conditions Entropy: Mean: Entities: Mean: Quanta Magazine published an interesting article in their Insights Puzzle column called Seeing Time Through a Liquid Crystal Display. Above is my version of the simulation, which operates on a basic level like the simulation presented in the article, but then adds in a few twists. At this point you should to read the arctile to understand the basic simulation.

Reilly has been learning Javascript, and one of the projects he wanted to do was a snow simulation. I guess growing up in the south snow is a rare and wonderous event for him.