Editing Creating the Simulation Environment (section)

===Algorithm for an Arbitrary Probability Distribution===

Often when generating particles in a simulation, particle energies, directions, and other properties are governed by a probability distribution. This being the case, a simple algorithm for applying arbitrary probability functions in a program is presented below. It should be noted that there are other methods to apply probability distributions and this is not a particularly efficient one, so if a simulation is large it may be beneficial to find another method. However, the method presented is very simple to apply, and thus is a good option for projects when efficiency is not a major concern.

 (0) Begin loop
 (1) Choose a random x value
 (2) Calculate P(x) of the randomly chosen value (must be adjusted, see note below)
 (3) Choose a random value between zero and one (uniformRand() function)
 (4) Compare the random number with the probability of the x value in question
      (4.a) If P(x) > uniRand : keep the value x (exit loop)
      (4.b) If P(x) < uniRand : discard the value of x (repeat the loop)

It is of great important the maximum value of P(x), where x is the classical variable, is one. To achieve this, find the value of x where P(x) is at its maximum, x_max, and divide each P(x) in the algorithm by P(x_max).

Using this method the algorithm will return x values in accordance with the defined probability distribution.