Winter is here once again, and the beauty of nature has become more subtle and fleeting. For those with a careful, curious eye, nature provides a canvas of feathery, crystalline designs in the form of frost.

Photo by RC Grimsley

Hoar frost, or plain frost, forms when water vapor changes from its gaseous state directly to its solid state of ice when it comes into contact with surfaces that are below 32 degrees. Once a “seed” has been established on a surface, super-cooled water vapor particles are slowly deposited as crystals. It frequently forms a delicate white film on the outside of car hoods and windshields, as well as on the inside surface of houses with old windows. (If your house windows have a lot of frost, you probably need to replace your windows, as they are inefficient and letting in a lot of cold from the outside.)

Rime frost is a thicker, less organized form of ice build-up. Rime frost occurs when very humid air encounters very cold surfaces. It is typically white and lumpy due to its relatively quick formation. Rime frost is much more common in conditions of high wind. (Think about Mt. Washington's weather observatory as an example.)

Frost is different from dew and black ice in that frost does not pass through a liquid state as it adheres to a surface. Dew forms when there is more water vapor than air can hold at a certain temperature, so it condenses out of the air and onto a surface. Warm air can hold more water vapor, while cool or cold air has a lower capacity. Black ice forms when rain, melted snow, mist, or fog freezes onto a surface. Unlike benign hoar frost, black ice can be treacherous for drivers and pedestrians who try to move across its slick surface.

Part of the beauty of frost comes from the fact that the crystalline patterns are fractals. Fractals are repeating units that are the same regardless of the level of magnification. Zooming in closely on a small piece of a fractal pattern looks the same as seeing the pattern on a large scale. Fractals are common in nature: snowflakes, frost, tree branching, snail shells in cross section, blood vessels in lungs, jagged coastlines, and watershed drainage patterns. In all these examples, the big picture looks very similar to its smaller parts.

One easy and common fractal in math is Koch’s snowflake.

 Step 1: Start with an equilateral triangle (blue).

Step 2: Divide one side of the triangle into three equal parts. Create another equilateral triangle using the middle section. Do this to all three sides of the triangle (white).

Step 3: Repeat this process for the sides of the six-sided blue and white star that results (yellow).

Step 4: Repeat this process for the blue, white, and yellow outer edges (red).

Image by www.en.wikipedia.org 

(For those who want to learn more about fractals, this is an excellent website: http://math.rice.edu/~lanius/frac/koch.html.)

The next time you see a patch of frost, take a moment to look more closely at the intricate patterns. Use a magnifying glass to see if the big pattern appears at a smaller scale. Use your camera to record Jack Frost’s work and send someone some warm greetings.