The grayed area of the table shows where the column values have reached a maximum value. The distribution values were discovered by investigating the number of partitions for a given number of spaces. The overlap between distribution values comes when the partitioning isn't thought of as a breaking apart of the integer, but instead an assembly of the integer. In other words, you start out with nothing but ones which represent the integer in it's most basic parts. By combining the parts and looking at only the combinations which produce a unique set of values, you generate the various partitions of the integer.
Further investigations into the number of partitions that contain a certain value or set of values can be explored and you will find that the distribution values are contained within the existing table. This and additional investigations reveal that the pattern is fractal in nature, because the same pattern keeps popping up. Later, I may point out many of the properties of the distribution table to demonstrate that reading the values diagonally, in reverse order or subtracting one row from another can address additional investigations on partitions.
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