firstfracverb

# firstfracverb - Fractals using iterated function systems...

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Fractals using iterated function systems, with affine transformations ACCESS July 2001 > restart:#fractals use a lot of memory > Digits:=4: #number of significant digits - this will #make computations go faster without sacrificing #visual accuracy - because IFS’s are self correcting. > with(plots): #we want to be able to see our fractals Warning, the name changecoords has been redefined The next procedure will take a point P=[x,y]) in the plane and let us compute its image under an affine transformation. We use the same letters for the transformation parameters as we did in the class notes: = AFFINE1 x y + a b c d x y e f > AFFINE1:=proc(X,a,b,c,d,e,f) RETURN(evalf([a*X[1]+b*X[2]+e, c*X[1]+d*X[2]+f])); end: > You should check that these are the transformations for the Sierpinski triangle > f1:=P->AFFINE1(P,.5,0,0,.5,.25,.5); f2:=P->AFFINE1(P,.5,0,0,.5,.5,0); f3:=P->AFFINE1(P,.5,0,0,.5,0,0);

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