Obviously this isn't realistic. Actual smoke plumes spread out vertically as they move with the wind. Let's call the horizontal motion "advection" and the vertical motion "turbulence". We can simulate both processes - turbulence and advection - by using the following simple procedure. All we need is a coin (in addition to our graph paper).
First, flip the coin. Every time we flip the coin the pollution speck moves one square to the right. If the coin turns up "heads", the speck also moves one square upward. If the coin turns up "tails", the speck moves one square downward.
Now, let's apply the same procedure to two specks at the same time. However, let's flip the coin separately for each speck.
You can see from the second animation that the specks spread apart from each other in a random way. At the same time, both particles are moving horizontally with the wind in exactly the same way. This process simulates both turbulence and advection.
THE REST IS UNDER CONSTRUCTION!
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