I’m pretty sure I made a comment about this or a similar post linked here a few years ago, including some graphics cooked up in Photoshop explaining the problems with the examples, but I can’t find it at the moment, and can’t be bothered to make new demonstrations.
Suffice it to say: unfortunately the lightness (a.k.a. value) of the color stripes varies tremendously from one example to the other in this post, which makes this a basically worthless comparison, as in general lightness contrast dominates other visual effects. If you swapped the lightness (e.g. in CIELAB or CIECAM02 color space) from the left and right examples while leaving the hue/chroma the same, you’d get the opposite results inre what looks “good”, which would reveal this “Müller formula” to be bogus (or at any rate radically oversimplified).
More generally, I’ve never seen a convincing exposition of similar color preference effects backed by data collected in a scientific paper with reasonable study design. It’s always handwavey 19th century nonsense, sometimes with a handful of preferences expressed by a tiny sample of homogenous survey respondents tacked on the end. Bad examples are endemic to the pseudosciency-color-theory genre, because most people work with terrible color models which are only marginally relevant to human perception.
The key to making color schemes for graphic illustrations or data visualizations look good is to use enough contrast (especially lightness contrast) between intentionally separate shapes so that distinct elements don’t accidentally blend together. (Note that sometimes you want certain elements to have lower contrast, but that should be an intentional choice, made for some obvious reason.)
Looking at nonsense.png actually supports the Müller formula. At least to me, the best-looking combinations are exactly the two that should be the best-looking according to the Müller formula. The version you created have color and brightness values that move counter the "natural brightness", and look uglier than the originals, just as the Müller formula predicts.
You missed my point, which was that the example was supposed to show how changes in hue affected whether something would look good, but the example showed dramatically varying lightness and chroma, in addition to the hue differences, thus making the comparison useless as a demonstration of the claimed effect. To make an example showing what the author of these examples wants to show, it would be necessary to keep lightness and chroma consistent from one set of color combinations to another, so that viewers can see the hue differences instead of being distracted by lightness/chroma differences.
If the “Müller formula” worked the way the author of these example images thought, then the color combinations at the right side after my lightness switcharound should still be “good looking”, but to me at least, with low lightness contrast, they instead start to look very muddy. Likewise, in my opinion the color combinations at the left of each example are improved dramatically by the increase in lightness contrast, even though they still have low chroma contrast and aren’t exactly my favorites.
Yeah, it seems as scientific as feng shui but if used just as a "plausible design recipe" I see it as valuable as any other strategy for color picking (i.e. if it works for a particular case then good, but if not, then try something else).
There is no actual Muller formula though. Though, I can see how you would build a color scale creator using the idea. I will see how it works with our data visualizations, and if so, d3 now has modules, I can build something for that.
I'd love to see a follow-up article on how material design colors were created. Tools such as http://mcg.mbitson.com/ seem to produce uglier colors, imo.
Suffice it to say: unfortunately the lightness (a.k.a. value) of the color stripes varies tremendously from one example to the other in this post, which makes this a basically worthless comparison, as in general lightness contrast dominates other visual effects. If you swapped the lightness (e.g. in CIELAB or CIECAM02 color space) from the left and right examples while leaving the hue/chroma the same, you’d get the opposite results inre what looks “good”, which would reveal this “Müller formula” to be bogus (or at any rate radically oversimplified).
More generally, I’ve never seen a convincing exposition of similar color preference effects backed by data collected in a scientific paper with reasonable study design. It’s always handwavey 19th century nonsense, sometimes with a handful of preferences expressed by a tiny sample of homogenous survey respondents tacked on the end. Bad examples are endemic to the pseudosciency-color-theory genre, because most people work with terrible color models which are only marginally relevant to human perception.
The key to making color schemes for graphic illustrations or data visualizations look good is to use enough contrast (especially lightness contrast) between intentionally separate shapes so that distinct elements don’t accidentally blend together. (Note that sometimes you want certain elements to have lower contrast, but that should be an intentional choice, made for some obvious reason.)