Generating 2-D random unit steps

  1. Choose a random number in the range and then set .

  2. Choose a random value for in the range and (choose the sign randomly too).

  3. Choose separate random values for in the range (but not ). Normalize so that the step size is 1.

  4. Choose a direction (N, E, S, W) randomly as the step direction (no trigonometric functions are then needed). Note, choosing one of four directions is equivalent to choosing a random interger on [0,3].

  5. Choose separate random values in the range . Although the step size is generally not 1, it becomes 1 on the average.


Although all these methods seem to be reasonable, only the last one gives us good results when we are dealing with a large number of steps.


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