## The Density Plot of the Prime Gaps is a Fractal

tl;dr: Inspect the last image below and check out gap-density.R. I just discovered something that made me smile: As I looked at the density plots of increasing numbers of prime gaps, a fractal emerged. Allow me to explain. First I get the prime gaps (basically, the distance between primes) with this perl code:

This […]

## Alternatives to the Logistic Equation

tl;dr: bifurcation.R Yesterday, I decided to plot the bifurcation diagram of the logistic equation.  This is a famous plot from the 70s, that many geeks will be familiar with (left).  It shows that simple systems can switch into “chaos mode” and begin to bifurcate wildly. To produce the graph, we use code in the R […]

## Musical Random Walks Over Weighted Graphs

tl;dr: https://github.com/ology/Music/blob/master/random-walk In this post, I illustrate a simple technique in Perl 5 to perform random walks over (node-edge) graphs, adding the named, “semantic” vertices to a MIDI score. The image on the left is not generated by the random-walk program, but is just a related illustration. :-) OK – on with the code! First, there […]

## Plotting Successive Primes Modulo A Number

tl;dr: https://github.com/ology/Math/blob/master/primes/sequence-pairs File this under Recreational mathematics… I have this passionate curiosity for seeing the primes “folded in on themselves” – constrained to a phase space.  I also have a burning desire to visualize successive events.  I suppose that I am searching for “strange attractors”, as with the famous water drip […]

## Visualize Move, Protection and Threat Status in Chess

tl;dr: https://github.com/ology/Chess-Inspector When I was a kid, my younger brother became a chess master and would regularly thrash me in the game.  Invariably this seemed to be because I would do something dumb like leaving my queen threatened and unattended. As with many budding CS students, I devised my own chess playing program, but in […]

## Artificial Psychologist

tl;dr: https://watson-pi-demo.mybluemix.net/ A new psychologist is in town and his name is Watson.  Watson’s above site just contains a text area and an Analyze button.  The instructions say to paste in something you have written. Being a curious cat, I had fun pasting-in famous quotes and passages from books, like Alice in Wonderland, etc. It was interesting to speculate […]

## Visualizing Chatter on a Polar Plot

What does IRC chatter look like on a polar plot, with lines linking the conversations?

## Successive Old Faithful Eruption Durations

Because of the observed data, a four group clustering emerges when you plot successive eruption durations, of the famous geyser.  That is, the x axis is the first eruption and y is the next.

## Fibonacci v Primes: Cage Match!

Today I decided to more deeply investigate this curious math thing I discovered (for myself) – Plotting the Fibonacci numbers by Prime numbers each by a given modulo.  “Fibo-what? Mod-what? So what!”, you say. :p code: https://github.com/ology/Math/blob/master/slice-seq and https://github.com/ology/Math/blob/master/slice-seq.R For the mechanics, I use Perl to produce the data and R to visualize it.

## Growing Melodies

Ever since I heard about evolutionary programming, I’ve wanted to try it with music.  On a recent weekend, I finally did just that! Some generated melodies are lovely in spurts but betray their purposlessness.  …Some just sound like Metroid on drugs. The code is here: https://github.com/ology/Music/blob/master/bitstring-fitness Update with less dependencies: https://github.com/ology/Music/blob/master/ai-genetic