Archive for the ‘Math & Science’ Category
Perlin Noise: Oscar-winning Randomness
Since when does math win Oscars? Back in 1982, Ken Perlin created a random distribution function that efficiently generates life-like textures for computer graphics. Featured in the movie Tron, Perlin won an Academy Award for Technical Achievement for his now ubiquitous formula. In this article, we’ll talk about the most famous math function used in computer graphics today.
Exploring Mandelbrot’s Mathematical Beauty
I was planning on posting this later, but in light of Benoit Mandelbrot’s recent passing, I think I’ll post it today. Back in 2002, I wrote a program to draw fractals from the Mandelbrot set. Immediately, I was fascinated by all the shapes and colors I could generate with a little math and a simple program. Over time, I started gathering more and more pictures. Here’s what I gathered, although I hope to expand and improve on the collection someday.
The Halting Problem: There’s No App for That
Think software can do anything? Think again. Theoretical computer scientists have come up with all kinds of airtight proofs about what computers can and cannot do. The most famous of these is the Halting Problem.
Wouldn’t it be nice to have a program that tells you when your software has crashed and will never quit? According to the Halting Problem, no such program exists. And, the proof is actually quite simple.
Counting Without Numbers: Parable of the Trader
"Many" bricks
I once heard this story in my probability and statistics class. The idea is actually closely related to combinatorics. Here’s my version of the story:
Once upon a time, there was a wealthy Wall Street trader who was looking to make a good deal. He found that bricks were selling for a price of $1 per brick. Normally, this trader wouldn’t buy and sell bricks at that price, but then he heard about these farmers from a distant land and came up with a scheme for cheating them out of making a good profit.
5 Reasons to Love Programming
It’s no secret that I love writing code. I’ve been writing software for over a decade, making programming not only my longest-running hobby, but the cornerstone of my career.
Why do I love it so much? Here’s my list.