Simulated Snowflakes
Science Fair 2004-2005
DCYSC Entry
Explain your science fair project.
Introduction
In this project, I attempt to develop a computer simulation of the formation of a snowflake, a
process characterized by the crystal lattice form of molecular bonding. While understanding the process of
snowflake formation has little immediate practical use, the crystal form of molecular bonding is very
common in our environment. Snowflakes are a universal medium in which the crystal growth can be easily
displayed.
Question:
Can a computer simulate the formation of snowflakes and, if so, to what degree of
accuracy?
Null hypothesis:
Computers will not be able to simulate the formation of snowflakes with a
molecular dynamics program because of the compute intensity. There will be some other kind of program
that will achieve the purpose.
Procedure
First, a program must be found or written that will simulate the formation of the crystal lattice. As
molecular dynamics programs are popular, many programmers have made their simulators available for
free download so that other programmers can use and modify them. Molecular dynamics programs simulate
the exact placement of a number of molecules and how the molecules affect each other. GROMACS is
highly recommended molecular dynamics program.
Little is known about how the water molecules bond to create branching instability. Furthermore,
it takes five minutes to simulate less than a second. Given the number of complexities, simulating a
snowflake with a MD program such as GROMACS is currently not possible.
Time for a new approach. The reason that MD didn’t work was (a. it was slow and (b. it didn’t
form branching instability. It’s possible that a program that calculated the probability of ice condensing
would work better. With this in mind, I found a paper that had some equations for this. I wrote the
equations into my program called ‘cellular automata’.
First, the computer makes a hexagonal grid, the shape of the snowflake. Each grid space is called a
cell. Then, each cell is assigned a ‘state of frozenness’, 1 being frozen and 0 being liquid. The computer
calculates how the temperature changes depending on how frozen the cell’s neighbor’s are. This creates a
pattern that will grow and branch out just like a snowflake does.
Conclusion
Although GROMACS gave a more accurate picture, the cellular automata program was more
successful in making a snowflake pattern. The computer was able to simulate the formation of the
snowflake.
I would like to thank my dad who taught me C++, checked GROMACS for viruses, and installed
Linux on my computer. My mom has helped me in writing my report and making it coherent. I got my idea
from making paper snowflakes and learning to program.
Word count: 435