proc iml;

/* For an explanation of how to construct an iterated function system in SAS, see

http://blogs.sas.com/content/iml/2012/12/12/iterated-function-systems-and-barnsleys-fern-in-sas/

*/

/* Each row is a 2x2 linear transformation */

/* Christmas tree */

L = {0.03 0 0 0.1,

0.85 0.00 0.00 0.85,

0.8 0.00 0.00 0.8,

0.2 -0.08 0.15 0.22,

-0.2 0.08 0.15 0.22,

0.25 -0.1 0.12 0.25,

-0.2 0.1 0.12 0.2};

/* ... and each row is a translation vector */

B = {0 0,

0 1.5,

0 1.5,

0 0.85,

0 0.85,

0 0.3,

0 0.4 };

prob = { 0.02 0.6 0.1 0.07 0.07 0.07 0.07};

L = L`; B = B`; /* For convenience, transpose the L and B matrices */

/* Iterate the discrete stochastic map */

N = 1e5; /* number of iterations */

x = j(2,N); k = j(N,1);

x[,1] = {0, 2}; /* initial point */

call randgen(k, "Table", prob); /* values 1-7 */

do i = 2 to N;

x[,i] = shape(L[,k[i]], 2)*x[,i-1] + B[,k[i]]; /* iterate */

end;

/* Plot the iteration history */

y = x`;

create IFS from y[c={"x" "y"}]; append from y; close IFS;

quit;

/* basic IFS Christmas Tree */

ods graphics / width=200px height=400px;

proc sgplot data=IFS;

title "SAS Christmas Tree";

scatter x=x y=y / markerattrs=(size=1 color=ForestGreen);

yaxis display=none;

xaxis display=none;

run;