Function iteration

*To*: mathgroup at christensen.cybernetics.net*Subject*: Function iteration*From*: seligjm at vax.sbu.ac.uk*Date*: Wed, 02 Nov 1994 10:17:14 BST

Andrew Laska writes: >I need help with a table of iterated results. >I have three discrete functions... >x =f(x ,y ,z ) > n+1 n n n >y =g(x ,y ,z ) > n+1 n n n >z =h(x ,y ,z ) > n+1 n n n >I wish to iterate these functions such that I get a list that looks >like >{x1,y1,z1},{x2,y2,z2},...{xn,yn,zn} where x1,y1,...,zn are the >numerical answers. An easy way to do this is to define a "vector functinon" : vf[q_]:={f@@q,g@@q,h@@q} The requires result is now given by: NestList[vf,{x0,y0,z0},n] Using his example: f[x_,y_]:= 1 - 1.4 * (x )^2 + y g[x_,y_]:= .3 * x then vf[q_]:={f@@q,g@@q} and finally: NestList[vf,{0,0},10] Out[4]= {{0, 0}, {1, 0}, {-0.4, 0.3}, {1.076, -0.12}, {-0.740886, 0.3228}, {0.554322, -0.222266}, {0.347552, 0.166297}, {0.997188, 0.104265}, {-0.287871, 0.299156}, {1.18314, -0.0863614}, {-1.0461, 0.354942}} Jon Selig