Sunday, January 13, 2008

Saturday, January 12, 2008

Cellular Automata_Diffusion-Limited Aggregation


Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by Witten and Sander in 1981 ,is applicable to aggregation in any system where diffusion is the primary means of transport in the system. DLA can be observed in many systems such as electrodeposition, Hele-Shaw flow, mineral deposits, and dielectric breakdown.
---Wikipedia

Friday, January 4, 2008

Shoal--Convex hull


600 points

200 points


In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X. ---Wikipedia


The gift wrapping algorithm is an algorithm for computing the convex hull of a set of points in two or more dimensions

Sunday, December 23, 2007

8(n) queens puzzle





The eight queens puzzle is the problem of putting eight chess queens on an 8×8 chessboard such that none of them is able to capture any other using the standard chess queen's moves. This means it is as if all the queens are different colours. The queens must be placed in such a way that no two queens would be able to attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general n queens puzzle of placing n queens on an n×n chessboard(n ≥ 4).

-- Wikipedia


The eight queens puzzle has 92 distinct solutions. If solutions that differ only by symmetry operation (rotations and reflections) of the board are counted as one, the puzzle has 12 unique solutions
The script uses backtracing to find all the distinct solutions for "n queens puzzle" problem