It seems to me that the answer is:
TERNANY - although I don't recognise this as a word, it is presumably some kind of pun on the word 'ternary'?
How did I get this? Well, first note that the diagram represents:
A scatter plot, where the 0-axes are alternately black and white, representing units, and the purple pixels represent the points that have been plotted upon it.
Read off the (x,y)-coordinates of each point (as hinted at by the use of 'coordination' in the flavour text), we find the following list of coordinates:
(0,1), (1,0), (1,2), (3,0), (2,3), (1,5), (5,1), (3,4), (4,3), (6,4), (4,7), (0,12), (10,2), (5,10), (7,9), (7,10), (6,12), (8,10), (10,9), (12,7), (8,12), (11,9), (10,11)
Next, use the second clue provided in the flavour text:
And - cued by 'plus' - add together the numbers in each coordinate pair to get the following list of numbers:
1, 1, 3, 3, 5, 6, 6, 7, 7, 10, 11, 12, 12, 15, 16, 17, 18, 18, 19, 19, 20, 20, 21
Following the second hint, we can now:
Treat these numbers as a dataset and plot each number's frequency of appearance as a histogram (to which there is a subtle graphical hint in the diagram itself, as a curved histogram-like shape can be seen among the purple plotted data points):
We can see from this that:
No number appears more than twice, and the range of the numbers is 21, which is divisible by 3 (and after all, the title tells us '3 is the key'...) - in fact it is 7 times 3, and we are looking for a seven-letter answer... so how about we try dividing this histogram into seven equal parts, and interpret each triple using ternary? So, dividing the histogram like this:
We can now extract the seven ternary triples: 202, 012, 200, 112, 001, 112 and 221.
These convert into decimal as: 20, 5, 18, 14, 1, 14 and 25.
And these then convert via A1Z26 into the final answer of TERNANY.
Disclaimer: This answer was arrived at entirely independently to others. My dataset is the same as @Randal'Thor's (just ordered differently) and was derived in the same way at a similar time, while @Avi's answer (with similar deductions after the publishing of the third hint) only loaded in my browser after pressing the submit button for this answer(!), which contains further steps and deductions not present in the other two :)