The graphic shows 3000 points generated as follows. Each points' coordinates were obtained as three consecutive pseudo-random numbers from the sequence generated by

x_n+1=65539 x_n mod 2³¹

(and then converted to numbers between 0 and 1 by dividing by 2³¹). [It is very common to produce pseudo-random numbers this way, by a linear-congruential recursive relation; the choice of 65539 for the multiplier and 2³¹ for the modulus were those made by the notorious pseudo-random number generator known as "RANDU", popular in the early 1970s. By rotating the figure (as described below), one can easily see what was wrong with this very popular generator. By contrast, go here to see an even worse variant of RANDU, and by contrast here to examine the so-called "Minimal Standard" to see a much better variant. In this and all cases referenced, 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.