## Sunday, April 29, 2012

### Deterministic generation of normally distributed values

I thought of this way to generate a series of numbers with a normal distribution without using any random numbers. First of all consider the numbers 10*pi, 100*pi, 1000*pi, etc... if you consider just the decimal part of each of these they vary uniformly between 0 and 1. *This hasn't been proven but it is believed to be true* Also consider 10*e, 100*e, etc.. with the same notion in mind. I wrote a floor function previously that I'll be using for this post. Then all that remains is plugging those for the two variables U and V into the box-muller transform.
Now my final equation is:
The values for t=1..10:
0.5426654684
0.9042166471
-.2031938572
.1624766993
0.6677675887
0.4311350734
-.1788312781
0.8176724812e-1
-.4680815243
1.275914647
...
it could generate numbers forever but I believe they will tend to a normal distribution. Either that or pi and e aren't as random in their decimal digits as they seem, either way I find it interesting.