(*Adapted by Rafael Luís: rafaelluis@netmadeira.com*)

(* Lozi Attractor for L(x,y)=(1-α|x|+y,βx), that is, ((Subscript[x, n+1]),(Subscript[y, n+1]))=(1-α|(Subscript[x, n])|+(Subscript[y, n]),(Subscript[βx, n])) *)

Clear[α,β]
α=1.5;
β=0.4;
Graphics[{Blue,
AbsolutePointSize[.1],
Point/@Drop[NestWhileList[{1-α Abs[#[[1]]]+#[[2]],β#[[1]]}&,{0,0},#.#<100.&,1,10^5],1000]
},Frame->True,FrameLabel->TraditionalForm/@{x,y},RotateLabel -> False,PlotLabel->"Lozi attractor"]