We all know about the Normal distribution and its ubiquity in all kind of natural phenomena or observations. But there is another law of numbers which does not get much attention but pops up everywhere — from nations’ population to stock market volumes to the domain of universal physical constants.

Benford’s Law, also known as the Law of First Digits, the Phenomenon of Significant Digits, or the Law of Anomalous Numbers is the finding that the first digits (or numerals to be exact) of the numbers found in series of records of the most varied sources do not display a uniform distribution, but rather are arranged in such a way that the digit “1” is the most frequent, followed by “2”, “3”, and so in a successively decreasing manner down to “9”.

The distribution of first digits should follow the pattern in the image below:

This distribution is specifically:

Digit   Benford [%]
=====   ===========
1       30.10
2       17.61
3       12.49
4       09.69
5       07.92
6       06.69
7       05.80
8       05.12
9       04.58

This project is a .NET console app project to play with Benford's Law on images and a text file with numeric values. You can fill the text file with a large, random data set from most any source to see if the data follows this law and if not, implying the data has been artificially altered. Likewise you can put a set of images (*.jpg, *.tiff) into the images folder to analyze the pixel values in them. If the image results deviate from the law it could mean the image has been processed or altered.