The graphic shows 3000 points generated as follows. Each points' coordinates were obtained as three consecutive pseudo-random numbers from the sequence generated by
xn+1=75 xn mod 231-1
(and then converted to numbers between 0 and 1 by dividing by 231-1). [It is very common to produce pseudo-random numbers this way, by a linear-congruential recursive relation; the choice of 75, i.e. 16807, for the multiplier and 231-1 for the modulus were made by Park and Miller (S. K. Park and K. W. Miller, "Random number generators: Good ones are hard to find", Communications of the ACM, 31(10):1192--1200, October 1988) and came to be known as the "minimal standard". By rotating the figure (as described below), one can easily see that what went wrong with RANDU is not an issue with this very popular generator. In this, and all other examples on these pages, the seed x0 was 123.]
The graphic may take 10-30 seconds to load, but once it does, you can rotate it and zoom in or zoom out (for the former, on a PC, just use the left mouse button; for the latter, hold down the shift key before you drag, and while you drag, the mouse vertically; and finally, if you hold the shift key while dragging the mouse horizontally, the figure rotates about an axis perpendicular to the screen).
The "Live" rotation of the Mathematica-generated graphic uses the LiveGraphics3D software; for more info on how to rotate Mathematica-generated graphics on the web, visit LiveGraphics3D.
Comments? Send them to Rick Kreminski.