blog - Bits & Bytes (Page 2)

Tupper's self-referential formula

So here's something cool. This formula: $$\frac{1}{2} < \lfloor mod(\lfloor\frac{y}{17}\rfloor2^{-17\lfloor x \rfloor -mod(\lfloor y\rfloor,17)},2)\rfloor$$ will literally plot itself if you look at the right region. where k is this 543-digit integer: 960 939 379 918 958

markov

Tweeting with Markov Chains

I'm not sure why I find this so surprising, but it's a somewhat trivial task to write a program that can spew out somewhat coherent sentences, as long as you have a large corpus to work off. Markov Chains Markov Chains are essentially state machines with probabilities assigned to each

math

1 + 2 + 3 + ...

Here's something mind-blowing: If you take the sum of the first couple of natural numbers you get the triangle numbers: $$T_{1} = 1$$ $$T_{2} = 1 + 2$$ $$T_{3} = 1 + 2 + 3$$ $$T_{n} = (n)(n-1)/2$$ So essentially the series 1 + 2 + 3 + 4 + ... is the area of an

sushi

大和

What better place to get sushi in Tokyo, than by going to an actual fish market? By the time we arrived at Tsukiji Fish Market (around 6:00AM in the morning), the lines were already pretty long. Daiwa Sushi (大和) had a significantly shorter wait. We probably only waited for

python

Towers of Hanoi

An age-old puzzle that's challenged kids and pancake chefs for ages: The goal of the puzzle is to move an entire stack of disks from one rod/plate to another with the following restrictions: Only one disk can be moved at a time. Each move consists of taking the upper

fractals javascript

Dragon Curve

The dragon curve or Heighway Dragon is a beautiful self-similar fractal first investigated by NASA physicists John Heighway, Bruce Banks, and William Harter. Jack [Heighway] came into my office (actually cubicle) and said that if you folded a one dollar bill repeatedly he thought it would make a random walk

python

Analyzing NYC Subway Data with Python

MTA provides a public dataset of turnstile data per station since May 2010. We can grab weather data from Weather Underground, who kindly provides historical weather data in CSV format. You can also grab the same data through their API. Data Munging The data we collected so far usuable yet,

quine

Quine

Inspired by this impressive piece of engineering, I tried to write my one quine in CoffeeScript. The trick I used was to encode the entire file into decimal ASCII and store it in the data array. To rebuild the actual code, you convert it back to characters. This lets you