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When speaking with a non-programmer friend, I happened to mention the concept of "beautiful code" and she wanted to understand what that meant, but I was at a bit of a loss as to how to explain it to someone who would have no context whatsoever.
When all code looks like gibberish to someone anyways, how can you explain what makes one piece of code prettier than another? Analogies could be useful too.
Language analogy
Think of your most favorite story. It is probably beautifully written. To a non-English speaker, just because they can't understand it or comprehend why it is beautiful doesn't detract from its beauty.
Construction analogy
Consider a shoddily built house. It has doors and windows that are obviously bricked over. The mortar is cracked in one corner where the foundation was insufficient. And no one can understand why there is a stairwell leading up to a 2nd floor that doesn't exist. The toilet is built next to the kitchen with no exhaust fan and situated such that the prevailing winds will blow the nasty bog odors through the rest of the house. The chimney from the open fireplace is 5cm away from some wood, ready to catch fire.
Contrast that with a house where everything is where it should be, it is low maintenance, perfectly insulated so that a bit of solar heat will keep it warm in winter, energy is recovered from the ventilation, so you have both fresh air, comfortable temperature and negligible power bills. It is built of non-flammable materials so that it can't burn down from a fire. It will withstand a 9.0 earthquake and an F5 tornado. It only costs 30% more to build than the other house, but will pay the difference off in 5 years. And it is aesthetically pleasing.
The GUI is like the outward appearance of a house. A user can recognize beauty in a GUI, just like they can appreciate a beautiful house. But perhaps even more importantly, the real beauty in the design in both houses and programs are the things that are invisible to the uninitiated, but important or nice to have regardless.
Think about a car.
Most of us look at the car, and can only see the body. If someone repairs some dings and puts a new paint job on the car, it will look much more beautiful. It's basically the same car, but that is all that we see.
A mechanic opens up the car, and looks at the engine. They see how good that engine is. They see that everything is arranged to be easy to get at, maintain, and work on. They see the parts and know how well designed it was. To an experienced mechanic, the engine of a well-maintained high quality car becomes a thing of beauty. They can't explain to you what makes it beautiful, but their notion of beauty is likely to translate into lower maintenance costs, a longer car lifespan and better performance. All of this adds to the worth of that car, even though you can't see it.
When you look at a website, or an application, you're looking at it like most of us see cars. When I look at code I'm looking at it like the mechanic looks at the engine of the car. You can never experience the beauty of that code like I do, it is literally invisible to you. But that beauty is important just like the mechanic's beauty is. It determines how well that software runs, what kinds of problems it will have, how easily the software can be improved, and so on. All of this adds to the worth of that software, even though you can't see it.
All of the code present, is required, and none of it requires explanation.
I would refer to poetry:
A well-written poem have a different feel to it than an extract from a badly-translated manual about the same subject.
Coding problems are about conceptualization, so beautiful code represents a remarkable conceptualization of the problem.
For example, we like it when one problem can be reduced to an existing solved problem, lending insight into the nature of the problem itself.
Sometimes a re-conceptualization of the problem can make it seem so easy; we speak of elegant solutions that require simple tricks that simplify a difficult task.
To me, the Quicksort is a beautiful example: pick a random element from an array, and then compare every other element in the array to it; if the number is less than it, put it in pile A; if the number is greater than it, put it in pile B. Now, by the triangle inequality, no element in pile A will ever need to be compared to any element in pile B. Recurse on A and B, and you're done.
No non-trivial code can be perfect because perfect code requires simultaneously satisfying goals that often conflict. Beautiful code, therefore, balances all the important attributes perfectly for the task at hand and comes closer to satisfying all of these simultaneously than most would think possible. In no particular order:
Jackson Pollock paintings are an example of something beautiful to some and gibberish to others.
If the person is well versed in mathematics, I like comparing beautiful code to an elegant solution to a problem.
Some aspects of good code is:
To me the language(s) are my tools.
And like any craftsman, I prefer my tools to be in mint condition.
The better the condition of the code, regarding clarity of concept, maintainability and readability. the better the code.
So for me, reading well written code is like opening a toolbox with well crafted tools.
I have used this analogy a couple of times with success. Especially people with a more practical or artistic background seems to understand the concept of clean/beautiful code this way.
I think it depends what you mean by beautiful code.
To me, code is beautiful when it’s readable. Aside from possible issues with programming concepts, a layman could read and, at least at a high level, understand what the code is doing.
As some other answers have discussed, code can also be beautiful in the sense that it achieves complex functionality by combining a couple of simple concepts. Not sure what sort of analogy would be best to explain that to a non-programmer, it depends on the layman. Puzzle toys come to mind, like the NeoCube.
In my humble and personal opinion, beautiful code is like a good novel book:
It's like a lean mean company where everybody knows their role, it's easy to figure out who is good at what, and there's no duplication of effort
Vs.
Office Space where mediocrity is championed, three managers have nothing better to do than bug you about TPS reports, the !@#$ing FAX MACHINE NEVER WORKS!!! and any given employee might only get about 15 minutes of actual work done a week. An employee might not even technically work there anymore because somebody forgot to fire him (it's hard to tell really because nobody works efficiently and it's hard to evaluate what they're trying to accomplish). And to get anything practical done requires navigating an absurdly over-complicated system that somebody read about and thought would look neat-o on their resume even though it doesn't actually solve a problem they had.
There is no "beautiful code", there are "elegant algorithms" and "elegant designs". Design can be understood by non programmers.
I hate programmers who argue about "beautiful code", because one way or another, they either doesn't really know how an interpreter or a compiler will digest it and what the machine will do, so it's more like a children showing his mom how wonderful his story is, but really, it's not.
Do you explain people why a nice picture is nice? No. You show them the picture (because, you know, a picture says more than 1000 words). So the best is, to show them a small piece of code that is really elegant, beautiful, perfect (and maybe as comparison how Joe Average would have coded it).
