AFAIU we don't use primes but the remainders of primes in the range of i.11. And the digits of pi have range i.10. So, ok it's one less. But they are actually the same because there's only 1 zero in the prime remainder sequence. So deleting 0 and scaling the prime remainders down by one makes the digit range equal for both: i.10.
Anyway, at first glance they are similar (random) streams of digits i.10 to me. But displaying them this way (random walk) shows that the prime remainders look less random. For the rest I can only say, the prime picture still puzzles me. Hallo Matthew Brand, je schreef op 08-01-10 18:35: > The digits might be random but the spacings between successive numbers > are constrained unlike for the sequence of primes? > > 2010/1/8 Aai <[email protected]>: > >> Probably a better idea is, as the author did, to compare e.g. with >> pi-digits. >> >> I obtained ~ 1.25 million digits of pi from: >> http://www.gutenberg.org/etext/50 >> >> freq of the digits: >> ({.,#) /. ~ ds >> 1 125083 >> 4 125372 >> 5 125880 >> 9 125689 >> 2 125594 >> 6 124796 >> 3 125792 >> 8 125376 >> 7 125452 >> 0 125505 >> >> fairly uniform distribution. >> >> And then apply: >> >> dr=: 0 0, 0 1, 0 _1, 1 0, _1 0, 0 0, 0 0, 0 0, 0 0,: 0 0 >> d=. ({.,#)/.~+/\ ds { dr >> 'gx gy '=. >: >./ XY=.(2{."1 d) -"1 {.~&2 <./ d >> >> >> Here's the alien: a very different picture. >> >> viewmat (2{"1 d) (<"1 XY) } 0$~ gx, gy >> >> # ds >> 1254539 >> gx,gy >> 1196 906 >> >> >> >> >> >>> For a start: replace >>> 11|p: i.y >>> with >>> 1 + y ?...@#10 >>> in primenebulaP >>> >>> >>> >>> Ik schreef op 08-01-10 13:38: >>> >>> >>>> Did already think along the same line. Time to start an experiment. :-) >>>> >>>> The author of the idea suggested it is. He showed also examples on the >>>> website of purely random nature: >>>> http://yoyo.cc.monash.edu.au/~bunyip/primes/random.html >>>> >>>> >>>> >>>> Hallo Matthew Brand, je schreef op 08-01-10 13:27: >>>> >>>> >>>> >>>>> Is there anything special about primes in all of this or will other >>>>> sequences of increasing integers with random spacing produce similar >>>>> pictures? >>>>> >>>>> 2010/1/8 Aai <[email protected]>: >>>>> >>>>> >>>>> >>>>> >>>>>> @ Devon and Viktor >>>>>> >>>>>> The dr I use was not a mistake. Experimenting with dr pointed me in this >>>>>> direction for obtaining a square picture. >>>>>> I also tried other values for prime 11 and concluded it being a good >>>>>> (the best?) choice for a pretty nebula-like picure. >>>>>> >>>>>> I also tried some x |. dr . That showed me that my original dr produces >>>>>> the nicest picture (i.e for me). >>>>>> >>>>>> -- >>>>>> Met vriendelijke groet, >>>>>> =@@i >>>>>> >>>>>> ---------------------------------------------------------------------- >>>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>> >>>>> >>>>> >>>> >>>> >>> >> -- >> Met vriendelijke groet, >> =@@i >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> > > > -- Met vriendelijke groet, =@@i ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
