If an 8000 "bin" histogram created between the min and max values in the data (each bin has the same width) are used, all of the individual numbers or data values will be put into the bins in the histogram. If you have 20 colours, you want to give one colour for each 400 points, so you increment through the bins until you find that including the next bin takes you over the next 400 point increment. The zone interval is a linear interpolation between the individual histogram bin range that "puts you over the top" for that 400 point set, based on the number of values taken from the "last" bin in order to make up an even 400 points for this range.

A data set has 10,000 points, and you want a 20-colour equal-area transform, so each colour should get 500 points. The values themselves range from 0 to 40,000, so first (internally) a histogram is made with 8000 bins:

Bin 1: 0 < x <= 5: 250 points

Bin 2: 5 < x <= 10: 300 points

Bin 3: 10 < x <= 15: 100 points

Bin 4: 15 < x <= 20: 400 points

etc...

Bin 8000: 39995 < x < 40000: 10 points

In order to get 500 points in your first bin, you take the first bin and part of the second bin - 250 + 5/6 * 300, so the range of your first colour zone is all values less than 5 + 5/6*(10-5), or 9.167.

For the next zone, you would take the remaining 50 points in Bin 2, add Bin 3, and continue adding bins until you get up to the next 500 points, etc., so the next range is 50 + 100 + 250 out of Bin 4, giving a range bound of 15 + 250/400*(20 - 15) = 18.125. Therefore, the zones are:

1. x <= 9.167 (min)

2. 9.167 < x <= 18.125

etc…