> retstart:

> plot((1+cos(3*t)+sin(3*t)^2),t=0..2*Pi,coords=polar,axes=none,scaling=constrained);

> restart:

> x:=cos(t):

> y:=sin(t):

> m:=[[x,0],[0,y]]:

> t:=n*Pi/50:

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

> restart:

> x:=cos(t):

> y:=sin(t):

> m:=[[x,y],[x-y,y+x]]:

> t:=n*Pi/50:

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

> restart:

> x:=cos(t):

> y:=sin(t):

> m:=[[x,y],[x-t*y,y+t*x]]:

> t:=n*Pi/50:

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

> restart:

> x1:=cos(t):

> y1:=sin(t):

> x2:=cos(2*t):

> y2:=sin(2*t):

> m:=[[x1,y1],[x2,y2]]:

> t:=n*Pi/50:

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

> restart:

> x1:=cos(t):

> y1:=sin(t):

> x2:=cos(3*t):

> y2:=sin(3*t):

> m:=[[x1,y1],[x2,y2]]:

> t:=n*Pi/50:

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

> restart:

> x:=0.7:

> a:=3.7:

> y:=a*x*(1-x):

> m:=[]:

> for k to 150 do m:=[op(m),[x,x],[x,y]]:x:=y:y:=a*x*(1-x):od:

> plot(m,scaling=constrained);

> restart:

> plot([[k*cos(t),k*sin(t),t=0..2*Pi]$k=1..20],scaling=constrained,axes=none,color=blue);

> restart:

> x:=cos(t):

> y:=sin(t):

> r:=((x-1)^2+y^2)^(1/2):

> m:=[x+r*sin(s), y+r*cos(s), s=-Pi..Pi]:

> t:=n*Pi/50:

> w:=evalf(m):

> plot([w$n=1..100],color=blue,axes=none,scaling=constrained);

> restart;

> m:=[cos(s)+r*cos(t),sin(s)+r*sin(t),t=0..2*Pi]:

> r:=cos(s):

> s:=n*Pi/50:

> plot([m$n=1..100],axes=none,scaling=constrained,color=green);

> restart:

> x:=cos(t):

> y:=sin(t):

> x1:=2/3*x+1/3*cos(2*t):y1:=2/3*y-1/3*sin(2*t):

> r:=((x-x1)^2+(y-y1)^2)^(1/2):

> m:=[x+r*sin(s), y+r*cos(s), s=-Pi..Pi]:

> t:=n*Pi/50:

> w:=evalf(m):

> plot([w$n=1..100],color=blue,axes=none,scaling=constrained);

> restart:

> x:=cos(t):

> y:=sin(t):

> x1:=3/4*x+1/4*cos(3*t):y1:=3/4*y-1/4*sin(3*t):

> r:=((x-x1)^2+(y-y1)^2)^(1/2):

> m:=[x+r*sin(s), y+r*cos(s), s=-Pi..Pi]:

> t:=n*Pi/50:

> w:=evalf(m):

> plot([w$n=1..100],color=green,axes=none,scaling=constrained);

> restart:

> x:=cos(t):

> y:=sin(t):

> m:=[x+t*sin(s), y+t*cos(s), s=-Pi..Pi]:

> t:=n*Pi/20:

> w:=evalf(m):

> plot([w$n=1..100],color=green,axes=none,scaling=constrained);

> restart:

> m:=1.7123:x:=0:y:=0:v:=[[x,y]]:

> for k to 200 do xx:=floor(x)+1:yy:=floor(y)+1:if (yy-y)>m*(xx-x)then
x:=xx:y:=m*x else
y:=yy:x:=y/m:fi:v:=[op(v),[1-abs(x-2*floor(x/2)-1),1-abs(m*x-2*floor(m*x/2)-1)]]od:

> plot(v,scaling=constrained);

>