Sunday, 13 November 2011

Divine geometry

Ok, eveyone take a deep breath, lets do some mathematics :) Before you all start clicking away from here, lets bring it straight back to art ! I'm sure you're all familiar with the rule of thirds in composition and design. The rule is just a very rough approximation of the classical golden section, a proportion based on a mathematical constant (phi). Phi can be calculated accurately from the Fibonacci sequence of numbers, a sequence that occurs regularly in nature, such as in the distances between the petals of some flowers. It also occurs in other examples of artistic beauty, notably music. Many famous works of classical art and architecture as well as things of natural beauty from the Great Creator himself have proportions that are based around the golden section, which approximates to the ratio of 1 to 1.618. The rule of thirds by comparison would give the ratio of 1 to 1.5. Not a massive difference, but is it significant enough to make or break a composition ?


Are you still there LOL. So, I thought I'd put it all to practice. I took out a steel rule and a calculator, measured the height and width of my working area of paper, calculated the divine proportions accordingly, and drew a horizontal and vertical line on the paper at the calculated positions. The base of the tall tree to the right of the painting is at the intersection of those two lines. I could have chosen any of four possible positions for the focal point, but I chose bottom right which gives more sky than land and should also lead the eye from left to right (hopefully). Has it made a difference to my composition, is it more hamonious, is it more pleasing to the eye or would it have been just as good if I'd used the rule of thirds or perhaps simply done it 'by eye' - as I usually do ?  Hmmm ....

Happy painting and a glorious Sunday to you all :)
 
Lake at Dusk, watercolour on Arches 300gsm/140lb Rough, 23cm x 31cm/9" x 12"

Postscript:

And by popular request, and just for comparison, here's a cropped image in which the base of the tree has been moved to lie at the intersection of the lines created by using the rule of thirds. Thanks very much to Keith for coming up with this idea - it saved me having to paint it again ;)

46 comments:

  1. Your painting is beautiful and I think quite like you have explained. ;-) Beautiful, soft grey green colours. The air is made serene and that can you see back in the water. Brilliant!

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  2. I followed easily - but then I am a maths whizzkid :lol:

    The painting looks gorgeous, the palette you've chosen beautiful.
    Only you can answer the questions you asked - does it feel more harmonious to you?
    You might have a natural gift to see all these by eye.. and practice gives you that eye, anyway.

    Try the same consigning the steel rule to the bin and see what you think then :)

    I think its a serene beauty ! xx

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  3. Great explanation of the rule of thirds. I also usually just do it by eye but it's clearly worth being a nit more exact about it. Lovely painting - very cool and serene.

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  4. Beautiful, magical painting, Michael and very well explained golden section rules. I would like, however, to have the other versions for comparison, have you done those too?

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  5. Interesting stuff, Michael! It does look serene and harmonious to me. But I just trust my eye and hope for the best. Wonderful painting and soft colours!
    BTW, have you ever heard of paint brand Old Holland? Found it recently, the factory is not far from my town.

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  6. Thank you all very much ladies!

    Renske - I really enjoyed this scene and kept it as serene as I could so I'm pleased you like it too :)

    Pat - running your own business as you do, you must love or hate numbers! Natural gift ... perhaps, but we ALL have that gift :)

    Vandy - it was an interesting experiment but I think I'll stick to doing it by eye in the future too. The cool palette really worked but was certainly not by design :)

    Sharon - oh boy, now I've started something. Perhaps one for a later post ;-) The interesting thing is it looks pretty neat upside down too, which would perhaps not be the case if I had done it less mathematically :)

    Judy - I normally just trust my eye too :) Yes, I have heard of Old Holland. I don't know much about them but I know they got reviewed by Bruce MacEvoy on www.handprint.com :)

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  7. Very interesting introduction, Micheal. Thanks to you I have realized that I had never followed this rule(s).....
    In my opinion your painting is really beautiful, even if I can not give an answer to your questions. Ciao!

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  8. I trust my eye, too. But it is interesting to see your result. I'd prefer more "no-rules" chaos, I think)).

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  9. I trust my eyes also. When I was in college we did have to figure these things out. I even had a class where we had to build a special tool, but I'm afraid until this post I had completely forgotten about that. I know what is pleasing to my:) Lovely painting!

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  10. Thank you very much, Tito. It was interesting to test the theory but I think we know when we get things right and should just follow our instincts :)

    Hi Irina and thank you very much. My art is chaotic enough so it was nice to plan and bring some order to the process for once :O)

    Hi Carrie. Thank you very much for your comment. I came at this from the 'other side' so to speak - as a mathematician practising art rather than an artist practising math. For me, the only rule is there are no rules to art :)

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  11. Your painting is really beautiful and soothing to the eye, but I personally would never be able to follow these rules. To me watercolor is freedom , instinct and emotion all mixed with a little something unexpected due to the no control of the media :-)
    Wish you a great week!

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  12. About Old Holland: very bad review, I saw. So I'd better not buy it. Thanks for the info!

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  13. I agree with Jane and other comments here.
    Painting must be free, the move must come from the heart, the feelings of the instant. Nothing to do with maths ! That's my point of view.
    By the way, I like very much your watercolor, the soft light and colors. Very good work indeed.

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  14. Michael, math is something I never could quite get...
    When it comes to painting I do follow (or try) to follow the thirds... is it also called the Golden Mean? or is that something else... OH, no I need a math teacher... lol ! BJ

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  15. Wow! I know the rule of thirds but not the calculations behind it, lol! My maths is shocking so it's a good job I didn't try to work it out! Anyway, there are reasons behind that rule and here it is for all to see. It's lovely! :0)

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  16. Hi Jane, thank you very much. I have to follow rules in my job as a software engineer every day but, like you, I prefer to use my instinct to do what I love the most - paint :)

    Hi again Judy. No problems, glad to help. I think their oil paints do get good reviews though. I say stick with the Talens but maybe try a few Schmincke and Maimeri too. They should be readily available over there :)

    Hi Hoghart, I agree completely, painting must come from the heart. These rules are really just guidelines and we can keep to them strictly, totally ignore them or meander from them. Thank you for your kind comments:)

    Hi BJ. Thank you! Yes the Golden Mean is the same thing. Leonardo da Vinci used it to paint the Last Supper apparently. If it's good enough for him ... but of course he was an engineer too - a brilliant one! By the way, you're brilliant with figures - artistically speaking that is :)

    Hi Sandra. Thank you for your lovely comment. If you need to see a proof with all the calculations I can send it to you :) Shouldn't you be finishing that bear ?

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  17. Your painting has a nice misty, serene atmosphere and its proportions look right. I don't think that a ratio of 1.5 vs 1.6 makes a visible difference to the human eye.
    BTW I have a very similar profession to yours, so you can't scare me with math ;) But like the rest, I think it's best not to follow strict rules.

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  18. Thank you very much Blaga and 'High Five' to a fellow scientist! My maths is not that strong so there's no chance of scaring you :) It may have been more revealing to have posted this without saying what I did and then to do a similar scene by eye. The jury is still out on this one :)

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  19. Good morning Michael for the second time. My first comment disappeared again. It was a long one so this is going to be short i`m afraid. Brilliant painting my friend. All the best.
    Vic.

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  20. Good afternoon Vic. Thank you for your lovely comment and for persevering to comment again! That keeps happening to me too my friend. All the best, Michael.

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  21. So is this what is meant by "Painting by numbers"? LOL. Great post Michael. ;-)

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  22. ROFL ... now THAT would have been a brilliant title, John. :) Thank you for your kind comment too !

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  23. You lost me at the word Fibonacci! But I like what you did with your composition! Please don't check the dimensions on mine :)

    The reflections are wonderful, and the painting is so calm and peaceful.. Fibonacci would be proud! :)

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  24. Interestingly, I would prefer to have the tree lower down and maybe a little more to the right. I've measured the cropped image and that would bring it almost exactly to the Rule of Thirds point.

    I wonder whether that makes me unusual. It would be interesting to know whether any studies have been done on the range of preferences in a population.

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  25. Hi Rose. Thank you very much for your lovely comments. I think this was a fun thing to do but I'll be putting my rule away so now worries :)

    Hi Keith. Thank you for your comment - super idea. I was toying with the idea of cropping it so I measured from the left and top to the base of the tree, scaled up by 3/2 to give a new bottom right hand corner, rescanned it and cropped it to the new marks. You can see the result underneath the original :)

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  26. I think the composition will work much better if the painting is cropped and suggest these proportions.Reduce the depth by cropping the bottom by one third of the distance between the "horizon" (water's edge treeline}and the bottom of the painting. Then reduce the width by one half the distance measured between the centre of the tall tree and the right hand edge of the painting. Best wishes.

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  27. Hi Roger - lovely to see you out and about again. I've just tried your suggestion quickly and I have to agree that it does give a nice composition. Thanks for your expert eye and advice on this one. Best wishes to you too.

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  28. My mind glazed over with the 1st sentence but I hung on in there. I think they both work well, but prefer the second. That's a good thing as I could never do the maths to do a painting by the correct mathematical thingy.

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  29. Thank you very much , Sue! Damn, I guess you won't be interested in seeing my calculator collection then ? ;)

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  30. I am afraid that you lost me with all of your math talk. I am no math whiz for sure! But I find it interesting to approach a painting this way and I do think the end result is very pleasing. I also really love the look of your tree line. Beautifully suggested. :)

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  31. I quite often use this rule when scribbling out thumbnails for compositions.... I don't always follow it but it can be really useful. The recession in this painting has worked really well.

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  32. Hi Crystal! LOL. Thank you very much for your lovely comment. I used Perylene Green (PBk31)for the trees, it's a wonderful moody pigment.

    Good morning, Lisa! Thank you very much for your lovely comment. The tapering zig zag in the clouds and reflection really helped the recession I think.

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  33. Michael, another winner from you. How lovely is this painting. Sometimes life can be so hectic and you have captured a peaceful moment that we all need at times. I must remember to come back to this painting.

    Great work Michael.

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  34. Why thank you very much, Joan, what a lovely comment! I hope to get round to seeing your latest post soon. Life is a bit hectic for me at the moment too :)

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  35. is a very serene and beautiful landscape, Michael : )

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  36. Thank you, Sadeu, for your lovely comment :-)

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  37. Dear Michael, I think there is plenty of harmony in both images. The rules you have explained have been widely followed by the painters of the past (at least, I am sure that Renaissance architects have strictly followed rules like these). I think our eyes have got used to these kind of proportions, and maybe we often use them unconsciously. Anyway, I also like the colours and the soft, blurred outline of the distant landscape in your beautiful painting!
    Have a nice weekend!

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  38. Hi Lucia! Thank you so very much for your lovely comments. It is a classical construction in architecture as well as art. You must know many examples but I read that the proportions of the facade of Notre Dame are based around the Golden Section. I think both compositions work equally well too :-)

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  39. I think that the second works better. Sometimes I follow the rules, sometimes no, but rules can help to kept the eyes of the viewer. Have a nice day.

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  40. Hi BrandNewStudio/Skizo! Thank you for stopping by and for your kind comment!

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  41. Michael, it's a very lovely picture however, though I prefer the golden rule one. Not that I use it, I'm afraid I'm very instinctive about composition. One thing I'm terribly envious about your blog is the amount of comments you get!!!Lucky blogger...

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  42. Hi Concetta. Thank you for your kind comments. This is the first time, and probably the last time too, that I use a ruler and calculator for my art. I normally use my instinct too. It seems to work the majority of the time ;)

    LOL about being a lucky Blogger! I can't believe how many lovely people do comment on my blog sometimes. However, I bet you aren't half as envious as I am of your blog - you are such a fabulous artist :)

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No silly verification words here - all comments are appreciated! Thank you :)