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.