Re: simplifying ulam spiral code

*To*: mathgroup at smc.vnet.net*Subject*: [mg56478] Re: simplifying ulam spiral code*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Tue, 26 Apr 2005 21:52:33 -0400 (EDT)*Organization*: The University of Western Australia*References*: <d4cmlr$39e$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Further to my previous message, improved code for Ulam's spiral appeared in the third issue of The Mathematica Journal, 1(3): 57 (1991). It used IntegerSpiral[n_] := {Re[#],Im[#]}& /@ Fold[Join[#1, Last[#1]+I^#2 Range[#2/2]]&, {0}, Range[n]] and explained that the idea is that the length of the limbs of the spiral follow the pattern 1,1,2,2,3,3,4,4,5,5,... and that each limb is at a 90 degree angle to the previous limb (multiplication by I in the complex plane). This is also a nontrivial use of Fold in the sense that the second argument to Fold is really used. Also, instead of using Pick, to select those points that have prime index from, say spiral = IntegerSpiral[60]; one can use primes = spiral[[ Prime[Range[PrimePi[Length[spiral]]]] ]]; Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul