Data-driven IFS

(* Data Driven IFS - Four Bins *)

Off[General::spell];

Off[General::spell1];

dlst = {};

(* paste the data between the {} in dlst = {}, comma separated numbers *)

dmax = Max[dlst];

dmin = Min[dlst];

drng = dmax - dmin;

f[1,x_,y_]:={0.5*x, 0.5*y}

f[2,x_,y_]:={0.5*x + 0.5, 0.5*y}

f[3,x_,y_]:={0.5*x, 0.5*y + 0.5}

f[4,x_,y_]:={0.5*x + 0.5, 0.5*y + 0.5}

ptlst={PointSize[.01]};

pt={0.5,0.5};

Do[{x=pt[[1]], y=pt[[2]],ind = Min[4, 1+Floor[4*(dlst[[j]] - dmin)/drng]], pt = f[ind,x,y], ptlst = Flatten[{ptlst,Point[pt]}]}, {j,1,Length[dlst]}];

Show[Graphics[{ptlst, Line[{{0,0},{1,0},{1,1},{0,1},{0,0}}], Line[{{0.25,0},{0.25,1}}], Line[{{0.5,0},{0.5,1}}], Line[{{0.75,0},{0.75,1}}], Line[{{0,0.25},{1,0.25}}], Line[{{0,0.5},{1,0.5}}], Line[{{0,0.75},{1,0.75}}]}], AspectRatio->1, PlotRange->{{0,1},{0,1}}]

(* Data Driven IFS - Nine Bins *)

Off[General::spell];

Off[General::spell1];

dlst = {};

(* paste the data between the {} in dlst = {}, comma separated numbers *)

dmax = Max[dlst];

dmin = Min[dlst];

drng = dmax - dmin;

f[1,x_,y_]:={0.333*x, 0.333*y}

f[2,x_,y_]:={0.333*x + 0.333, 0.333*y}

f[3,x_,y_]:={0.333*x + 0.667, 0.333*y}

f[4,x_,y_]:={0.333*x, 0.333*y + 0.333}

f[5,x_,y_]:={0.333*x + 0.333, 0.333*y + 0.333}

f[6,x_,y_]:={0.333*x + 0.667, 0.333*y + 0.333}

f[7,x_,y_]:={0.333*x, 0.333*y + 0.667}

f[8,x_,y_]:={0.333*x + 0.333, 0.333*y + 0.667}

f[9,x_,y_]:={0.333*x + 0.667, 0.333*y + 0.667}

ptlst={PointSize[.01]};

pt={0.5,0.5};

Do[{x=pt[[1]], y=pt[[2]],ind = Min[9, 1+Floor[9*(dlst[[j]] - dmin)/drng]], pt = f[ind,x,y], ptlst = Flatten[{ptlst,Point[pt]}]}, {j,1,Length[dlst]}];

Show[Graphics[{ptlst, Line[{{0,0},{1,0},{1,1},{0,1},{0,0}}], Line[{{0.333,0},{0.333,1}}], Line[{{0.667,0},{0.667,1}}], Line[{{0,0.333},{1,0.333}}], Line[{{0,0.667},{1,0.667}}]}], AspectRatio->1, PlotRange->{{0,1},{0,1}}]