(*Adapted by Rafael Luís: rafaelluis@netmadeira.com
 2016-09-11: adapted for Mathematica v.10 by Ross Moore *)

(* Henon Attractor for H(x,y)=(y+1-((αx)^2),βx),that is, 
((Subscript[x, n+1]),(Subscript[y, n+1]))=(1-((Subscript[αx, n])^2)+(Subscript[y, n]),(Subscript[βx, n]))*)

Clear[α,β]
α=1.4;
β=0.3;
Graphics[{Blue,
AbsolutePointSize[.03],
Point/@Drop[NestWhileList[{1-α#[[1]]^2+#[[2]],β#[[1]]}&,{0,0},#.#<100.&,1,10^5],1000]
},Frame->True,FrameLabel->TraditionalForm/@{x,y}, RotateLabel->False
,PlotLabel->"Henon attractor"]