# Can we see shape of normal curve somewhere in nature?

I do not want to know if some phenomena in nature have normal distribution, but whether we can somewhere see shape of normal curve as we can see it for example in Galton box. See this figure from Wikipedia.

Note that many mathematical shapes or curves are directly seen in nature, for example golden mean and logarithmic spiral can be found in snails.

First naive answer is whether nonskewed hills would often "fit" normal distribution :-).

• This example is a favorite of mine. Commented Oct 10, 2012 at 12:23
• @cardinal That's an intriguing example, but wear on steps is highly unlikely to be at all Normal. In fact, it would be a puzzle if it were. The CLT might possibly be invoked to describe horizontal variation in where people walk, but that will not lead to a Gaussian shape in the wear on the step.
– whuber
Commented Oct 10, 2012 at 14:40
• Many years ago, the East Wing of the National Gallery of Art in Washington DC had a beautiful (and unintentional) example of a normal distribution showing on an exterior wall where two exterior walls met at a 45-degree angle instead of the usual 90-degree angle. People presumably had touched the edge to see if it felt sharp, and the smudges from their fingers left a stain on the wall which showed as a bell curve (rotated 90 degrees clockwise) at about chest height. On a more recent visit, I found that the exterior walls had been cleaned and the smudges had disappeared. Commented Oct 10, 2012 at 15:02
• I have not seen wear like that, @cardinal. In your model the wear would be much flatter near the peak than a Gaussian and--of course--would be confined within natural limits, unlike any Gaussian. (The latter is not such a big deal because we cannot demand that the Gaussian fit perfectly.) The wear on steps I have examined is far flatter than a Gaussian. (Often it is bimodal, too, because most long-lived stairs have been used in both the up and down directions.) A better model would be a convolution of a fairly narrow Gaussian with a uniform distribution.
– whuber
Commented Oct 10, 2012 at 15:16
• This blog post shows the example that @Dilip mentions as well as one example of wearing patterns on stone steps (with links to other pictures of wear patterns). Some might find it interesting. Commented Oct 10, 2012 at 17:20