Noise-spheres

FIGURE 31.2. Noise-sphere for the Cliff RNG. No particular unwanted correlations are evident,... 

Figure 31.2 (discussed in more detail in the next section) indicates that the Cliff RNG produces essentially uncorrelated numbers, because no particular features are evident in the collection of little spheres. As a counterexample, examine the noise-sphere in Figure 31.3, which omits the 100 from the expression 100 x log(A ) for the Cliff RNG. The nonindependence of the numbers is clearly seen. In the next section. 

FIGURE 31.3. Noise-sphere for a bad random number generator. 

I describe the noise-sphere and further suggest its usefulness as a simple way to check the quality of random number generators. 

To produce the noise-sphere figures, simply map the output of an RNG to the position of spheres in a spherical coordinate system. This is easily achieved with a computer program using random numbers X , n = 0, 1, 2, 3,..., A (0 [Pg.238]

Note that although the Ulamized variables are distributed uniformly on the interval (0,1), unfortunately the variables do have correlations. This is also true for the logistic variables, as evidenced by the noise-spheres in Figures 31.6 and 31.7. Therefore, users of this approach will have to sample the generated variables at some suitably large interval to eliminate correlations. I recommend users skip iterates, taking every tenth iterate, at which point no correlations are visually apparent (Figure 31.8). 

FIGURE 31.6. Noise-sphere for logistic variables, lag = 1. Here no points are skipped. By skipping points (see Figures 31.7 and 31.8), correlations are reduced. 

FIGURE 31.7. Noise-sphere for logistic variables, lag = others are discaided.)... 

Humans Cannot Produce Random Numbers The Lure of Random Numbers Randomness The Cliff RNG Noise-Spheres Explore Extraterrestrial Lands The Bizarre Logistic Equation The Logit Transformation Pretty Good Random Numbers Flipping a Quantum Mechanical Coin Randomness and Infinity... 

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