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Troubling Bug involving RandomReal, NestList, and Table

• To: mathgroup at smc.vnet.net
• Subject: [mg86236] Troubling Bug involving RandomReal, NestList, and Table
• From: "jwmerrill at gmail.com" <jwmerrill at gmail.com>
• Date: Thu, 6 Mar 2008 03:02:06 -0500 (EST)

When making tables of 250 or more directions, Mathematica seems to
forget how to do arithmetic.  I realize these "random" directions are
not properly uniform, but that's beside the point.

$Version
> "6.0 for Mac OS X x86 (32-bit) (April 20, 2007)"

randomDirection3[] :=
 NestList[Sqrt[1 - #^2] &, RandomReal[], 1]

ListPlot[Table[randomDirection3[], {249}], AspectRatio -> Automatic]
ListPlot[Table[randomDirection3[], {250}], AspectRatio -> Automatic]

> [Graphs you'll need to generate for yourself]

Variance[Table[Norm[randomDirection3[]], {249}]]
Variance[Table[Norm[randomDirection3[]], {250}]]

> 1.49104*10^-33
> 0.0513843

What!?!

Jason Merrill

• Follow-Ups:
  • Re: Troubling Bug involving RandomReal, NestList, and Table
    • From: Darren Glosemeyer <darreng@wolfram.com>