THINGS TO TRY WITH MATHEMATICA

1. STREAM PLOT

Here is a stream plot that shows the directions of wind across Australia. The higher wind speeds are represented by brighter colors. To do this yourself, the outline function needs to be manually entered, but you can find all the details on how to do this on the Wolfram blog. Stream plots are commonly used to visualize differential equations ( http:// bit. ly/ WeatherPatterns).

2. SUNSPOT CYCLE

Witness the 11-year sunspot cycle, using publicly available data. Between 1640 and 1710, there were abnormally few sunspots, which coincided with the European “mini ice age.” In general, if you’re looking for frequencies in noisy data, a good trick is to convolve your data with a moving average kernel, to smooth it out before using Fourier analysis ( http:// bit.ly/SunspotNumbers).

3. CELESTIAL NAVIGATION

An old Maori proverb says, “Before you embark on a journey, make sure you know the stars.” Here, you can get your bearings by measuring the angles of altitude to planets, stars, or the moon at a specific time. The celestial sphere is approximated by Earth moving through a circular orbit at constant speed, otherwise things get ugly ( http:// bit.ly/CelestialNavigation).

4. SNOWFLAKES

Cold outside? Have a play with some different kinds of snowflakes. This one is generated using hexagonal cellular automata. All snowflakes exhibit hexagonal symmetry, due to hydrogen bonding in water molecules. When they freeze, the crystals are formed into a hexagonal arrangement, because of the layout of the charges ( http:// bit.ly/ SnowflakeLikePatterns).