What is Pink?

Pink is also known as 1/f and Zipfian. It refers to a balanced distribution of frequencies. In order to have any pinkness, what you are measuring must have distinct items that can be counted. For instance, you can measure the pinkness of a pile of coins because there are distinct kinds of coins that can be counted. You could not measure the pinkness of a pile of snowflakes because there is only one of each snowflake (assuming the old saying is correct).

To measure the pinkness, you first count the frequency of each type of item in the group. Using the coin example, assume you have 6 quarters, 12 dimes, 3 nickels, and 4 pennies. Next, put the frequencies in decending order: 12, 6, 4, 3. If the distribution is pink, the second number should be 1/2 the first number. The third number should be 1/3 the first number. The fourth number should be 1/4 the first number. That pattern goes on and on for each number (the fth number should be 1/f the first number). As you can see, our coin example is in perfect pink balance.

Another way to view this balance is with a log graph. Instead of having the X and Y axis of the graph being simple numbers, they are the log of the values. So, if the value you want to plot is (100, 10), you plot (log(100), log(10)), or (2, 1). If you plotted our coin example in this way, you would end up with a straight line with a -1 slope. That -1 slope means that it is pink balanced.

I personally don't use the log graph because I have found that purely random values have a mean line near -1, but the line is nowhere near straight. It is simply too hard to detect how near to pink a distribution is.

Instead, I give a distribution a rank from 0% to 100%. Any distribution with less than two values cannot be measured. I normally rank them as 0%, but that has a lot to do with the situation. With 2 or more values, I can check each value and build up a value that shows what percent of the distribution is pink.