Subject: Re: [stella] entropy & randomness From: "Thomas Jentzsch" <tjentzsch@xxxxxx> Date: Wed, 10 Oct 2001 10:05:55 +0200 
B. Watson wrote: > The Suicide Mission routine... [snip] > I ran a meg's worth of bytes generated by this algorithm (recoded in perl) > through a program called `ent' that's supposed to analyse the randomness of > a series of numbers, here's the results I got: > > Entropy = 8.000000 bits per byte. > > Optimum compression would reduce the size > of this 1048576 byte file by 0 percent. > > Chi square distribution for 1048576 samples is 0.13, and randomly > would exceed this value 99.99 percent of the times. > > Arithmetic mean value of data bytes is 127.4993 (127.5 = random). > Monte Carlo value for Pi is 3.107380323 (error 1.09 percent). > Serial correlation coefficient is 0.500001 (totally uncorrelated = 0.0). I've done the same tests with the River Raid LFSR, here are the results: (The complete two bytes squence repeats after 57337 values.) *** River Raid lowbyte *** Entropy = 8.000000 bits per byte. Optimum compression would reduce the size of this 57337 byte file by 0 percent. Chi square distribution for 57337 samples is 0.03, and randomly would exceed this value 99.99 percent of the times. Arithmetic mean value of data bytes is 127.4978 (127.5 = random). Monte Carlo value for Pi is 3.137714525 (error 0.12 percent). Serial correlation coefficient is 0.000013 (totally uncorrelated = 0.0). *** River Raid highbyte *** Entropy = 8.000000 bits per byte. Optimum compression would reduce the size of this 57337 byte file by 0 percent. Chi square distribution for 57337 samples is 0.03, and randomly would exceed this value 99.99 percent of the times. Arithmetic mean value of data bytes is 127.4978 (127.5 = random). Monte Carlo value for Pi is 3.123064044 (error 0.59 percent). Serial correlation coefficient is 0.000013 (totally uncorrelated = 0.0). While Chi square is still very bad, the Monte Carlo and Serial correlation test look much better. I think, a high serial correlation should be avoided in games, because that's something the human player will notice. So that's maybe the most important test for us. Have fun! Thomas _______________________________________________________ Thomas Jentzsch  *** Every bit is sacred ! *** tjentzsch at web dot de  _______________________________________________________________________ 1.000.000 DM gewinnen  kostenlos tippen  http://millionenklick.web.de IhrName@xxxxxx, 8MB Speicher, Verschluesselung  http://freemail.web.de  Archives (includes files) at http://www.biglist.com/lists/stella/archives/ Unsub & more at http://www.biglist.com/lists/stella/
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