[HN Gopher] When random numbers are too random: Low discrepancy ...
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       When random numbers are too random: Low discrepancy sequences
       (2017)
        
       Author : ibobev
       Score  : 22 points
       Date   : 2024-01-07 21:24 UTC (1 hours ago)
        
 (HTM) web link (blog.demofox.org)
 (TXT) w3m dump (blog.demofox.org)
        
       | dang wrote:
       | Discussed at the time (not much, but gwern):
       | 
       |  _When Random Numbers Are Too Random: Low Discrepancy Sequences_
       | - https://news.ycombinator.com/item?id=14439705 - May 2017 (1
       | comment)
        
       | debatem1 wrote:
       | Interesting article. The difference between the square root of
       | two and pi sequences is surprising to me; is there some intuitive
       | reason why pi looks so much more regular?
        
         | bsza wrote:
         | 7 times pi is very close to a whole number, so the pattern will
         | repeat with a very slight shift every 7 iterations.
        
         | kragen wrote:
         | if there's a good rational approximation to some number _x_ =
         | _n_ / _m_ + _e_ where _n_ and _m_ are integers and _e_ is
         | small, then every _m_ multiples you get back to almost the same
         | place; only the residual difference _e_ remains. so you get _m_
         | clusters of points that are each spread apart by _e_. after
         | enough multiples, these clusters grow big enough to overlap,
         | and then you start to see clusters corresponding to the next
         | approximant
        
       | gxs wrote:
       | Whenever this is posted, it sort of reminds me of the IRS and one
       | way they use to detect fraud.
       | 
       | They observed that sometimes, the amounts in the tax returns were
       | too "random" though not in exactly the same sense as the article.
       | 
       | For example, people manually filling out bad tax returns would
       | never use an amount like $5,000 because the number didn't feel
       | random enough.
       | 
       | This type of analysis is always fascinating and I still see new
       | applications from time to time.
        
         | quickthrower2 wrote:
         | Also: https://en.m.wikipedia.org/wiki/Benford%27s_law
        
         | thwarted wrote:
         | There's also Benford's Law, which is related to the growth of
         | numbers, which is used to detect fraud.
         | 
         | https://en.m.wikipedia.org/wiki/Benford%27s_law
        
       | magicalhippo wrote:
       | I found that the Physically Based Rendering book[1] has some nice
       | material on low discrepancy sequences in chapter 8, specifically
       | 8.6 and 8.7. It also contains some neat comparisons of how it
       | impacts rendering.
       | 
       | [1]: https://pbr-book.org/4ed/contents
        
       | sfpotter wrote:
       | A totally different but very nice approach to generating uniform-
       | ish node distributions is described in this paper:
       | 
       | https://www.sciencedirect.com/science/article/pii/S089812211...
       | 
       | Useful for PDE and geometry.
        
       | IshKebab wrote:
       | This article was written before this one:
       | 
       | https://extremelearning.com.au/unreasonable-effectiveness-of...
       | 
       | You should definitely read that one instead. It's such a great
       | method (and article) that I'll even forgive their use of
       | "unreasonable effectiveness".
        
       | quickthrower2 wrote:
       | Had this problem helping 4 kids play a game where one is secretly
       | randomly selected, and the same person got selected more than
       | half the time. However since the game hinges on guessing who the
       | picked person is, it needs to be random!
        
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       (page generated 2024-01-07 23:00 UTC)