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(click here to skip the UK-specific political anecdote & get straight to the art)

As a child growing up in Thatcher’s Britain I remember vividly when the political landscape changed. The new party were such a departure from the previous decade they even had the word “new” in the title (we all overlooked the other connotation of “labour”, we were that eager for change). I recall celebrating the results of the general election by going out & buying a copy of James Gurney’s Dinotopia. New Labour quickly disappointed but that book never did.

As someone who is quite disparaging of much of the modern art movement it was a relief to find someone painting the fantasy genre without throwing out the rule book when it comes to realism – just because the subject is imaginary doesn’t mean that it deserves special pleading for how light bounces off it. Gurney made it all seem so easy. I had hundreds of art questions that nobody seemed to be answering:

1) How blurry should the edges of my shadows be and why?
2) How much light should reflect off objects close to the source and how much less light should reflect off things further away.
3) If I know the sky colour, ground colour, & the depth of a puddle what shade should the water reflect?
4) how do I predict the colour of the overlap of two leaves if I know their thickness, distance, and the colour of the light shining through them?

Most of the artists I met were from the school of observational art, where art theory questions like these made little sense: why would you need to know how much more the fingertips are illuminated by a hand-held candle than the chest, when you can just compare the fingertips & chest of the life model in front of you? I ended up getting a feel for some of these measurements by trial and error without really knowing why they work. My brain knew what worked and what didn’t so I just kept tinkering with the results but the answer to these and many other riddles eluded me. Every now and then in my travels I come across a blog post or book chapter that touches upon these sorts of subjects in part and they’re like little treasure troves when they do – firing off all sorts of imaginative musings. I’d like to share two of them with you today.

The Blur Factor
I found this while rummaging through the tutorials on ConceptArt. I’ll find the link and put it up later – it will need to be re-found. The article was a Victorian-style manuscript in PDF form discussing the science of colour and light. One of the subjects covered was how shadows blur:

We tend to think of light waves radiating out of a light source the way petals radiate out of the head of a flower. This is too simplistic a scenario. Light travels out from a light source in every direction. This is most evident in the blurriness of shadows. To find out how sharp or fuzzy your shadow would be with any given light source or object, try drawing crossed guidelines from the edges of your light source to the area the shadow is cast – crossing at the edge of the object casting the shadow (see diagram). You will see that the less oblique the angle, the larger the light source, and the further the shadow is thrown, the blurrier the shadows get.

I was blown away by this simple revelation, and the next one’s even better.

The Inverse Square Law
This one came from none other than James Gurney in his recent work Colour and Light (sorry James, I have to use the UK spelling even though it’s your title).

Suppose I see a painting of a man walking along the street. There’s light bouncing off his shiny bald head so I know there’s a light source above him. I see the same light reflected in his patent leather shoes too – the light is a quarter as bright on the shoes as it is on his pate. My brain knows without understanding why that the light source is about four metres off the ground. My brain is subconsciously aware of the effects of the inverse square law of light, which states that the brightness of a light reflected on an area diminishes at a rate of distance from light source squared. Put simply: a light hitting something 1 metre away will be 1/4 as bright 2 metres away; 1/9 as bright 3 metres away and so on. The light on the man’s shoes in the painting was 4 metres from the bulb, so 4m squared (16) times weaker than it was a metre away. The light on his head was 2 metres from the bulb so 2m squared (4) times weaker than a metre away – 4 x stronger than the shoe reflection.

Do you really need to know this stuff? Yes and no: if the difference in light had been different our brains would have just made a different mental note of how far away the light source was off-canvas but the brain knows when something should be visible on canvas too. Get the proportions wrong and your principle subject is being illuminated by an object on the page that clearly isn’t a light source, or your subject is being lit by multiple light sources shining from their own isolated dimension without any relation to one-another. You’ll look at your finished piece and know that something’s wrong – your brain just won’t accept it as real, the suspension of disbelief has been broken.

I may add another diagram to the inverse square law section if you folks feel it’s needed.

I’m sure there are many more sources out there that touch on the application of maths in art, I’d love to hear of your experiences.