In order to model the growth of our snowflake, we came up with the following algorithm:

1)  Put a snowflake seed on the origin.  We decided to use a hexagon eventually.

2)  Determine the maximum distance from the origin to any existing part of the flake.  Call this R.  Call the diameter of each particle D.

3)  Plop a new particle down at a random spot on a circle of radius R + D.

4)  Let the new particle take a random walk.

5) a)  If the particle walks into the existing flake, it sticks.  Time for the next particle!
    b)  If the particle gets a distance 5R away from the origin, kill it.  Time for a new particle!

6)  Let it grow until 5000 particles have been added.  Then quit.

7)  Calculate the number of particles in each 1 degree wide slice of pie.

8)  Analyze the results!  (See the "Results" page)
 

So, it's time to find out what happened!  See if you can make a snowflake like ours in the picture, by playing with our applet on the "applet" page.  Also, if you ever meet Lam Chi-Hang, tell him what a great guy he is for having an applet available for us to modify on his web page!  [3]  We basically modified his code to start with a hexagonal seed, and to output the data we required.
 

MAIN PAGE    SNOWFLAKE SHAPES   DIFFUSION

OUR SPIFFY MODEL OF DENDRITIC GROWTH

OUR HOT APPLET OF DENDRITIC GROWTH

THE RESULTS OF OUR HOT APPLET OF DENDRITIC GROWTH

LINKS