I see 4 colors. Blue, green, red and pink.
When I use ColorPic I get a lot more hex values (colors) than that when sampling various spots on the spiral.
125, 202,75
148, 194, 63
7, 252,146
43, 237, 125
212, 168, 25
79, 176, 182
191, 64, 229
127, 127, 202
OK, I think I see what you’re saying. When you zoom the image with Chrome or Firefox the renderers put new colors at the boundaries between the image’s colors. But I think such interpolating pixels are called anti-aliasing. 
When I look at the image rendered with such zooming I see not only the three obvious new colors (magenta/green, orange/green, magenta/orange) but variations in the colors within the boundary region, as would be expected with sophisticated anti-aliasing, so the total number of distinct (r,g,b) values is huge. (I also note that the boundary regions are several pixels wide, as though the interpolation algorithm assumes the original is band-limited and applies some diffusion.)
All of which is irrelevant to the thread topic, of course. I once had the words “color” and “scientist” in my job title, yet still find these paradoxical images almost unbelievable!
What are some examples of these coordinates?
Well I got it right… my logic was “It sure looks like four, so that can’t be the answer. So it’s probably three.”
I did pretty much the same. I wondered if it might only be two, but there aren’t enough juxtapositional possibilities with only two.