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Nickname: Clive Maxfield     Articles(444)     Visits(533485)     Comments(79)     Votes(236)     RSS
There is so much amazingly cool "stuff" to see and do that I'm amazed I find the time to get any real work done. In my blog I will waffle on about the books I'm reading, the projects I'm building, and the weird and wonderful websites I blunder across. Please Email Me if you see anything you think will "tickle my fancy."
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Posted: 06:58:43 PM, 05/05/2014

Applying golden ratio in industrial design


It is no longer surprising to hear that this column relates to my ongoing Bodacious Acoustic Diagnostic Astoundingly Superior Spectromatic (BADASS) Display project. As you may recall, this little beauty is going to boast a 16 x 16 array of tricolored LEDs. In my previous blog on this project, in which we discussed the physical implementation and presentation, I noted that I had spaced out the LEDs more on the horizontal axis than on the vertical axis so as to increase the visual appeal of the display.


My vertical spacing between pixels is 33.33mm. This spacing is fixed because I'm using NeoPixel Strips from Adafruit -- the type with 30 NeoPixels per meter -- with the LEDs controlled by an Arduino Mega boasting an Atmel microcontroller. For my display, I decided to use a multiplication factor of 1.5, thereby giving me a horizontal spacing of 33.33mm * 1.5 ≈ 50mm.


A reader then suggested this:


You might want to consider employing the Golden Ratio (1.618:1 -- close enough for government work) in your rectangular layout. Doing so several times would be even cooler.


Hmm, that's certainly something to think about. In mathematics, two quantities are said to be in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. This is much easier to visualize graphically (well, it would be, wouldn’t it?) as illustrated below:


On the left we see a "golden line," while a "golden rectangle" is shown on the right. If we do the math, as illustrated below, we discover that the golden ratio works out at ≈1.618.


The golden ratio pops up all over the place in nature. For example, it is expressed in the arrangement of branches along the stems of plants, the branching on veins and nerves in animals, the proportions of chemicals in compounds, the geometry of crystals, and… the list goes on.


Many people seem to find things in proportion to the golden radio to be aesthetically pleasing. Based on this, some artists and architects have created their works so as to reflect this proportion (many of the proportions of the Parthenon on Greece are said to exhibit the golden ratio, for example).


Now, I was aware of the golden ratio (What engineer isn’t?), but I've never actually heard about it being employed in industrial design, so I decided to perform a simple experiment. Remember that each of my LEDs is going to be accompanied by a 20mm-diameter brass washer. First, I created an array in which the horizontal and vertical separations between elements were both 33.33mm as illustrated below:


Horizontal separation = 1.0x vertical separation. (Click here to see a full-sized version that you can print out and experiment with yourself.)
Horizontal separation = 1.0x vertical separation.

Next, I made the horizontal spacing 1.5X the vertical spacing (the way I currently have things set up on the BIGASS Display), that is, 33.33mm * 1.5 ≈ 50mm as illustrated below:


Horizontal separation = 1.5x vertical separation. (Click here to see a full-size version that you can print out and experiment with yourself.)
Horizontal separation = 1.5x vertical separation.

Finally, I related the horizontal spacing to the vertical spacing using the golden ratio, that is, 33.33mm * 1.618 ≈ 54mm as illustrated below:


Horizontal separation = 1.6x vertical separation. (Click here to see a full-sized version that you can print out and experiment with yourself.)
Horizontal separation = 1.6x vertical separation.

I then went for a wander around the building to see what people thought. Well, wouldn’t you know it? Almost everyone had gone out for lunch! Happily, I did manage to track down two engineers. I talked to them independently and I didn’t mention anything about golden radios. Just to give them some reference to work from, however, I did explain that this was to be an array of LEDs presenting the spectral information from an audio stream, with the amplitude of the various frequency elements being presented on the vertical axis.


One of the engineers said he preferred the first pattern -- the one with equal horizontal and vertical spacing -- on the basis that one could present more information in a smaller area. Well, that certainly makes sense in an engineering-over-aesthetics sort of way. Interestingly enough, the other engineer said he preferred to have a wider horizontal spacing for visual interest. Furthermore, after glancing back and forth for a while, he said that -- although he couldn’t explain why -- he was more drawn to the last example (the one employing the golden ratio).


The difference between my 1.5 ratio and the golden ratio, which resulted in horizontal separations of 50mm and 54mm, respectively, is only 4mm, but that was enough to persuade this engineer to prefer the golden ratio.


Of course, a sample of two people is statistically meaningless, but it does make you think. I'm not ready to change the layout of my BIGASS Display quite yet (since the thought of re-laying out all 256 LEDs brings tears to my eyes), but I'm not ruling it out either.


As I mentioned earlier, I've never actually heard about the golden ratio being employed in industrial design -- have you? Also, if you have the time, it would be great if you could click the links above, print out the larger versions of my images, perform your own survey amongst your coworkers, and then report your findings back here. Based on these results, I will decide if a change in direction is on the cards for my BIGASS display.

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