# How to spot/measure artifacts produced by several rotations of 2-dimensional data?

I am trying to transform dataset to mulitiply its size but preserve its initial random nature.

I have 5-dimensional numerical dataset which represent particles in plane, produced by Monte Carlo simulation. Dataset consists of energy, position(x,y), and direction cosines (x,y) for particles. This is scatter plot of my particle positions I have rotated this plane 5 times and combined results into one new dataset which now has 5 time s more particles.

My question is: Is there a method of statistical analysis which would give me some quantitative results of how much have i disrupted randomness by rotating it ? I am aware of visual artifacts that can be spotted after several rotations (example: if i rotate by 72deg 5 times (up to 360), there should be pentagram-like pattern in scatter plot, for 60 degres 6 times - hexagram-like pattern etc.), but i'm interested in more elegant solution for analysis.

• Could you explain the purpose of the rotations and your particular meaning of "random" in this context? BTW, although you may be using five numbers to represent the values, this is a four dimensional dataset: it samples a vector field in the plane. – whuber Apr 6 at 18:41
• This data represents an acutal beam of particles. By rotating and combining the rotated with the original data i can double the amount of particles in my dataset. This does not affect the energy deposition in material because the energy spectrum is the same, and the profile of the beam is still effectively the same. However, if i do this several times, i'm changing the overall profile. – Stevan Apr 7 at 19:36
• The meaning of random is that these particles are produced in monte carlo simulation. They go through several interactions which have stochastic nature and the result is this dataset which is simply collection of all the particles in one plane with their respective energies and direction cosines. – Stevan Apr 7 at 19:43