The properties of colour and beyond

Christopher Alexander did not stop at the fundamental properties of forms but also tried to find fundamental properties in other aspects of design. He studied colour to a great extent and surfaced 11 properties. Try as he might, Christopher Alexander claimed he could not find a way to map the properties of colour to the existing 15 properties of forms directly[NoO4-04]. Instead, he did so with some overlaps.

  1. Hierarchy of Colours
    (levels of scale)
  2. Colours Create Light Together
    (positive space)
    (alternating repetition)
  3. Contrast of Light and Dark
    (contrast)
  4. Mutual Embedding
    (deep interlock and ambiguity)
  5. Boundaries and Hairlines
    (boundaries)
  6. Sequence of Linked Colour Pairs
    (gradients)
    (the void)
  7. Families of Colour
    (echoes)
  8. Colour Variation
    (roughness)
  9. Intensity and Clarity of Individual Colour
    (strong centres)
    (good shape)
  10. Subdued Brilliance
    (simplicity and inner calm)
    (not-separateness)
  11. Colour Depends on Geometry
    (local symmetries)

— Christopher Alexander, The Nature of Order, Book 4[NoO4-04], p. 173.

There are fewer properties of colours than there are of forms, but they cover a very similar set of attributes. Colours are used in various ways, from images to photo composition to wallcoverings to the exterior colouring of houses, cars, and sites. Whatever the usage of colour, it is seen. A web page uses colour, and so does a painting in a gallery. They may not be in the same league, but perhaps that merely depends on the painting and the site. In each case, the spectator of the colour views a scene in which the colour has its chance to shine. So, rather than talk about buildings, paintings, rugs, or objects, I will refer to the entire set of observable ‘colourables’ as scenes.

First, I will attempt to describe a few of the properties as I did for the 15 properties of form. I won’t do that for all the properties of colour, as you don’t need to know all of them to understand how they are similar and how they differ.

Hierarchy of Colours

Hierarchy of Colours is introduced in The Nature of Order, Book 4[NoO4-04] on page 174.

As with levels of scale, a scene has proportions of colour. With levels of scale, identifying the proper proportions relies on the repeated or contrasting parts. With colour, each pigment’s hue, saturation and brightness will affect how much of the image it should cover. The hierarchy of colours is numerical, based on the area of the image that is covered by each colour[NoO4-04]. Invariably, a good ratio is not an equal ratio. Symmetry is never relaxed with colour.

I also note how a heavy colour will appear to take up more space even if it consumes slightly less. To balance a scene, a weighty colour must either dominate or recede. ‘Heavy’ does not refer to dark but always means an imposing colour. I suggest a brilliant green is a heavier colour than a pale pink. I also note that colour weight is very often evaluated relative to the other colours in a scene, so a strong blue in one scene recedes in another by lack of contrast.

The ratios, like with levels of scale, are found by observation and adjusted into place. They are often proportional, in the realms of 2:1 to 5:1, but also include sub-sequences of ratios. A good combination of red, blue, and yellow might be 7:4:1, with the yellow so intensely brilliant, it must be tamed and surrounded by the closer weighted blue and red[NoO4-04]. But colours can work even when they are at more extreme ratios than the physical, as the presence of a minimal quantity of a vibrant colour can impact the entire image by contrast. So, you can often see good combinations where the ratio is as high as 20:1. But images muddied by too many colours have no intense primary. Some colour needs to be the dominant one. In the remaining space, another colour needs to dominate that too.

But dominating the other colours usually leads to having less meaning. Typically, the rarer colours control the message of the scene. The small amount of black or yellow in a light or dark background will dominate the structure, if not its overall hue. This juxtaposition, which defines the visible structure, leads to the next property.

Colours Create Light Together

Colours Create Light Together is introduced in The Nature of Order, Book 4[NoO4-04] on page 179.

A colour on its own says little. For it to have meaning or convey a sense of softness, harshness, warmth, or serenity, it must be brought together with another colour. The obvious case we can think of is the orange and teal colour grading in many modern films. The need to make flesh tones pop led to many movies being recorded and colour-graded to a uniform blue–orange wash. These complementary colours work well to increase the vibrance in each other, even when we have already seen a hundred overly graded productions. They are fundamental colour theory contrasts of hue. But creating light does not have to be about contrast; just what makes an impact by relation. Some colours are raised in their value for a scene by a nearby colour acting to reinforce how deliberate or nuanced the choice was. The difference between red and gold is not so huge, but so much artwork with red–gold colour exists because the red reinforces how pure the gold is, and the gold reminds us of how warm red is when next to an orange or yellow colour.

Christopher Alexander puts this property against positive space[NoO4-04], seemingly because a colour creates a field in which another colour ‘shines’. But he also connects it to alternating repetition. This link reminds us that contrast is the element, not the colours that complement each other. It’s the enrichment that has been brought about.

It’s worth noting that colours support each other, even when they are nearby neighbours, as long as their proportions are right and they have some other way to cast light on each other. This leads to the next property.

Contrast of Dark and Light

Contrast of Dark and Light is introduced in The Nature of Order, Book 4[NoO4-04] on page 186.

Two colours that generally work well together can muddy themselves by not taking care of light and dark[NoO4-04]. There’s hue and saturation in colours, but there’s also brightness. Each primary colour has a natural level of lightness. Green is the brightest, then red, then blue. If you intended to create a nice contrast with red and green but brought the green down to a darker shade, the complement would be weaker. Some artists would call this working with values, not colour. The concept is simply that an image should work as well in black and white as when colour is perceived.

What this means for us

Rather than go into detail on all the remaining properties, you have an idea of the contents of each of them, and you can begin to see how these connect to the fundamental properties of form. The properties of colour are similar, but even when they are very similar, some differences stand out. This makes sense, as how we evaluate these properties has so much to do with what looks natural, and what looks natural is that which naturally occurs.

I believe, in domains of perception by humans, there will be other sets of fundamental properties. Immediately, we may assume there are properties for music, food, art, dance, poetry, and prose. I would not want anyone to presume these lists are final, but I present them here as examples of what we might find if we were to look for properties in other domains.

  • Music — Western world variety

    • Hierarchy of Cadences: almost levels of scale, but closer to echoes and alternating repetition but also local symmetries.
    • Harmony and Discord: contrast and gradient but also not-separateness.
    • Repetition with Variation: not roughness or alternating repetition, but strong centres or levels of scale or gradient.
    • Symmetry of Structure: like echoes and local symmetries.
    • Dynamics: like contrast and the void.
    • Gradient of Complexity: gradients and levels of scale.
    • Echoes of Motif: echoes, but also alternating repetition and simplicity and inner calm.
    • Segments in Time: like boundaries but also some of deep interlock.
    • Key: simplicity and inner calm, good shape, and not-separateness.
    • Clarity: positive space (not having three bass guitars and a singer).
  • Food

    • Contrast: just one or two at most of each food group, but unrelated to the contrast property of forms. This is closer to strong centres.
    • Full Palate: the presence of most elements in the meal, if not each part of a meal, bringing balance. Good shape might be the closest property of forms.
    • Differing complexity: like levels of scale or gradients for the elements of a meal. If everything is trying hard to be the centrepiece of the plate, nothing is.
    • Separate but complementary: deep interlock and ambiguity by making foods that work well together because they offset each other’s weaknesses (a salty meat with a starchy side, a creamy sauce on dry food, or a tangy wet mixture, such as in lasagne).
    • Sequence of granularity: chunks of something in grains or sauce, not two types of chunky things together or two sauces mixing, but salads often break this.
  • Art

    • All the same properties as architecture. This one sticks out to me as it’s the same for any art-form from weaving (Turkish rugs) to sculpture. Art is part of the lived visual domain so shares all the properties of forms as they often are forms and compound ones at that.
  • Dance

    • Complementary Top and Bottom Half
    • Lead and Follow
    • Rhythm at Many Scales
    • Contrast with or against Co-dancers
    • In Place, Around, Along, Reverse
    • Flow and Lines
    • Balance and Energy
  • Poetry or prose

    • Hierarchy of Subject
    • Reveal/Guide Alternation: sequences of pique interest, guide reasoning, reveal conclusion.
    • Variation at All Levels: line length, paragraph length, paragraph and line structure.
    • Repetition and Avoidance of Repetition: in words or style, repetition is a property of its own, but repeating a lot is a mess.
    • Level of Language audience-specific level of wording, keeping it consistent.

It may be my inability to produce good properties for these domains, but I have noticed something: music is not intensely full of properties. Many animals also use a dance or sound to indicate things, so some properties exist. However, they don’t appear to be fundamental. They are almost idiomatic of a species. We know music has changed over the centuries. Different cultures have different forms in their compositions. The set of properties of music is likely stronger than for prose and poetry but much weaker than for art.

Food is also weaker. This may be because we’ve only been making meals to satisfy the eyes for a few thousand years; before those times, perhaps food was just food. Are cakes and courses a relatively recent invention in an evolutionary time frame? Art is a strong contender for properties because it stems from the same roots as architecture. But dance is again only middling. Many animals dance, and we’ve likely been dancing as a species since before we had words to describe it. But I believe it’s idiomatic to a species, not a natural outpouring of the environment in which we exist.

As each domain moves further from our evolutionary basis, it loses the chance for us to have found or sought universal properties. This does not bode well for code or organisational structures.

Is there a reason these fundamental properties exist in differing strengths in these other domains? Why is it that the further we step away from our evolution, the weaker the properties seem to be?

Perhaps the answer is that 15 fundamental properties are fundamental to growth and adaptation. Similar fundamental properties will not exist where the natural reification of a compound is not via a sequence of steps. The fundamental properties only exist because they match the process by which things reach their final form. The properties relating to this unfolding process exist because these forms still exist after millions of iterations of unfolding processes.

Why do I suggest this? Because of the quality without a name. We judge with our evolved sense of quality, our innate sense of what is right. This sense of quality has been trained over millions of years to match what is supportive in the environment in which it was taught. These properties list the metrics our evolved self uses to determine what is good. I believe Christopher Alexander discovered the scientific metrics of quality for humans.

But there is some strange hope that some fundamental properties can be found outside the elements of our ancient world. For example, prose does not appear to be a naturally emerging element of the universe, so any set of fundamental properties can, at best, only loosely mimic the true fundamental properties. And yet, even in this domain, we have some evidence of the quality without a name.

Robert M. Pirsig wrote about the aspect of quality in rhetoric. He claimed his students could read two passages and know which was better[ZatAoMM74], even if they did not know why. And by know, he meant they would agree with him, but in essence, this is the same as Christopher Alexander’s experiments discovering overwhelming agreement in his test subjects.

Robert M. Pirsig explored the elements of quality much further in his second book, building a picture of how it works. He explained how quality is fundamental, and the sense of it preceded our development of analysis methods[Lila91]. To use his terms, we perceive quality without defining it (he called this ‘dynamic quality’) and only then name it, quantify it, and build our analysis methods and reasons around it (he called this ‘static quality’). But it’s all the same quality all the time.

If there are fundamental properties of prose, then this disproves any theory stating they only exist for something ancient and evolutionary. It also suggests the unfolding nature may not be required and may be specific to only some domains. Let’s assume the fundamental properties of architecture and art result from an unfolding process of nature. In that case, we should look for the fundamental properties in whatever process creates good quality in that domain.

We should be able to find fundamental properties of organisational structure or anything else humans can accurately compare. After all, we know the difference between a good-feeling organisation and a less-than-good one. Finding those fundamental properties is a complex task that will take a long time, but each domain will have some and will work to guide the production of a better outcome.

But for domains where we can’t trust human instincts, such as those where the environment and fitness are alien to us, we must first find the measure—the fitness function. Code has a growth process, but we can’t easily tell good code from bad. Finding the properties here will take more effort. A better, healthier process should lead to the properties, and if we were to chance upon the properties first, they could lead to the process. How we find either is still up for debate.