(* bifurcation map, takes a while to run *)


list = {}
For[c=0.5,c<2,c+= 0.01,
	x = 0;
	Do[x = x^2-c, {j,100}];
	y = {};
	Do[x = x^2 - c;
		yv = N[Round[300*x]/300.0];
		If[MemberQ[y,{c,yv}] == False,
			AppendTo[y,{c,yv}];
			AppendTo[list,{c,yv}];
			
		],
		{j,100}
	];
];

ListPlot[list, Axes -> None]