Particles explained using Gifs!!

Over the past few months, I have been reading, understanding and implementing a number of existing algorithms in Computer Vision domain. Implementing particles and particle based algorithms have really had me excited and almost on the edge of my seat. One may ask what makes particles so interesting?? Let me try to get the concept through.

Particles, just like most existing algorithms in computer science, are inspired by nature. Have you ever seen a beam of sunlight coming through a window and illuminate a bunch of floating particles (impossible in London though I have seen it before)? When you see these tiny particles, you notice that they are suspended in air and that it's very difficult to predict their motion unless you disturb the surrounding air. This simple concept is vital for many computer algorithms that model motion/dynamics of an object.

Particles, along with their randomness, can be simulated inside a computer program. The simplest of such algorithm is called Random Walk, where a particle is modelled with its current position/state alone and a random displacement/jump determines its next position in time. Here I have shown one Random Walk particle:

A Single Random Walk Particle

Designing an algorithm - from ideas to code

I had always been interested in solving sudoku puzzles, partly because there are too many combinations that make each Sudoku unique. Since my work involves writing and using programming in different scenarios, I thought why not try using my skills on Sudoku. So there I was on a London Underground train to Barbican - looking at a Sudoku puzzle at the back of a morning newspaper, wondering how I can write an algorithm to solve it. I figured out a few simple tricks that I have always used in algorithm design. Here I explain what thoughts I had while designing my very own Sudoku solver and how I transformed those ideas into a working prototype.

First of all lets have a look at a typical Sudoku puzzle and some basic rules:

Sudoku Puzzle

Yes - it has got everything to do with numbers!! lots of numbers!

A Sudoku puzzle typically has 81 boxes where each box can have a number between 1 to 9. However, all these boxes follow some rules that make it all interesting. You may have noticed 3x3 squares grouping the number boxes. A correct solution of Sudoku ensures no repetition of numbers from 1 to 9 inside each of the 3x3 squares, in each horizontal line and each vertical line. When solving a Sudoku puzzle, this is exactly where I look for a solution, and exactly where my thought process starts for my Sudoku solver algorithm.