A Program to Simulate Diffusion Limited Accretion


So, what do I mean by 'Diffusion Limited Accretion'?

It's actually a way to simulate the growth of crystals one particle at a time. The sort of crystals simulated are crystals growing from a solution or ice crystals growing across a windscreen, that sort of thing. I discovered the idea on Paul Bourke's personal web site - definitely a site for a comprehensive read-up about this type of mathematics.

Anyway, I implemented the idea because it looked as if the resulting images could make nice, interesting cross stitch patterns.

The program works by placing a particle in a confining shape (circle/ellipse or square/rectangle), and allowing it to randomly wander every which way until it crashes into something. Then it sticks, and the process starts off with another particle. The bigger the starting picture, the longer it takes for the particle to crash into something, and you need more particles to make an interesting picture, so as the size of a picture doubles, the time for the picture goes up by 16 times. The picture can be coloured depending on the distance the particle is from the centre, or remain monochrome. It's up to you.

The images can be coloured with graduated colours from the centre, or remain black & white. The bigger the picture, the longer it can take. The one above took about 3.5 hours working in the background of a fast PC. The ones below took a couple of minutes. I tried to make a couple that could be used as place mat patterns when stitched at 14 count. These are below:

The images saved can go straight into my Cross Stitch Charting Software to make a chart.

The program can be downloaded below. The program is included in the zip file.

Download the Diffusion Limited Accretion Program. (1216 kb)

The program is a 32 bit Windows program, and is known to run on Windows 7 (32 & 64 bit versions) and Win 10 (64 bit). It may run under WINE on Linux. It should work in any 32 bit windows operating system. The program is a single file .exe file and executes in any directory you extract the file to. It writes no files other than the .bmp image file.

Chestnut Pens Downloads Page
Chestnut Pens Miscellaneous Pages Home
Chestnut Pens Home